text
stringlengths 0
190k
|
|---|
quant-ph9501010.txt |@word consider:2 focus:1 generalize:1 follow:3 centers:1 localized:1 whose:2 finally:2 program:1 th:1 stochastic:2 analogous:1 case:2 zhang:1 very:1 wave:11 nieto:5 difference:1 condition:2 presented:2 dia:2 large:1 convenience:1 truax:1 optics:1 dfpd:1 falco:1 osmotic:2 sign:1 zero:1 dynamics:9 linear:4 what:3 appear:2 morse:7 current:1 above:5 new:1 principal:1 method:2 seeks:1 satisfy:2 groups:1 along:1 equations:3 galilei:1 obtained:3 study:3 allows:5 fabrizio:1 action:2 oschl:1 followed:1 apply:1 readily:1 would:2 sake:1 classically:1 therefore:1 december:1 associated:5 theoretical:3 formally:1 operators:1 odinger:15 berlin:1 normalized:1 hold:1 must:1 reconstructed:1 springer:1 originally:3 oscillator:9 remain:2 following:3 example:3 proof:1 give:2 process:1 expanding:1 states:30 minimum:3 numbers:2 sense:2 verlag:1 end:1 feature:1 recovers:1 how:1 gcs:5 simplicity:1 product:2 description:4 after:1 applications:3 tries:1 natural:2 dynamical:6 light:1 explicit:4 correspond:1 so:1 fundamental:2 keeps:1 representation:3 martino:5 equation:19 restriction:1 feedback:2 areas:1 satisfied:1 through:5 statistical:1 mentioned:1 satisfies:1 still:1 derive:1 group:2 symmetry:1 interesting:1 sα:3 solving:1 adimensional:1 expectations:2 writing:1 resorting:1 complex:1 systems:7 jacobi:1 mail:3 main:1 defining:1 eventually:1 non:8 outlined:1 obeyed:3 hamilton:1 they:5 now:3 discuss:2 teller:1 easily:1 finite:2 always:1 hamiltonian:2 applied:2 2m:6 universit:2 traces:1 characterized:1 mean:1 baronissi:1 illuminati:5 energy:1 hard:1 displacement:8 solution:3 obtains:1 entering:2 quantum:5 our:3 beyond:1 eq:1 out:1 shown:2 since:1 rev:7 re:1 siena:5 hydrodynamic:4 theory:1 barrier:1 interactions:2 fisica:2 beginning:1 e0:2 skagerstam:1 language:1 napoli:1 readjusting:1 could:2 wrong:1 keep:2 motion:9 turn:3 first:1 origin:1 major:1 probability:1 rydberg:1 variables:1 approximate:1 precisely:1 electronic:3 equating:1 given:2 necessarily:1 gcss:7 glauber:2 dipartimento:2 system:3 centripetal:1 their:3 brevity:1 ranging:1 recovered:1 explanation:1 continuous:1 part:2 simulate:1 2aq:2 x2:1 schr:15 coefficients:2 see:1 annihilation:1 determined:1 were:1 powers:2 modern:1 qˆ2:1 seek:1 any:1 elsewhere:2 latter:1 able:1 mechanism:4 note:1 instance:2 potential:34 generalized:11 indexed:1 coincide:2 canonical:2 heisenberg:2 exactly:3 unless:1 price:1 who:2 wells:1 most:1 madelung:2 phase:4 class:1 surprising:1 considered:1 coincides:1 exp:11 velocity:2 physics:1 fact:3 phenomenon:1 show:1 timedependent:1 relation:1 d2:1 ground:8 naturwissenschaften:1 feng:1 based:1 written:1 jan:1 only:3 integrable:1 hamiltonians:3 continuity:1 di:7 dependent:12 de:11 overall:1 expectation:2 beam:1 dt:9 dp:7 dq:3 evolution:6 densities:1 arxiv:1 yield:1 collegato:1 including:1 coefficient:1 packet:9 depends:2 result:3 subject:1 satisfying:2 definite:1 symmetric:5 state:16 classes:1 between:1 conceptual:1 approach:2 preserve:2 terms:3 nature:2 importance:2 attention:1 jr:2 reaction:4 uncertainty:5 quantization:1 unisa:2 expression:2 finds:1 among:1 co:1 characterization:2 simple:1 harmonic:10 dimensional:1 simply:1 respect:1 pq:1 described:2 trajectory:2 three:1 been:1 strategy:1 pd:1 ph:1 abstract:1 choose:1 corresponding:1 coherence:3 coherent:23 understand:1 kicks:1 present:1 p2:2 aq:3 utmost:1 pacs:1 might:1 value:1 will:5 while:1 behavior:1 squeezed:2 inspired:1 procedure:2 coupled:1 ip:1 thus:3 quantize:1 reads:2 itself:1 different:3 same:2 unity:1 drawback:1 quant:1 wavepacket:1 several:1 independent:7 closest:1 singapore:1 hand:2 driven:3 experimenter:1 aξ:1 potentials:6 off:1 center:6 minimize:2 well:1 analysis:1 without:5 salvatore:1 coordinate:3 repulsive:1 just:1 being:1 identify:3 atomic:1 klauder:1 useful:1 eigenstates:1 letting:2 preprint:1 density:3 workers:1 had:1 quadratures:1 lets:1 lett:5 solvable:1 transformation:1 momentum:1 real:1 represents:1 read:1 results:2 possible:2 simmons:2 know:1 world:1 isolates:1 mod:3 displaced:2 appearing:3 like:1 particle:2 identifying:1 follows:4 reduces:2 yields:3 sezione:2 arbitrary:1 become:1 stationary:2 reduced:1 parity:1 sketch:1 interest:1 methods:1 classical:25 back:5 gilmore:1 moreover:1 b8:2 describing:2 inserting:1 scientific:1 elucidate:1 paid:1 qˆ:5 silvio:1 properties:1 actual:1 carried:1 dependence:1 act:1 introduced:1 perelomov:1 computational:1 spreading:3 functional:1 due:1 references:1 operator:11 gruppo:1 there:1 u0:4 dispersion:4 italia:2 way:1 salerno:2 delocalized:1 was:2 function:1 complete:2 form:5 but:1 gaussian:2 line:1 ha:1 padova:3 infn:3 applying:2 us:1 limit:3 problem:1 define:2 mechanics:1 constant:6 configurational:2 verifies:1 proven:1 general:9 dξ:1 pˆ:1 ax:1 formalism:1 no:1 when:1 overcompleteness:1 field:2 other:4 details:2 conclusion:1 picture:3 bundle:1 generated:1 a2:1 allowing:1 needed:1 structure:1 coulomb:1 expands:1 d23:1 interval:2 packets:4 depth:1 nelson:1 time:21 observables:1 resolution:1 original:6
|
quant-ph9501011.txt |@word replacing:2 limited:1 concept:1 consider:17 represent:2 washed:1 retain:1 results:7 eds:2 mild:1 commute:2 comments:1 computation:1 c2:2 bergmann:1 operationally:1 expressions:4 causes:1 devoted:1 particles:6 feeding:1 depend:1 calculate:3 indices:1 tr:11 corrections:1 tp:2 environment:9 finally:6 program:1 th:2 under:8 tf:6 pay:1 include:2 eliminate:3 division:1 adiabatic:1 amplitudes:4 advantage:2 g0:16 very:4 implicitly:1 continues:1 ψk:5 wave:29 handling:1 every:3 mixing:5 affect:2 emphasized:1 difference:1 exact:2 condition:20 disconnected:1 dim:1 school:2 basics:2 prize:1 presented:2 did:2 turns:1 t2:34 solution:3 t1:36 hartle:2 discrete:4 insights:1 pˆ2:1 δnm:1 restoring:1 avoiding:2 small:5 eigenvalues:7 shows:1 a124:1 ρout:11 inserting:1 strongly:4 smaller:1 tel:3 tem:1 foundation:1 consistent:3 doted:1 direct:7 modified:1 past:1 second:10 displays:1 zz:1 further:6 dynamics:3 amplified:1 quite:1 theory:8 even:1 what:7 abc:3 plays:1 sub:9 apparatus:2 deeply:1 section:19 selected:31 bergman:1 expressed:9 current:1 ˆa:3 experiment:11 above:12 new:6 construction:2 ˆk:9 satisfy:4 pictorially:1 evolving:3 discontinuity:1 simultaneously:1 notions:1 degree:1 symposium:1 respectively:9 component:5 equals:1 here:2 anandan:3 ulb:1 explore:1 objects:1 possibility:5 groups:1 alone:1 strong:9 equations:3 suggest:1 obtained:11 search:1 tunneling:1 clarify:1 involved:1 study:4 vectors:1 later:1 suggests:2 suggestion:1 published:1 usually:1 suitable:2 changes:1 involves:1 york:1 criticism:1 ψm:1 formulated:1 useful:2 griffiths:2 scales:2 explained:1 outcomes:1 md2:5 unitary:1 issue:1 total:15 during:3 imaginary:3 select:2 tn:13 fed:1 takes:4 working:1 massar:2 probabilities:16 ψs:1 bush:1 next:5 classically:1 depicted:5 ψi:10 call:4 therefore:25 attribute:1 taken:1 cαβ:1 means:3 25th:1 ψf:15 reflects:1 more:7 separated:2 israel:1 formally:2 relax:1 becomes:2 operators:11 ti:6 odinger:5 cij:2 appendix:4 normalized:15 particular:4 known:4 cases:6 δcc:1 circumstances:3 md:42 mg:1 valued:2 134b:1 ed:2 postselection:1 equation:22 work:2 suggestive:2 anm:1 taup:2 ij:1 values:24 g02:5 backwards:2 following:6 making:2 my:1 example:10 history:1 figure:9 give:3 process:12 expanding:1 share:1 ani:1 states:64 lorentz:12 performed:2 reconstruct:2 arise:2 specific:1 simulation:1 occur:2 calculated:1 absolute:5 information:8 scalar:1 end:1 straightforward:3 rather:2 s2:2 discussion:3 returning:1 orthogonality:3 regions:1 how:10 vancouver:1 ig:1 pure:1 significance:1 instead:4 ordinary:6 axis:1 ensemble:14 classify:1 exemplify:4 simplicity:2 product:16 description:17 may:18 after:10 derived:4 confirmed:1 collection:2 impulsive:1 hence:7 tries:1 faculty:1 bˆ:1 horizontal:1 da:9 types:1 maxk:1 natural:3 dynamical:2 third:1 σ1z:2 computations:1 πi:6 approximation:1 lines:4 correspond:8 element:8 generic:26 negligible:2 fundamental:1 correlation:3 sc:1 s1:2 operations:4 restriction:3 acts:1 interpretation:6 words:2 indeed:5 over:2 satisfied:4 interpreted:2 course:4 cambridge:1 including:2 discrepancy:1 hypersurface:2 agricultural:1 satisfies:4 still:5 pointer:17 its:1 before:9 τn:1 derive:3 c2a:1 τi:4 interesting:3 temporal:1 d32:1 actually:2 aviv:3 h2:1 strange:1 degrees:1 systems:4 relate:1 mail:1 main:2 lz:3 lx:10 instantly:1 maximal:1 non:53 good:1 motivated:1 combination:1 weakness:1 questions:1 nonorthogonal:1 s2z:1 yz:1 they:7 identically:1 singlet:2 formulating:1 now:19 discuss:1 nor:1 easily:2 term:7 finite:3 englert:1 always:3 university:5 hamiltonian:4 arrows:2 hermitian:22 2z:7 events:1 orthonormal:3 sufficiently:5 ψin:3 each:12 found:4 entirely:1 uninteresting:1 erice:1 mean:1 subsystem:1 ann:1 domain:1 square:6 significantly:1 evolve:3 σ2z:2 there:12 energy:1 directions:1 reduce:1 gaussian:1 related:5 t3:4 elementary:4 ξj:4 extended:1 grav:1 measurement:67 quantum:20 our:20 operation:1 avoided:2 eq:14 event:1 special:8 out:6 canada:1 large:17 shown:3 matrix:2 space:27 spectrum:2 since:13 induces:1 rd:1 re:3 contained:1 dominated:1 denoted:1 hepth:2 ref:10 correct:1 predicted:1 decoherent:1 provide:1 linear:9 barrier:1 written:4 argument:2 diagonal:4 free:2 standard:4 difficulty:3 completely:2 ρin:11 advantages:2 verify:1 dx:1 imagine:1 ask:2 equipped:1 md1:5 correction:1 definition:3 interaction:18 prepare:1 language:1 recast:2 determining:1 could:4 impose:1 viewing:1 british:1 times:6 motion:4 ordering:1 disturbed:3 place:9 specification:2 consequence:4 uses:1 generalizations:1 south:1 first:15 major:1 already:3 probability:36 omitted:1 variables:1 thesis:1 number:3 lahti:1 devices:5 choose:1 least:1 another:4 changing:1 xs:2 open:3 causing:1 aharonov:14 constructing:2 given:59 πa:2 πf:8 reference:2 needed:1 introduction:1 unknown:2 interact:1 behaves:2 sackler:1 system:73 construct:3 unruh:3 their:1 intermediate:14 observations:6 phd:1 worlds:1 htotal:1 final:37 interacts:4 too:3 shifted:1 collapse:7 cologne:1 academy:1 exactly:1 albert:4 took:1 measurable:1 assumption:1 part:5 because:1 differentiate:1 somewhat:1 x2:1 branches:4 eliminated:1 x1:2 than:1 lebowitz:2 remember:1 distance:2 parts:1 determines:4 effective:2 roles:1 aab:3 sections:2 zero:1 limiting:2 preparation:2 whenever:2 appealing:1 future:3 contrary:2 amplitude:43 were:2 tion:1 providing:2 achieved:1 descriptions:1 pre:29 fig:2 fashion:1 sees:2 disturb:1 remained:1 boston:1 unchanged:1 modern:1 measure:17 locations:4 generalization:1 lim:1 say:13 anw:2 acknowledgment:1 manner:1 conjugate:1 need:8 take:6 seem:2 confirms:1 any:18 viewed:1 complete:4 decomposing:1 generalizes:1 traditionally:1 smallest:1 presents:1 studying:1 latter:6 ideas:1 note:6 sciences:1 high:2 internal:4 generalized:9 hs:3 finding:1 canonical:1 simultaneity:1 accuracy:4 criteria:1 play:2 continuous:1 multiple:25 trace:1 shall:20 measures:4 clearer:1 falls:1 most:5 said:1 propagate:1 brout:1 occurred:3 successive:8 device:23 probabilistic:18 class:5 stands:1 coincides:1 recasting:1 constructed:2 observation:9 considered:1 notations:1 average:6 attempting:1 implications:4 order:3 traditional:2 proceedings:2 points:1 symmetrically:1 principle:3 exp:6 velocity:1 left:3 physics:7 notion:3 fact:6 laws:1 science:1 incorporate:1 selection:13 particularly:1 show:12 reductions:1 discovered:3 purely:1 spaces:1 relation:5 solutions:1 reznik:4 analogue:1 trivial:2 find:18 q1:1 partially:1 q2:1 ensembles:4 xmd:2 situations:2 edited:1 distributed:1 histories:1 universal:1 should:8 only:33 sequential:3 coefficients:2 developed:1 hamiltonians:1 local:30 achieve:1 carolina:1 continuity:1 do:4 his:1 handle:1 notation:3 get:4 zurek:1 express:2 db:2 expectation:2 obtain:8 corr:1 ˆab:20 cannot:2 dz:4 closely:1 expresses:1 combinations:4 hii:9 dt:2 averaged:1 areas:1 well:5 evolution:23 instant:2 conditions:53 arxiv:1 greenberg:1 yield:7 qa:1 twice:1 intervals:2 common:1 mapped:1 ly:6 gell:2 valid:1 view:4 body:2 set:14 computed:2 observer:8 observes:2 frame:8 correlations:9 observed:11 see:14 result:13 existence:1 terms:18 incorporating:1 techniques:1 closer:1 recording:1 invoked:1 eigenfunctions:1 visiting:1 ways:1 review:1 appear:1 symmetric:9 opened:1 state:154 determined:16 various:6 closed:3 between:29 conceptual:7 simplifying:1 reading:4 approach:4 law:1 discovery:1 available:1 notice:7 recently:1 august:1 complementary:1 initially:2 weak:68 however:19 vanishing:1 no:8 article:4 ket:2 distribution:5 thank:1 suggested:4 both:7 essentially:1 outcome:3 prescription:2 2n:2 limits:1 taking:1 uncertainty:14 according:8 etc:1 connection:1 σx:1 context:2 retarded:3 contribution:2 argue:4 expression:9 zˆ:1 mann:2 δaa:1 arbitrarily:1 aa:4 relevant:1 cn:7 cm:3 point:6 simple:4 steinberg:1 ca:3 corresponds:6 dimensional:1 represented:4 simply:6 invariant:2 respect:3 trˆ:7 vaidman:12 conference:2 forms:1 unusual:1 described:12 much:1 deep:1 basis:16 would:10 rewrite:1 due:8 been:5 parentani:2 reduction:24 cauchy:1 interest:2 basic:11 expected:1 transformed:1 ph:2 ak:10 define:8 via:3 direction:7 grqc:1 corresponding:4 observable:15 quantities:10 occurs:3 formed:1 subspace:1 covariance:2 wish:2 observers:3 observe:3 determination:4 external:3 hmd:3 last:3 c1:4 general:19 spin:10 spain:1 expended:1 case:46 hdt:1 uncertain:1 splits:1 exponential:1 operational:1 harder:1 conserved:1 value:37 will:8 while:11 suppose:10 shift:1 situation:3 property:5 region:1 procedure:3 remembering:1 real:3 studied:2 spacelike:2 coupled:2 almost:1 1z1:1 von:4 contrasted:1 thus:2 site:1 surface:1 numerical:1 itself:2 invalidates:1 return:1 leaving:1 demolition:3 examine:3 summarize:1 different:14 σz:2 perform:2 distributions:3 make:2 lett:4 same:15 clearly:6 reconstructed:1 complex:6 quant:2 emphasize:1 schematic:3 advances:1 modification:2 several:4 couple:1 umh:1 independent:3 used:6 columbia:2 raymond:1 singapore:2 a2w:4 acting:1 conceived:1 effect:2 flows:1 hand:3 v1:1 moment:1 strength:6 moving:3 necessity:1 entanglement:1 frequently:1 totally:2 normalization:2 recent:1 lev:1 weakly:1 schr:5 reflection:1 fully:3 nevertheless:2 try:1 nonetheless:1 epr:10 remain:1 dadb:8 directly:3 without:2 solve:1 components:8 convenient:1 coordinate:2 position:1 consistency:3 otherwise:1 spend:1 usual:12 bellow:1 popescu:1 less:2 being:1 generally:7 accurate:3 v6t:1 hphys:20 rest:2 gravity:1 seen:1 rohrlich:1 stored:1 identify:3 unifies:1 world:2 alternative:1 macroscopic:5 mittelstaedt:1 projection:8 pictorial:2 disturbance:1 preprint:1 density:3 regarded:1 ela:1 seems:1 cc:1 add:2 interested:2 combine:1 location:10 versa:1 coded:1 transformation:3 amusing:3 identical:2 makes:1 fluctuating:1 bij:1 branch:1 depends:1 eigenvalue:1 read:1 replaced:2 showing:1 decomposed:1 possible:10 additivity:1 possibly:1 reaction:1 entangled:3 similarly:2 using:6 replace:1 advanced:3 formal:2 loss:1 imposed:2 like:17 particle:5 sakharov:1 systematically:2 follows:5 reduces:1 velocities:1 o2:6 substitution:1 ignore:1 continue:1 yields:8 either:3 arbitrary:3 beverly:1 stationary:1 reduced:6 mathematical:1 classified:2 neumann:4 classical:3 yamaguchi:1 cabc:1 conditional:5 some:20 back:3 understood:3 evaluated:1 proper:1 classes:4 exists:1 happens:3 obviously:1 slice:1 undisturbed:3 confirm:1 affects:1 measurements:31 recorded:4 subclass:3 backward:2 does:11 decomposition:1 bra:2 provides:1 greenberger:1 proc:1 prob:15 o1:10 measuring:17 object:2 scientific:3 bb:1 sensible:1 selecting:2 equivalent:2 use:7 expansion:3 amato:1 protective:2 although:5 2m:2 post:39 transported:2 hilbert:18 simpler:1 nj:1 rare:2 usa:1 extension:4 getting:1 freedom:2 triviality:1 discussed:6 generated:1 o:10 page:1 practical:1 covariant:5 range:1 must:8 stand:1 act:2 mixed:5 introduced:1 aˆ:8 equally:1 rev:7 strangeness:1 previously:1 into:1 h1:1 twostate:1 down:1 prepares:1 appropriate:2 right:2 references:1 determine:4 operator:29 proportional:1 additional:2 vˆ:2 comparing:3 measured:12 unmodified:1 initial:20 long:2 spindel:1 start:1 describes:3 inner:7 way:7 discontinuities:1 forward:10 was:15 naturally:2 function:23 elsewhere:1 form:8 phenomena:2 collapsed:1 regard:3 but:13 idea:1 idealized:1 failure:1 repeated:3 hi:18 hn:1 larger:2 implies:2 proposal:1 he:3 compute:1 type:2 ˆs:4 ig0:5 up:5 us:15 international:1 liouville:1 projecting:1 limit:9 sum:1 grasp:1 problem:3 invoke:1 similar:4 called:1 mechanics:15 ψout:3 ab:7 constant:1 spelled:1 defined:14 recognize:1 abstract:1 describe:13 linearity:1 frames:3 denote:2 v2:1 dashed:2 single:4 exist:1 aw:30 formulation:10 formalism:12 commuting:2 physical:15 again:1 functions:5 δbb:1 nm:3 dotted:1 locality:1 asymmetry:1 extract:3 separating:1 weaken:1 when:17 casher:1 reality:2 field:1 other:14 role:3 details:1 investigations:1 spatial:1 department:2 coherence:1 sufficient:2 picture:3 stat:1 elements:10 superposition:5 provided:1 remains:1 problems:3 inherently:1 prepared:3 meaning:5 15b:1 ubc:2 variable:2 lution:1 astronomy:1 structure:1 upwards:2 independently:1 correlated:6 regime:9 coupling:19 vice:1 assume:6 requires:1 interval:10 interacting:1 rule:1 original:1 discontinuously:1 2im:1 came:1 time:37 observables:29 n2:1 quantity:4 starting:1 having:1 restored:1
|
quant-ph9501012.txt |@word partial:2 peshkin:3 similarity:1 directions:1 magnetic:30 separates:1 results:1 illustrated:2 eds:2 scalar:4 commute:2 fig1:1 reasoning:1 causes:1 whose:9 depend:2 nonlocal:4 charge:1 preserved:1 under:1 analogous:1 division:2 supported:1 amplitudes:1 provides:1 very:2 rise:1 springer:1 wave:2 electron:10 every:1 refractive:1 affect:1 trouble:1 difference:3 exact:1 condition:4 leads:1 school:1 hamiltonian:7 notes:1 large:1 vector:2 manifestly:1 relation:1 torques:1 force:3 measurable:4 unpolarized:2 approximation:1 zero:5 enclosed:2 l2y:1 l2x:1 dynamics:1 even:3 index:1 what:1 appear:1 exactly:5 expressed:1 uniform:1 experiment:5 new:4 technology:1 ever:1 contrast:2 satisfy:1 outgoing:1 exchange:1 never:1 component:1 here:2 pumping:1 separation:1 alone:1 path:10 along:2 equations:9 appears:1 box:1 lipkin:1 institute:1 shift:15 vectors:1 p2:2 action:2 shaded:2 named:1 spatially:1 marked:1 replace:1 neutrons:6 visible:1 frame:1 apply:1 total:1 kobayashi:1 use:1 usa:1 eφ:2 arms:3 classically:3 depicted:1 therefore:1 forces:1 more:1 israel:2 formally:1 hermitean:1 rehovot:1 becomes:2 operators:5 conducting:1 particular:1 foundations:1 cases:1 iii:1 must:1 states:3 none:1 defines:1 mc:1 mb:1 science:1 equation:2 work:1 mv:1 obvious:1 exceptions:1 example:1 cone:1 claim:1 figure:1 chosen:1 process:1 allowed:1 purposes:1 involve:2 numbers:4 sense:4 axis:1 influenced:1 argonne:2 eng:1 precessing:1 discussion:1 acts:2 how:2 criterion:3 significance:1 instead:1 ordinary:4 verlag:1 sin:1 information:1 may:1 earlier:1 containing:1 plane:4 demonstrating:2 waves:2 choice:2 dynamical:3 schematically:1 light:1 so:7 fundamental:1 correlation:3 interpretation:1 help:1 indeed:2 over:2 move:1 satisfied:2 murray:1 interpreted:2 course:1 experiments:3 through:3 experimentally:1 differs:1 japan:1 still:1 its:2 energies:1 actually:1 aviv:2 fig:11 lx:1 ly:1 return:1 autocorrelations:2 rotations:1 precess:2 effects:2 they:4 symposium:1 rotation:1 now:3 discuss:1 nor:1 eigenvalue:1 finite:1 university:1 identified:1 applied:1 magnitude:1 transmitted:1 fields:4 2m:3 side:1 domain:2 another:1 series:2 energy:7 interferometer:10 frequency:4 measurement:2 quantum:9 laboratory:1 ev:1 eq:5 really:1 shown:2 ezawa:1 goldhaber:1 3rd:1 space:1 gradient:1 furthermore:1 since:2 interference:1 replacing:1 acting:1 conjectured:1 lecture:1 correct:1 independence:2 shows:1 theory:1 associate:1 differ:2 free:2 org:1 asi:1 definition:1 interaction:2 geometry:1 moment:6 times:1 motion:10 length:2 place:1 integrand:4 relate:1 variables:2 faculty:1 number:3 restrict:1 spinning:1 xy:3 directly:1 carry:1 tel:2 angular:8 aharonov:15 given:8 eqs:2 sackler:1 relations:1 1a:1 their:8 1b:1 passed:1 final:1 gives:1 acquire:1 optical:1 shifter:2 x2:1 anandan:3 x1:1 png:2 observed:3 kind:1 polarized:6 showed:1 see:1 limiting:1 intensities:3 were:1 outcome:1 result:2 sab:23 torque:7 argument:1 winding:5 seen:1 apparently:1 any:9 paths:3 strength:1 outbound:2 note:1 sciences:1 ideal:1 potential:3 analogy:1 objective:2 differences:1 electric:7 though:2 who:2 experiences:3 phase:18 measured:1 why:1 mach:2 consequences:1 average:2 feynman:2 proceedings:1 points:3 electrons:1 principle:5 mechanical:1 velocity:1 physics:6 fact:2 quantity:3 ambiguities:1 phenomenon:2 show:3 random:1 gauge:10 solutions:1 find:1 shield:1 spite:1 explain:1 outside:2 topological:12 jan:1 only:11 factor:2 adequate:1 local:14 pointed:2 do:7 means:1 beams:2 expectation:5 cannot:3 exchanges:1 during:3 dr:2 neither:1 precession:10 traverses:1 allman:4 arxiv:2 ascribable:1 traversed:1 predicted:1 contain:3 obscure:1 inside:1 view:1 set:2 reference:1 national:1 packet:1 relative:8 argued:1 depends:7 projections:2 arm:4 instance:1 commutation:1 nuclear:1 definite:2 symmetric:1 state:3 closed:1 between:6 invariant:5 justified:1 solenoid:2 µb:1 available:1 terms:2 however:9 extent:1 topology:4 both:1 cos:1 many:1 region:6 equal:2 contract:1 σz:8 σy:10 σx:10 present:1 context:2 refraction:1 argue:1 schroedinger:1 comes:1 point:3 simple:1 character:1 semiclassical:2 represented:1 simply:2 contemporaneous:6 moreover:1 throughout:1 considering:2 ps:1 pp:2 described:4 nomura:1 locally:1 three:1 been:5 much:1 interest:1 basic:1 ph:2 refuted:1 direction:7 describe:1 observable:6 gas:1 zeilinger:3 external:3 weizmann:1 evidence:1 spin:23 those:4 bτ:1 novel:1 uncertain:1 value:7 eigenstate:1 will:2 while:1 replaced:2 involved:1 cylinder:1 changed:2 gorini:1 vol:1 ii:1 characterize:1 il:1 vanish:7 faraday:1 different:2 same:8 wherein:1 unity:2 quant:2 split:1 figures:1 gets:1 neutron:25 independent:4 http:1 raymond:1 rotor:1 i1:1 zehnder:2 i2:1 upon:10 effect:36 hand:1 v1:2 v2:2 potentials:1 angle:3 recent:2 immaterial:1 no:16 spent:1 analysis:1 bohm:12 precesses:2 experimental:2 components:6 position:2 model:2 usual:4 rest:1 assigned:1 underlying:1 useful:1 scattering:1 enters:1 conclusions:1 had:1 except:1 causing:1 nato:1 lett:6 contrary:1 spin1:1 transformation:1 momentum:9 identical:1 badurek:1 aspects:1 around:1 rev:8 format:1 possibly:1 know:1 confined:2 using:2 part:1 necessary:1 like:2 particle:5 follows:2 ignore:1 flux:3 either:2 beverly:1 mathematical:2 because:5 classical:4 exposed:1 some:2 experienced:1 mirror:1 δn:1 merge:1 electromagnetic:6 opposite:1 integration:1 does:3 expressing:1 murayama:1 measures:1 obey:2 2µb:3 tonomura:1 conventional:1 hilbert:1 about:2 would:1 discussed:1 nonvanishing:1 range:1 frigerio:1 introduced:1 considerations:1 contains:3 maxwell:8 within:1 integral:3 remarks:1 right:1 references:1 determine:1 operator:5 proportional:2 area:2 assumed:2 there:4 question:1 way:4 analyze:1 was:3 interferometry:1 function:1 complete:1 eab:3 but:8 idealized:1 true:1 absent:1 made:3 cylinders:3 surprising:1 society:1 transmits:1 ωt:3 us:1 international:1 limit:1 autocorrelation:6 fluctuations:4 problem:1 similar:1 called:2 mechanics:8 ac:6 ab:18 defined:1 abstract:1 measure:2 influence:1 deep:1 general:1 conserved:1 our:1 physical:3 incorrect:1 again:2 functions:2 locality:3 when:6 vanishes:3 casher:3 field:44 other:3 role:2 normal:5 department:2 out:2 illusion:1 time:6 meaning:2 variable:1 correlated:1 dφ:2 values:4 interval:3 experimenters:1 resembles:1 observables:1 laws:1 requires:1
|
quant-ph9501013.txt |@word measurements:2 systematic:1 interference:5 magnetic:1 varying:2 bandgap:6 results:2 leads:3 eds:2 quadrature:1 fig5:1 azbel:1 fig3:1 edu:1 go:1 gaithersburg:1 gk:1 misconception:1 layers:1 certainly:1 barnett:1 1µm:1 technique:2 rf:1 present:1 th:1 under:2 analogous:1 include:1 eliminate:1 alternating:1 random:1 far:2 frequencies:1 wave:12 electron:2 ultraviolet:2 refractive:1 experimentally:1 difference:2 continued:1 splitter:4 differentiated:1 transmission:18 notes:1 fig4:1 standards:1 large:2 coincidences:1 small:2 fig2:1 dip:1 added:2 abbreviated:1 slower:1 insignificant:1 b27:1 consistent:2 fig1:1 prediction:2 sign:1 approximation:1 rate:3 today:1 design:1 further:2 bandgaps:2 index:3 errors:1 sub:2 apparatus:1 sun:1 assistance:1 while:2 expressed:1 uniform:1 version:1 sokolovski:1 above:1 elucidate:1 new:2 method:2 contrast:1 supporting:1 evanescent:1 degree:1 residual:1 ranges:1 met:1 berkeley:4 path:1 along:1 quite:1 change:2 hass:1 obtained:1 great:1 property:1 parameters:1 institute:1 shift:3 study:3 changed:1 reports:1 controversy:2 simultaneous:1 stressed:1 skepticism:1 delays:1 plotted:1 via:1 useful:1 transit:1 stingl:1 layer:4 modifying:1 traversing:1 counts:1 causal:1 would:3 probabilities:1 give:2 predictions:3 properties:1 process:2 sample:5 therefore:2 taken:1 theoretical:4 mckinney:1 more:2 introducing:1 coating:3 hauge:2 envelope:1 berlin:1 normalized:4 particular:1 antennas:1 objections:1 iii:1 prism:4 md:2 springer:1 leavens:1 tunnel:1 setup:1 work:4 theories:3 superluminality:2 arrive:2 spontaneous:1 example:2 compare:2 figure:9 mirrors:2 predict:1 discussed:2 organized:1 involve:1 trieste:1 minimum:4 numbers:1 sense:1 exclude:1 occur:1 multilayers:1 ratio:2 decaying:1 rather:1 travel:3 american:1 delay:27 very:1 enders:2 significance:2 opt:2 verlag:1 sin:2 fs:8 intended:1 superluminal:5 modulation:1 earlier:1 different:3 produce:1 data:10 parallel:1 dynamical:1 effective:1 light:6 counter:1 summing:1 st:1 so:2 correlation:1 order:6 help:2 office:1 over:2 soc:2 years:1 experiments:3 through:11 statistical:1 differs:1 captions:1 ieee:1 its:3 before:2 horizontally:1 tending:1 group:18 thank:1 decay:1 ln:1 τg:1 τc:1 pulses:1 better:1 complex:3 fig:3 travelling:2 freely:1 ideal:1 versus:2 them:1 ya:1 scaling:1 band:3 effects:4 they:5 half:2 now:1 subluminal:3 dielectric:8 represents:1 fully:2 university:1 did:1 magnitude:2 transmitted:5 each:1 found:1 quarter:5 side:2 energy:2 sov:2 related:1 constitute:1 interferometer:2 frequency:6 expect:1 connor:1 measurement:2 quantum:4 our:12 special:1 out:3 shapiro:1 leave:1 shown:3 jackson:1 borderline:1 furthermore:1 since:5 rev:23 research:2 content:1 may:4 bragg:1 internet:1 squares:1 issue:1 disagreements:1 shows:2 after:2 theory:8 barrier:13 possibility:1 standard:2 paucity:1 california:1 york:2 ask:1 org:5 beginning:1 generate:1 pairs:1 interaction:2 determining:1 could:3 hong:1 used:1 times:8 filter:1 length:3 plane:2 exponentially:1 chiao:7 barriers:2 facilitate:1 first:3 placing:1 manuscript:1 striking:1 wiesendanger:1 reflected:1 instances:1 approximately:1 another:1 electronic:1 little:1 needed:1 leading:4 ruggeri:1 reflectivity:1 their:5 stephan:1 too:1 articles:1 john:1 structures:1 ranging:1 mandel:1 holden:1 uttiker:8 optical:3 convinced:1 than:8 png:10 reflection:1 translating:1 polarized:3 johnson:1 second:2 submitted:2 minimize:1 a45:1 amplitude:1 were:4 garrison:1 dielectrics:1 topics:1 exceeded:1 slid:1 curves:3 close:1 need:1 seen:3 clearly:1 relatively:1 paths:1 conversion:1 traditionally:1 angle:10 academic:1 studying:1 able:3 mid:1 polarization:3 high:2 potential:1 take:2 analogy:1 finding:1 detector:1 n00014:1 circles:1 formulas:1 towards:1 scripta:1 opposite:1 incidence:14 reach:1 extending:1 preliminary:2 pair:1 transverse:3 measured:2 interferometry:2 appear:4 mugnai:4 deviations:3 nonlinearity:1 calculated:3 detectors:1 physica:1 martini:1 feynman:1 proceedings:1 part:2 principle:1 velocity:2 effect:5 left:1 physics:4 fact:1 show:2 violation:1 supported:3 infrared:1 bring:1 attempts:2 planning:1 thickness:2 find:2 causality:2 spite:1 situations:1 explain:3 ishii:1 pump:2 should:1 jan:1 only:1 experiment:3 factor:1 quasimomentum:1 identification:1 ocs:1 local:1 chamberlain:1 meanwhile:1 dependent:1 between:3 stop:1 beam:6 brillouin:1 kurizki:2 during:1 precession:1 substrate:1 arxiv:6 baz:1 microscopy:1 tuned:1 investigate:1 traversed:1 predicted:1 including:2 discussing:1 hκ:1 sipe:1 thesis:1 dump:1 national:1 packet:2 observed:1 see:4 result:1 discussions:1 simultaneously:1 arm:1 concern:1 closer:1 exploited:1 placed:1 scattering:1 state:1 unable:1 various:1 simplest:1 arrival:2 august:1 nature:2 scanning:1 wm:1 incident:3 comm:1 nimtz:3 distinguish:1 suppressed:1 originates:1 received:1 essentially:1 limits:1 many:1 region:2 according:1 attributed:1 propagation:8 figures:1 femtoseconds:2 refraction:1 agresti:1 workers:1 experimental:4 ch:1 timescale:2 conclude:1 appeared:2 ca:1 excess:1 period:1 coincidence:4 semiclassical:3 respect:2 cw:1 ps:5 described:3 analogies:1 due:3 been:4 mark:1 much:3 axis:2 interest:2 reflective:1 ph:8 improve:1 ann:1 angled:1 direction:1 describe:2 kronig:1 both:9 photon:6 cos:1 traversal:1 bulk:1 observe:1 determination:1 external:1 angles:4 those:2 naval:1 microns:2 laser:2 reciprocal:1 pacs:1 solid:1 value:1 air:9 will:1 near:5 steinberg:10 behavior:2 error:1 tunneling:17 mitchell:1 yablonovitch:2 landauer:7 real:2 seven:1 studied:1 characteristics:2 wkb:1 thus:2 discrepancy:8 equal:4 characterize:1 itself:1 busch:1 technology:1 definitive:1 confirmed:1 φt:5 grant:1 perform:1 suggest:1 format:5 same:3 any:2 periodic:2 quant:7 plates:1 several:2 investigated:1 http:5 raymond:1 upon:1 drives:1 moment:1 portal:1 stack:2 recent:1 lower:2 off:1 center:1 thicknesses:2 nevertheless:1 variety:1 well:3 remain:1 analysis:1 thought:1 ky:1 de:2 edge:3 position:3 model:1 parametric:1 spend:1 contenders:1 unified:1 proposed:2 less:1 being:3 spielmann:1 accurate:1 photonic:6 aside:1 sources:1 bandwidth:1 world:1 speed:1 yet:2 previous:1 preprint:1 conclusions:1 photons:14 point:2 had:1 except:1 improvement:1 wavevector:1 source:1 extends:1 lett:12 untherodt:1 remaining:1 momentum:1 identical:1 march:1 wavefronts:1 loss:1 corresponds:1 vacuum:1 confined:1 using:3 mod:2 dimensional:2 like:1 submission:1 workshop:1 signal:2 martin:2 popular:1 output:1 stationary:4 therein:2 sketch:1 right:2 wavepackets:2 deal:1 conditional:1 some:2 krausz:1 understood:2 experienced:1 jeffers:1 mirror:17 duration:1 extended:1 kdp:1 ourselves:1 scale:2 describing:1 lead:2 confirm:1 electromagnetic:1 garrett:1 normal:3 microwave:2 heitmann:1 does:3 deficit:1 semiconductors:1 propagating:2 noise:2 scientific:1 reaching:1 microwaves:1 equivalent:1 oscillating:1 agreement:3 constructive:1 paper:1 how:1 wong:2 imaginary:3 subtract:1 emits:1 bz:1 comparison:1 about:4 eaves:1 mccumber:1 anomalous:1 dependence:1 ports:1 kwiat:5 magazine:1 larmor:16 ou:1 consequently:1 cutoff:1 conserving:1 within:3 numerically:3 sol:1 down:1 phase:6 references:2 einstein:1 france:5 classical:1 multilayer:3 there:5 available:5 nucl:2 dispersion:1 width:1 plenum:1 appl:1 low:4 way:2 conceivable:1 was:2 chu:2 function:4 head:1 medium:2 elsewhere:1 form:1 offer:1 femtosecond:3 penney:1 adjusting:1 but:9 larger:1 faster:4 sterke:1 whether:2 inside:1 uv:2 particle:1 crystal:2 limit:2 ωl:4 pumped:1 fluctuations:1 similar:1 constant:1 certain:3 measure:2 am:2 general:2 trombone:4 single:3 exist:1 wavelength:2 physical:1 again:1 functions:1 compared:1 nm:5 no:1 whereas:1 when:3 field:2 narrowband:1 other:3 papers:1 department:1 revision:1 deviation:1 repeat:1 variation:1 peak:7 dissipation:1 gap:1 sides:1 structure:3 zeilinger:1 correlated:2 longer:1 packets:3 rule:1 portion:2 time:36 understand:1 stacks:1
|
quant-ph9501014.txt |@word limited:2 nelson:1 reversibility:1 four:2 entropy:2 controversial:1 anticorrelated:1 consists:4 spacetime:3 relationships:3 nous:1 maximally:1 calculate:1 paris:8 contained:1 presents:2 whatsoever:5 under:7 hermann:1 ontological:27 plants:1 conjecture:1 kent:2 neue:1 rise:1 replaces:1 every:42 selleri:1 affect:4 believed:3 school:6 internally:1 cause:3 solution:6 herbert:1 convenience:1 vector:24 guiding:2 succession:1 indices:1 paperback:1 concise:3 consistent:50 pulse:1 feasibility:1 elegant:3 second:7 street:1 rigorous:2 eigenspaces:1 even:29 established:4 incompatible:2 ˆx:2 ˆy:2 ˆz:2 selected:1 asia:1 als:1 birkhoff:3 en:2 jerome:1 above:41 ˆi:1 ever:5 consisting:5 seeks:1 ated:1 philippe:1 bi:10 simultaneously:4 seventh:1 never:9 abstractly:3 here:28 met:1 asymmetry:2 represented:6 path:3 ascribing:1 obtained:8 items:1 study:7 changed:1 stipulates:3 approaches:7 reports:2 controversy:1 drm:1 drn:1 california:3 suitable:1 changes:4 york:13 blackbody:1 projection:14 classification:1 discontinuous:1 explained:8 natural:3 julia:1 highly:3 brought:1 visible:2 moral:3 tp:2 idiosyncratic:1 stand:1 total:6 bra:3 would:38 chooses:1 inevitable:2 definiteness:1 call:4 therefore:42 indiana:1 25th:1 type:18 until:9 separated:2 composite:7 odinger:75 decomposed:1 aware:1 berlin:4 tying:2 excellent:1 hold:15 circumstances:1 me:1 obeying:1 springer:3 morally:1 room:1 permits:1 work:24 theories:15 ere:2 neurons:1 concepts:5 experts:1 my:1 example:26 impose:1 give:19 relativistic:2 weinberg:1 involve:3 degenerate:1 david:21 cushing:1 guarantee:1 end:6 dalibard:1 turn:7 provide:5 travel:1 feature:5 how:19 significance:1 symposium:3 ordinary:6 preferable:3 lam:1 description:13 inherent:3 replacing:1 coined:1 after:18 containing:2 lab:3 barriers:1 wrong:3 lumi:1 law:2 parallel:8 types:4 attempt:6 third:3 βi:1 complexity:4 ultimate:2 correlation:3 nonsensical:1 order:18 operations:6 restriction:1 interpretation:250 office:1 devote:1 over:14 vary:2 satisfied:7 murray:4 london:6 thesis:8 experimentally:2 japan:3 satisfies:2 pˆw:2 before:6 sciences:4 fit:2 somewhere:2 exhibits:1 writing:3 better:2 physicist:2 production:2 erences:1 roland:8 hidden:74 eugene:1 maximal:2 treating:2 them:12 affected:1 combination:2 enrico:3 bang:1 effects:15 they:39 schools:1 altogether:2 silver:1 sans:1 represents:5 reasonably:1 alternately:1 explode:1 filling:1 each:50 side:3 mean:4 independent:3 series:4 principles:2 comprises:3 used:25 god:2 dewitt:4 angular:2 particles:36 re:1 unrelated:1 estudios:1 dowker:2 medicine:1 rm:3 rn:17 ri:5 rj:4 foundation:1 perception:2 turning:1 linear:21 barrier:2 associate:1 herman:1 given:41 free:16 standard:6 wanted:2 universally:1 9ew:1 ange:1 consciousness:9 r1:16 recovering:1 created:1 decohering:4 disturbed:1 tempting:1 unknown:2 moving:3 onto:13 separable:12 already:6 features:1 attractions:1 primary:1 philosophical:14 unspecified:1 another:11 einen:1 separably:1 cartesian:2 similarly:1 deutsch:1 approximately:2 needed:1 master:1 observations:1 tom:1 postulate:16 john:22 murayama:1 insightful:1 centred:3 collapse:43 rest:4 albert:15 took:1 rejected:4 speakable:1 joos:1 predictable:1 somewhat:2 corresponded:1 maintaining:1 peculiar:3 distance:2 showed:5 surrounding:1 rate:3 project:4 matter:9 classes:5 historical:3 atomique:1 ram:1 mind:71 spectrum:8 talking:6 seen:11 seem:10 unaffected:2 tells:2 contents:1 forced:1 mermin:5 person:5 analyzers:1 convenient:4 latter:4 isolated:2 thorough:1 causing:7 forces:2 completed:2 decoheres:3 broglie:16 though:4 object:16 wells:1 involving:3 letter:1 phase:4 acknowledgements:1 observation:9 michel:1 incomplete:2 consumed:2 devastating:1 detectors:2 inferred:1 dr1:1 bracket:1 principle:13 chris:1 dov:1 notion:3 dot:2 saying:9 dr2:1 bomb:8 subtly:1 unified:1 vigier:3 random:3 ending:1 attempts:3 radio:2 earth:2 shaffer:1 summarised:1 proposed:11 representing:1 explain:11 greenberg:3 do:36 mixture:1 establishes:1 di:7 de:35 perceive:14 preferred:11 eitan:1 σ1x:1 photoelectric:1 uncountably:1 dx:2 new:23 dv:6 reconstruct:4 dt:7 du:4 dr:4 ds:2 dq:2 hall:1 runs:1 covering:2 textbooks:1 fields:1 stora:1 twice:1 multitude:1 ban:2 implication:8 kochen:2 e89:3 respond:1 bordas:1 schreiber:2 observer:31 observes:5 radium:1 evolving:1 observed:9 depends:6 decided:2 projections:3 discussions:4 disturbing:6 λi:1 best:7 techniques:1 instance:1 said:4 singularity:1 tensor:3 away:4 ensures:1 artificial:1 eigenstates:5 symmetric:2 simplest:1 µe:1 sorts:1 previous:5 approach:29 accord:2 triplet:1 terms:33 extend:1 nature:9 literally:1 weak:2 omn:26 wi:17 equals:1 inextricably:1 vernon:1 harvard:1 florence:1 eipx:2 eipy:1 suggested:18 ranges:1 essentially:4 cor:1 expos:1 irregular:1 compton:3 against:5 else:3 und:2 une:2 logic:26 contribution:1 argue:1 suggest:5 presumably:3 appeared:1 royal:1 berkeley:4 2nd:3 active:2 healy:1 symmetries:1 testable:2 conference:2 recognises:1 commutative:1 nomura:1 basis:22 union:4 observing:4 ai1:1 three:11 been:45 quickly:1 t2:9 much:10 interest:3 basic:2 expected:1 celebration:1 entities:2 life:10 retrospect:1 quantities:2 concerning:2 hennessy:1 coherent:3 axiomatics:1 chile:1 pinch:1 worked:1 reassuring:1 spin:49 applied:7 exception:1 east:2 air:1 aim:1 near:2 ain:1 suppose:31 viii:1 applies:5 property:12 precede:1 procedure:2 seven:1 robert:6 speech:1 iv:11 ii:91 disjoint:3 im:3 il:3 track:3 ignoring:1 ie:30 confirmed:1 atmanspacher:1 perform:5 things:5 make:9 slac:1 complex:2 quant:1 split:11 several:9 inventors:1 evolve:8 schiller:1 i1:4 everett:18 published:4 schen:1 hand:9 potentials:1 insisted:1 simulates:1 wimmer:1 weakly:3 settled:1 epr:14 academic:5 prescribes:1 claims:3 jean:1 left:6 criticism:18 αjk:1 αjl:4 just:17 physique:2 newton:1 starting:2 gravity:1 assigned:1 via:2 thanks:1 human:14 facts:33 followed:2 jacobson:1 scattering:1 yet:2 divide:1 enters:1 dialogues:1 bunge:1 candidate:3 infinitely:1 similarities:1 regarded:2 had:10 belongs:1 easy:7 apart:1 gave:3 spinoza:2 gellmann:1 possible:39 spanned:3 plenum:2 possibly:2 wojciech:8 αj1:5 unique:2 unfounded:1 advanced:1 occurring:1 appearing:1 texts:1 performing:5 diffraction:2 niels:9 specific:8 arbitrary:6 interestingly:1 towards:1 right:2 deal:1 people:3 successfully:1 santiago:2 dead:15 underly:1 born:7 critique:2 interf:1 library:4 sociology:1 cooper:1 electromagnetic:1 normal:2 comments:2 everything:3 linearly:1 grundlagen:1 indication:1 core:1 bold:2 dropped:2 rina:2 predicting:2 illustration:1 translated:1 fermat:1 post:1 properties:16 meyer:1 chapter:121 accepts:6 o:1 distinct:3 magazine:1 ensure:3 spins:1 cosmologists:2 efforts:1 slightly:6 considerations:1 raised:2 statements:2 ecanique:3 presence:1 obtaining:4 bound:2 intellectual:2 son:1 down:31 lies:5 hermitian:2 doctrine:8 amsterdam:5 refined:2 often:11 rely:2 support:1 initial:27 approximate:3 class:2 influencing:2 physicists:10 way:35 imperceptible:1 editions:1 nbse3:2 was:72 across:1 happy:2 medium:1 form:28 piron:5 attempted:2 converse:1 sketched:1 physikalischen:1 mysterious:1 removed:1 true:24 full:1 versions:2 assessment:1 attached:5 maximum:1 devices:3 tell:6 dordrecht:3 fermi:4 emotional:2 quantised:1 jauch:5 emit:1 b1:2 zeroes:1 proved:5 b2:2 item:1 czachor:1 abstract:12 evidence:4 peres:3 conserved:1 proves:2 exist:12 perez:1 distributions:2 check:11 constructed:1 astonishing:1 nj:5 faithful:1 locality:26 agreeing:1 nb:3 generally:5 vanishes:1 reality:11 successful:2 interested:1 role:11 holding:1 papers:10 test:2 vanished:1 company:2 absurd:3 picture:15 superposition:13 models:7 dies:1 felt:2 mecanique:1 rendus:3 variable:3 neuroscience:1 ballentine:1 happening:1 pion:1 assume:10 interval:1 packets:5 necessitates:1 together:1 fact:45 time:97 observables:33 quantity:1 inc:1 concept:5 customary:1 remarkable:1 global:1 alternatives:4 leads:5 supplement:2 grateful:1 commentaries:1 milk:2 certainly:1 inverse:1 depend:9 clarification:1 editors:20 environment:5 violation:1 finally:7 analogous:1 must:30 reassemble:1 division:2 advantage:2 orthogonal:16 erale:1 unfamiliar:2 choice:9 entries:1 trouble:1 1s:1 minute:1 interferometry:1 perceived:3 impressive:1 presented:18 did:8 die:7 leave:1 discrete:5 settle:1 stipulated:1 der:13 revolution:1 says:1 deutschen:1 measurable:7 specker:2 αi1:3 editrice:1 spectral:1 appear:9 wavelike:1 uniform:1 current:8 annals:6 paradoxes:1 goes:1 treatise:1 international:9 ghirardi:1 satisfy:5 postulates:5 αik:3 hairs:1 unobserved:1 french:6 understanding:4 erhard:2 alone:1 along:5 appears:1 change:7 ensembles:4 box:6 exemplified:1 institute:5 petersen:2 vectors:6 eduction:1 bow:1 simultaneous:1 suggestion:4 usually:1 conveniently:1 studies:2 emerge:3 useful:15 griffiths:13 extra:7 problematic:2 merely:9 prefer:2 marked:1 flexibility:1 centenary:1 lansing:1 planck:7 additive:3 projector:11 concentrate:1 prove:4 positive:4 helvetica:3 predictions:24 predictability:1 live:2 explicitly:6 opposed:2 criteria:3 symbolized:2 compactly:1 squid:1 theoretical:5 today:8 introducing:3 sharing:1 duality:3 apparent:6 appendix:1 everywhere:1 virtue:2 cases:2 capturing:1 fly:1 cation:1 valued:2 abner:1 originally:3 soul:1 cat:49 reviews:3 values:23 growing:1 making:5 german:3 grained:23 dedicated:1 want:1 figure:3 predict:5 december:9 arise:2 locks:1 performed:16 allowed:5 conversely:2 occur:5 english:7 rays:2 requirements:1 winter:1 s2:13 discussion:18 spreads:1 mistakenly:1 strikingly:1 contrasts:1 pure:3 dutton:1 coleman:2 parameter:1 economy:1 map:12 product:5 quantenmechanik:5 influenced:1 may:183 max:6 needs:2 φi1:3 grounds:1 date:1 revealed:4 eighth:1 man:1 waerden:1 aj:2 branches:13 outline:3 succeeded:1 conscious:11 whenever:3 futures:2 yielding:3 cosmology:5 switch:1 so:47 sn:2 representation:6 talk:20 typical:4 exclusive:3 comfort:1 indeed:7 pointed:2 shaky:1 mainly:3 unacceptable:4 argues:5 course:48 introductions:1 experiments:22 rayonnement:1 statistical:17 argued:4 still:11 pointer:9 derive:5 group:1 summands:5 interesting:3 jim:1 coordinates:28 forms:5 suspicion:1 constitutes:4 mail:2 main:7 instantly:2 correspondence:2 non:40 thereby:1 views:7 conversations:1 tjk:1 processes:2 introduce:1 records:2 half:13 sorted:1 now:41 discuss:4 developments:2 term:10 name:2 james:10 interpr:2 advent:1 beings:3 establishing:2 orthonormal:3 realistic:5 stockholm:1 entirely:3 cliffs:1 realism:3 spinor:1 domain:7 square:2 fired:1 eg:19 revised:1 manifests:1 year:1 doubtful:1 χin:1 happen:4 avoided:1 es:28 intended:2 shown:13 finegrained:1 3rd:3 space:56 greeks:1 interference:4 looking:6 seriously:1 emerged:3 suggesting:1 formula:4 correct:7 shows:4 decoherent:26 earlier:5 reformulation:4 theory:113 χi1:1 state:195 variant:2 divergence:1 possibility:4 quite:3 advantages:1 axioms:5 fixed:11 derivation:1 language:5 collapsing:1 transition:3 motion:2 thing:5 principe:1 place:9 βn:1 view:15 think:4 frequent:1 first:24 emotion:1 intuition:2 henry:3 symmetry:1 clause:1 variables:52 coming:1 kafatos:1 parkinson:1 reductionism:2 xx:1 simplified:5 long:3 directly:7 theorems:1 carry:2 impossible:6 ring:1 open:5 george:5 little:7 necessarily:4 checked:9 1x:3 joseph:1 convention:1 white:2 gives:14 pittsburgh:2 brains:1 continuous:3 proving:1 accurately:1 bloomington:1 x2:4 eliminated:1 x1:4 photographic:8 than:14 semantics:1 nathan:1 accordance:4 require:1 transferred:1 modelled:5 future:11 were:19 bauer:1 iˆ:6 inferring:1 gathering:1 whitley:1 rene:2 argument:5 say:20 buried:1 recover:5 any:75 subsystems:1 offering:1 isolate:1 ideas:13 note:25 equipment:1 ideal:5 potential:11 take:13 forming:1 objective:4 gleason:12 differences:1 multiple:1 trace:3 opposite:3 arguing:1 analyse:1 price:1 neatly:1 israeli:1 paid:1 algebraic:9 synthese:1 importantly:4 pair:2 garrett:1 precludes:1 pages:15 overlooked:1 inequalities:4 especially:4 surprising:3 considered:20 later:14 implications:6 feynman:1 typically:2 beables:1 laws:5 precise:2 festschrift:2 show:3 leibniz:1 cheap:1 spaces:8 inconsistent:2 corner:1 fifth:1 dice:2 title:1 conduction:2 aψ:1 proportion:5 histories:174 fluid:1 pˆ12:1 m2y:8 only:58 going:3 helix:1 zeh:2 boyle:1 narrows:1 optimism:1 viewpoint:2 get:1 expectation:2 truly:1 leon:1 cannot:39 invariant:2 conjunction:4 bardeen:3 secondary:2 regarding:3 prima:1 podolsky:6 yield:4 summary:1 roger:2 predicted:10 schuster:1 discussing:4 reveals:3 physically:3 fries:1 violated:2 comparable:1 blurred:1 relative:2 namely:10 college:3 eliminating:2 apologies:1 nonlocality:16 encouraged:1 caldeira:1 fails:2 satisfying:3 commutation:2 crystal:2 ways:8 review:30 definite:36 outside:7 polymath:1 jth:1 between:21 affecting:2 accustomed:1 prentice:1 reading:1 checks:5 αn:11 arrival:1 notice:1 august:8 screen:1 jr:1 erard:2 densely:15 ji:2 spark:1 interfere:1 come:3 motivations:2 reaction:1 perceptions:2 many:93 according:17 σz:2 σy:3 σx:3 comes:2 zvi:2 stance:1 generalisation:1 jammer:1 overview:1 margenau:3 insist:1 maintained:1 werner:2 anti:3 assertions:21 associated:54 bizarre:4 considering:6 epistemology:12 arts:1 cities:1 aˆ:21 barry:4 zettl:1 workshop:2 hardly:2 sensibly:2 wants:5 concentrated:1 direction:2 grqc:1 observable:38 formed:1 photon:2 andrew:2 observers:11 observe:3 wake:1 external:13 penn:1 vagueness:3 careful:1 irrelevant:1 realities:4 those:13 pilot:3 case:29 boris:1 cast:5 xiii:1 promising:1 situation:12 tunneling:3 philosophies:1 coupled:1 dubious:3 superconducting:2 someone:5 presentations:1 technology:2 everyday:3 worry:1 different:51 formalism:30 verified:1 considerable:1 april:5 commuting:4 formulations:4 same:36 attributing:2 epistemological:15 arguments:3 physical:95 events:2 investigated:3 assigns:2 singapore:3 grw:1 allocation:1 devoid:1 harris:1 arose:1 totally:3 wholeness:4 quasiclassical:11 bryce:3 undefined:1 brill:1 no:61 accountable:1 without:31 solve:3 mann:12 components:2 coordinate:16 model:33 unconvincing:1 dimension:2 muon:1 being:28 captures:2 guided:2 sights:4 actions:2 σny:2 ucsbth:3 relevant:9 kill:1 aspect:6 summed:1 ψini:7 speed:1 multidimensional:1 multiples:1 weekly:1 villars:2 hint:1 thinking:2 seems:11 except:4 pile:1 treatment:3 extensive:1 eigenstate:8 momentum:22 real:9 aspects:5 around:6 kills:2 eigenvalue:8 rules:43 replaced:4 tik:1 sums:1 walker:2 early:1 predetermined:6 measurments:2 listening:1 vacuum:2 using:33 accepted:8 vague:7 ruled:3 englewood:1 particle:86 identifying:1 exploit:1 serves:1 chamber:4 either:15 always:23 stationary:1 reduced:2 reidel:3 reaches:1 conditional:2 pacific:1 specified:1 complementarity:5 etique:1 intact:2 thinks:1 reasons:2 provided:2 βj1:1 confirm:1 footing:1 ryan:1 critical:1 entails:2 provides:2 measuring:26 destroys:2 tomorrow:6 scientific:11 decohere:2 sixth:1 equivalent:7 communicate:1 notably:3 pascual:2 ratios:1 found:15 ontology:20 comparison:2 central:7 origins:1 capable:1 discussed:18 generated:1 mutually:6 obeys:2 ox:1 mixed:8 discusses:6 sensitively:1 sketches:3 cambridge:13 inclusion:4 instruments:1 grainings:2 dissipation:1 references:2 determine:6 einstein:17 operator:31 jerusalem:3 legget:1 stare:1 her:2 springerverlag:1 normalised:12 assumed:16 strictly:3 there:104 dispersion:12 strict:1 cats:2 italia:1 futile:4 sealed:1 bubble:3 assumes:4 witt:1 survives:1 emergence:2 complete:12 enough:3 fundamentals:1 huji:1 abhandlungen:1 alain:2 amongst:2 sophisticated:1 philosophers:1 suffers:2 trying:2 dissipative:2 october:6 applying:7 flato:1 multiplicity:2 dirty:1 ωn:1 agree:1 eigenvector:2 obtains:2 detailed:1 gone:2 ac:1 ai:22 ah:1 describe:8 am:4 deep:2 general:21 imagination:1 associating:1 governed:2 formulation:47 corresponding:24 moves:2 bishop:1 again:11 synchronised:1 ideally:1 deserve:1 rosen:7 sublattice:3 field:13 valid:10 mathematics:7 undung:1 deviation:1 briefly:3 vocabulary:1 separate:5 carnegie:2 includes:2 a1:5 commutator:1 important:14 bounded:1 serious:1 included:3 building:1 remote:6 calls:3 wife:1 ments:1 mass:4 parallelism:5 recognising:1 decoherence:22 resolution:1 original:9 represent:7 descartes:3 consider:22 caused:2 lack:5 splitting:3 commute:5 talks:2 follow:1 zinn:1 reasoning:8 causes:20 carpet:1 content:1 chain:1 equivalence:7 tr:38 nonlocal:11 former:2 tn:28 daniel:2 spain:1 th:5 ti:11 stochastic:3 presentation:9 belonging:3 fay:1 straightforward:1 sitting:1 very:25 brownian:1 kψ:1 coloured:1 corollary:1 sons:1 interpreting:1 decide:1 got:1 difference:5 hooker:1 condition:3 splits:3 generalised:5 osi:3 bypasses:1 unlike:1 hamiltonian:28 louis:11 list:2 t1:33 large:5 independence:1 subquantum:3 generalises:3 small:2 possibilities:2 programme:12 abstracted:1 past:10 zero:8 further:10 dissertation:1 what:48 sub:1 richard:2 sum:11 brief:4 emotions:2 version:15 subspaces:7 scientists:7 themselves:2 revealing:2 mmv:1 christian:1 component:24 answers:1 behaviour:8 tracks:1 eih:1 directions:1 november:1 strong:1 equations:2 search:5 antony:2 allows:8 experience:2 prior:1 amount:1 hoffman:1 social:2 action:8 pˆj:3 shorthand:1 family:1 maths:1 establish:3 select:1 readily:1 conventional:6 takes:7 probabilities:31 contains:2 charge:4 ψt:3 chaotic:1 ψi:62 taken:8 achieving:1 more:50 mellon:2 knows:3 zeitschrift:4 operators:33 stable:1 constructs:1 surprisingly:1 tested:3 controlling:1 encouragement:1 particular:29 known:13 foundations:14 solvay:2 evolves:22 none:4 r2:4 erratum:1 science:15 equation:46 des:3 vs:1 nine:6 indicating:2 learn:2 abandon:1 history:29 compare:3 rosenfeld:2 stated:1 neglected:3 accept:4 states:67 contradicts:1 numbers:3 sense:37 sharp:3 information:18 respective:1 awkward:3 terribly:1 rather:20 acts:1 hugh:4 fame:1 maps:2 influences:4 reject:5 acta:3 conceptual:3 explains:1 ensemble:21 δij:1 algebra:5 emulate:1 wiley:1 derived:11 reflect:1 tries:2 justin:1 buffer:7 seemingly:2 waves:6 ethics:1 derives:1 response:1 gauthier:2 short:1 read:1 prefers:1 register:1 ledoux:1 negligible:1 fundamental:10 help:1 ith:2 september:4 developed:4 stays:1 held:1 paper:4 through:7 committed:3 existence:11 kibble:1 its:43 style:2 rapidly:2 fined:1 solving:1 boson:1 actually:9 detected:2 strange:10 microscopic:8 systems:46 radical:3 followers:2 travelling:2 might:16 finer:1 good:3 abandons:1 propose:2 industrielles:1 arsenal:1 obeyed:1 motivates:2 oxford:5 suffice:1 smoothness:1 association:4 mystery:1 easily:6 gets:3 occasions:2 loosely:1 2y:1 infer:1 asher:2 micro:2 iff:7 inequality:1 stopped:1 turns:6 2m:4 subsystem:6 mental:2 undetectable:1 energy:4 hard:2 idea:44 macmillan:1 deterministically:3 extended:2 expect:9 measurement:99 quantum:330 columbia:1 operation:1 beyond:2 event:3 really:10 hartle:21 ezawa:1 solved:3 nuovo:1 since:19 research:1 denoted:1 induced:1 issue:1 occurs:7 benjamin:1 belief:1 team:1 pub:1 difficulty:7 reason:10 base:1 disposition:1 imagine:3 put:6 beginning:1 fiat:1 definition:23 pairs:1 retained:1 eventuality:1 persons:1 recast:1 perceptible:1 computers:1 howard:1 gruyter:1 benedict:2 american:12 due:8 expedient:1 undergo:1 assign:1 major:1 valentini:2 rooted:1 probability:68 feel:2 relate:2 number:10 instances:1 done:5 embraced:1 story:1 fuller:1 temperature:1 introduction:20 leading:1 interact:4 least:6 tradition:1 assumption:8 statement:6 essays:1 scheme:2 recovered:3 too:3 calculations:2 relationship:6 behind:2 immediate:2 prediction:4 part:20 jordan:2 blindly:1 off:1 translation:8 believe:5 convinced:1 separability:3 kind:4 leggett:5 double:6 albin:1 aims:2 recording:1 determined:5 pairwise:1 supposed:3 treated:12 motivation:2 exert:1 reproduces:1 ages:1 beziehungen:1 conjugate:1 elsevier:1 copenhagen:12 routledge:3 thought:4 tiomno:1 constructions:1 retracted:2 pa:2 self:28 stapp:1 finding:9 play:4 added:1 measures:9 compl:1 most:27 plan:1 significant:1 nothing:10 accepting:2 measured:29 branching:6 clear:14 sometimes:11 coincides:1 unreasonable:2 physica:3 traditional:1 electrons:3 reflections:1 exp:17 velocity:4 usual:1 physics:93 bulletin:1 lying:3 wording:1 ambiguities:2 particularly:6 phenomenon:14 summer:3 authors:3 scattered:2 registers:1 relation:3 carefully:3 fine:18 find:9 emulsion:3 completion:8 reminiscent:1 causality:6 depended:2 parameters:2 justice:1 nonlocally:3 writes:4 assertion:17 surveyed:1 factor:1 his:22 hit:1 gains:1 notation:6 dependent:4 σnz:2 zurek:9 sensible:2 methods:1 famous:4 σnx:2 closely:4 reply:1 during:1 dethe:1 him:1 budapest:1 exhibiting:1 continuum:1 arxiv:1 seperated:1 wightman:1 clocks:1 common:4 sustainable:1 obscure:2 gell:12 zur:1 wrote:6 annalen:3 redefine:1 set:113 achieved:6 undergoes:1 plausible:2 see:22 individual:3 bare:1 descriptions:1 cleverly:1 close:1 theoretic:2 paul:7 definitely:2 preparation:1 tome:1 probable:1 currently:1 familiarity:1 eorie:3 various:5 captured:1 probably:1 conditions:7 15th:1 available:3 interpretational:8 complementary:2 initially:6 complement:5 attention:2 vanishing:1 succeed:1 piran:1 opposition:1 distinguish:1 preprint:4 dualism:5 both:18 last:6 sensitive:1 les:3 context:8 whole:10 finds:1 experimental:14 arbitrarily:2 point:23 simple:3 eikx:2 corresponds:13 proton:1 dimensional:8 simply:15 throughout:1 pr:17 pp:5 described:26 publishing:2 quantisation:4 add:1 reduction:3 describes:4 coarse:2 collected:1 nato:2 ph:1 pi:3 pn:7 attractive:2 addison:2 modern:9 partly:1 gaz:1 wheeler:1 modelling:4 gap:1 vaguely:2 2im:4 lives:3 systematic:1 despite:2 assigning:2 p2:5 p1:10 fur:4 look:7 reliable:6 expanded:1 empirical:1 espagnat:8 cern:1 while:14 superposed:1 mitchell:1 guide:1 unitary:5 credence:1 century:1 vol:1 etation:2 von:15 probabilistically:3 disappointing:1 reads:1 itself:6 belong:3 benign:1 retrodiction:1 scientifiques:1 modification:2 neutron:1 development:3 literature:3 temporary:1 paths:2 fulfilment:1 yesterday:1 domains:4 moment:4 levels:1 uses:4 purpose:1 necessity:1 koch:1 uˆ:2 recent:1 eigenvectors:3 task:1 older:1 try:1 analysis:5 obviously:1 concrete:2 edge:1 lucien:1 consistency:4 chemistry:3 lin:2 comprise:1 ealit:1 construct:3 masakazu:1 intervals:1 atomic:5 questions:4 world:61 love:1 alternative:27 letting:1 cut:10 kluwer:2 readers:1 decayed:2 signals:1 source:2 location:3 theorem:37 relevance:1 contrary:2 transformation:4 putnam:1 march:3 lacking:1 demands:1 big:4 showing:2 advocate:2 tunnelling:1 game:1 dewdney:8 hiley:9 logical:8 integer:1 bit:2 projects:7 formal:3 imposed:1 semi:2 follows:23 signal:5 manifest:1 ignore:1 arthur:4 yields:2 popular:2 essential:1 terminology:1 mathematical:9 sketch:1 neumann:15 hinted:2 some:79 back:5 understood:3 experienced:1 examples:3 sight:2 tij:3 universes:6 scale:1 describing:6 nondeterministic:1 affects:1 decision:2 measurements:15 per:2 contrast:2 behave:5 eliminate:1 tends:3 greenberger:1 varying:1 run:1 bb:1 idealistic:3 jumps:1 obscures:1 agreement:2 bj:8 bk:2 step:2 santa:5 dictated:1 hilbert:35 analysing:2 integers:2 anything:2 eaire:2 exaggerated:2 completing:2 range:1 extensions:1 biennial:1 silence:1 seeing:4 clinton:1 into:41 within:17 integral:2 isomorphic:1 appropriate:4 proportional:3 nobel:1 realisation:2 criticisms:1 statistics:8 span:2 interacted:1 extremely:4 placing:1 question:10 specifically:2 u2:1 borel:14 forward:1 opens:1 record:2 rimini:1 himself:3 elsewhere:4 collapsed:5 memory:1 immigration:1 subjectively:1 reed:1 repeatedly:1 newer:1 delta:1 line:3 collapses:9 jonathan:5 rejection:1 cie:1 ut:3 probabilistic:3 up:51 us:16 un:1 ui:6 malik:1 continuously:1 fluctuations:5 similar:2 called:44 precipitated:1 uber:4 individuality:3 constant:5 cin:1 defined:44 countably:2 congruence:2 influence:3 doesn:2 duration:1 single:12 pˆ:43 home:1 βjl:1 graham:1 denying:1 defines:5 countable:1 peter:1 paradox:3 tentative:2 amounts:2 fixing:1 malicious:1 plugged:1 application:2 conceptions:1 points:7 gra:1 department:8 sykes:1 realisable:4 nice:2 explaining:1 elements:3 calculating:1 favourite:2 problems:4 prepared:1 helping:1 meaning:5 evan:1 structure:8 feasible:3 independently:5 correlated:8 implies:11 practically:2 neill:1 required:4 resolving:1 graining:10 grossly:1 implied:3 correlates:1 presenting:1 hamilˆ:1 far:10 konishi:1 requires:2 having:6 once:2 partial:3 gr:14 illustrates:1 results:38 existing:3 proposition:1 uner:1 overlap:2 houches:2 go:2 psycho:3 contributions:2 issues:8 inspire:1 pˆa:23 excludes:1 simon:2 pˆi:2 concerned:4 deterministic:23 send:1 pˆn:10 pˆu:2 excluded:3 pˆv:3 include:11 sent:1 presently:1 misinterpretation:1 implicitly:1 wave:105 electron:9 manipulated:2 telling:2 matrices:3 squids:1 entire:10 positions:3 notes:3 tokyo:2 michael:6 wait:1 pˆ1:12 pˆ2:5 manifestly:1 eigenvalues:5 barbara:3 noted:4 smaller:1 imply:5 dualistic:1 picked:3 subtle:2 manipulating:1 dynamics:5 believes:4 fonction:1 measurment:6 erwin:3 3y:1 plays:2 indisputable:1 apparatus:32 chicago:1 giving:13 anton:2 expressed:8 access:1 consistently:1 experiment:40 concisely:1 unpredictability:1 body:10 led:3 degree:1 respectively:11 pushing:1 adrian:1 following:33 objects:7 eiky:1 others:11 arons:1 invented:2 implicit:1 extreme:2 great:3 m3y:8 clarendon:1 technical:11 involved:2 larger:1 contradiction:2 leaving:3 suggests:5 survey:2 situations:1 existent:2 makes:8 involves:3 depinning:1 named:1 formulated:8 clark:1 scales:2 ears:1 outcomes:1 hardy:1 boolean:8 apply:4 ninth:1 causal:5 use:11 refers:1 superpositions:1 usa:2 remains:1 mid:1 pedagogical:1 next:4 classically:5 doubt:1 examination:1 exhaustive:2 stage:1 historically:2 sort:3 clever:1 formally:3 started:2 becomes:5 labelled:1 sharply:3 informally:1 baby:1 iii:121 discontinuously:2 account:6 isomorphism:1 animals:6 challenge:1 when:38 insists:2 reproduce:2 lorentz:1 obvious:4 freedom:4 meet:3 lockwood:2 coffin:1 proof:15 weaker:1 plate:6 process:10 ontologically:1 proportions:2 purposes:2 crick:2 high:4 slit:2 assumptions:4 something:3 stories:2 interrupted:1 dk:2 invoke:1 decaying:1 sit:1 holds:2 negation:3 arrangement:1 located:1 varies:1 animal:2 instead:17 mysteries:1 verlag:3 stock:1 plato:1 philosophy:24 collection:3 impulsive:1 physik:7 society:3 ties:2 grangier:1 referring:1 ambiguous:5 stein:1 introduced:10 advocated:2 nickel:1 light:7 lines:1 correspond:8 element:3 advocates:1 allow:6 transitivity:1 s1:15 horne:3 six:3 wigner:3 move:3 interpreted:1 report:7 including:6 mentioned:2 yamaguchi:1 galaxy:1 perfect:4 write:11 le:2 decay:2 chosen:3 mendelson:1 degrees:2 choose:8 communication:3 redhead:1 criterion:1 defining:2 weber:1 fourth:2 orthodox:40 wolfgang:1 repercussions:1 practice:15 flew:1 emphasised:4 mention:1 das:1 exploration:1 inducing:1 outlines:1 worlds:66 february:2 dirac:11 tonian:1 university:27 traced:3 identified:3 unpredictable:1 l2:2 editor:13 truth:1 identifies:1 traces:2 subset:10 ohmic:1 completions:1 doing:3 related:4 constitute:1 elementary:3 kobayashi:1 decays:1 bernard:3 measure:23 our:11 transitions:2 aˆ1:1 special:7 out:34 conceptually:1 m2x:4 matrix:31 lecture:2 wick:1 induction:1 mati:1 achievements:2 marek:1 aˆn:1 aˆh:6 interactions:1 diagonal:1 aˆb:1 completely:9 surely:2 tied:1 lajos:2 shum:1 monographs:1 interaction:15 prepare:1 dubbed:1 determining:2 could:28 ask:1 times:19 length:4 specification:2 hence:2 repeats:1 facilitate:1 south:1 atzer:1 blackwell:1 reflexive:1 powerful:1 iht:21 decides:1 precisely:4 reference:3 start:3 data:3 adjoint:27 behaves:4 system:142 relations:4 their:23 attack:1 perfectly:7 behaved:1 final:4 mandel:1 lot:1 tuple:1 academy:2 doomed:1 exactly:2 adjusts:1 constituent:2 july:5 theorie:2 completes:1 dynamical:1 achieves:1 colleagues:1 ben:1 holland:7 penrose:1 isolation:2 pointers:1 cimento:1 submitted:2 halliwell:6 claim:1 incompleteness:1 sec:1 providing:2 result:49 false:5 qˆ1:1 comfortable:1 fail:3 dictate:1 need:4 apparently:2 clearly:5 viewed:3 documents:1 studying:1 able:8 si:1 mechanism:7 arm:2 decomposing:1 concerns:1 singh:1 subject:1 mit:2 persistence:1 accuracy:3 heisenberg:17 unless:2 who:13 centro:1 qˆn:2 gravitation:2 eight:1 qˆi:4 qˆj:1 definitions:1 intrinsic:1 why:9 subjective:1 consequences:8 nobody:1 neutral:2 face:1 pˆα:3 proceedings:17 pˆβ:1 sciama:1 se:2 mechanical:13 occasion:2 shimony:1 χi:10 chances:1 text:1 niel:1 anyway:1 chapters:5 purely:8 debate:2 q1:9 ni:1 based:5 knowledge:9 earned:1 commutators:1 should:30 jan:1 lemma:2 princeton:8 anthropic:1 ambiguity:6 isham:2 local:19 hope:3 meant:2 means:13 familiar:3 overall:2 joint:1 words:13 exchanges:1 arranged:1 entity:4 fe:2 qp:2 evolution:15 qr:2 brain:32 differential:2 qc:13 stuff:1 she:1 avoidable:1 contain:2 qi:9 qj:2 qn:7 intervening:4 conform:1 constructing:1 exists:12 correlations:5 humans:9 packet:3 edition:6 usefulness:1 expects:2 closer:2 imposition:1 attempting:1 arguably:2 tend:3 premises:1 written:14 difficulties:3 envisage:1 closed:14 confusion:3 progress:4 neither:7 ends:1 reproduced:24 importance:6 emitted:1 however:52 job:1 hypothesis:1 ket:2 distribution:5 barrett:1 restrictions:2 interpretations:15 limits:1 taking:2 la:13 equal:15 minds:32 etc:3 hψ:2 utilising:1 heart:1 trajectories:1 otherwise:4 ch:8 co:2 conclude:3 cc:1 invasive:2 ca:3 sequences:1 respect:10 superselection:4 implicate:1 addition:2 copies:3 treat:5 certain:9 define:10 arises:1 controlled:2 received:1 route:1 sufficient:4 subspace:1 zeilinger:3 ensuring:1 m1x:9 fellow:1 present:10 nick:1 laser:2 abandoned:2 subsets:4 appearance:3 value:33 promotes:1 will:114 determinism:20 indeterminism:2 revisited:1 happened:1 uncertainty:7 dieter:1 ripe:1 almost:7 vi:7 damtp:1 thus:10 site:1 surface:1 helped:1 examined:1 quantique:2 lifetime:1 φin:1 miracle:1 greater:1 russell:2 perhaps:18 radiation:1 lett:1 highlighted:1 parts:2 pauli:4 units:1 φi:7 finite:3 privileged:2 difficult:5 experimented:1 material:2 infinity:1 reinterpretation:1 complemented:1 conceived:1 effect:11 phd:3 actualit:1 experimenter:4 infinite:4 landau:1 identity:2 numbered:1 schr:76 reflection:1 geroch:1 fully:5 nevertheless:8 well:15 bohr:57 bohm:54 patterns:1 mathematische:1 baltimore:1 sets:22 firstly:3 position:49 realised:3 onde:2 less:5 obtain:9 detail:2 sources:1 underlying:13 distant:16 predicts:6 years:1 momenta:4 macroscopic:24 rapid:1 bibliography:22 density:44 bell:34 mathematically:2 belinfante:1 lattice:12 ignorance:1 book:2 combine:1 nor:5 propositions:5 practise:1 warrant:1 unprecedented:1 details:5 resolved:1 tests:2 spinless:2 fate:2 devised:1 built:1 five:1 know:11 press:26 immediately:6 variants:2 intersection:4 semiclassical:2 necessary:14 like:14 success:2 alternatively:3 profound:1 lose:1 become:4 works:8 page:6 parity:1 because:21 dispensed:1 classical:47 sequence:13 foreseeable:1 phenomena:5 alive:17 βi1:1 choosing:1 star:1 proofs:7 happens:9 form3:1 congress:2 lead:7 esp:1 broad:2 avoid:4 philosopher:1 manipulations:1 does:55 assuming:14 whereas:4 limitations:2 obey:3 reaching:1 selecting:4 journal:19 analysed:5 wesley:2 variation:1 although:33 nail:1 7th:1 swept:1 simpler:3 gained:1 deriving:1 about:69 actual:1 carried:5 extension:1 cb3:1 universe:67 certainty:2 nondeterministically:1 introduces:3 dependence:2 ondes:1 bertrand:1 a2:3 transitive:1 projectors:23 equally:6 own:17 letters:16 h2:5 pergamon:4 warrants:1 h1:5 washington:1 functional:2 criticised:9 tackle:1 ayres:1 weather:2 eine:1 primas:1 pointless:2 van:2 additional:1 francis:2 imperial:1 trigger:2 quanta:5 inner:3 inspiration:1 misner:1 uncontrollable:1 naturally:2 function:88 north:3 triggered:2 but:82 hu:2 volume:7 basil:3 repeated:5 construction:2 contradictory:1 gain:1 violate:1 he:18 made:20 compute:1 places:1 instructive:1 whether:17 meeting:3 variations:7 placed:3 below:3 frequency:2 limit:4 problem:29 walter:1 display:2 mechanics:193 gesellschaft:1 irish:1 hepp:1 whatever:2 inadequate:2 universal:8 contribute:1 linearity:3 meaningless:3 twist:1 relates:1 flight:1 erie:1 identities:2 mercader:1 functions:2 qβ:1 nonetheless:1 impossibility:3 horgan:1 other:64 eiht:1 branch:8 illusion:2 conclusion:21 kinds:1 resembles:1 june:4 ultimately:2 inherently:3 deborah:1 chance:2 disjunction:4 lifschitz:1 fundamentally:1 u1:2 came:2 eon:1 rule:15 intentionally:1 understand:3 unspeakable:1
|
quant-ph9501015.txt |@word discards:1 extrapolated:1 consider:4 represent:1 rev:20 magnetic:4 lack:1 reversibility:1 results:2 existing:1 leads:2 eds:3 controversial:1 edu:1 follow:3 gk:1 causes:1 whose:1 terms:4 calculate:1 γs:1 concerned:1 technique:1 answered:1 strikingly:1 present:4 th:1 under:1 include:1 case:4 amplitudes:2 straightforward:2 outside:2 far:5 2re:1 impart:1 translations:1 springer:1 wave:7 electron:1 difference:4 entire:4 exponential:1 hamiltonian:1 transmission:7 leavens:2 occurs:1 large:3 vector:1 small:4 eigenvalues:2 falck:1 ueda:1 noted:1 approximately:2 b27:1 ψi:5 measurable:1 past:1 rate:1 a41:1 displays:1 gaithersburg:1 copenhagen:1 odd:2 kitagawa:1 even:1 what:1 plays:1 appear:1 apparatus:4 clock:2 contributions:1 sum:1 interactions:1 near:1 thickness:2 sokolovski:3 above:4 new:3 increasing:1 method:1 contrast:1 outgoing:1 behavior:2 exchange:1 κd:4 2kx:1 answers:1 highly:1 κx:8 sinh:3 berkeley:3 represented:1 consideration:1 along:2 standard:6 property:3 suitably:1 shift:10 study:1 approaches:5 commonly:1 controversy:1 suggests:1 amount:1 extremes:1 resulting:3 action:5 opinion:1 devices:1 makes:1 examining:1 regardless:1 projection:2 jin:2 barker:1 merely:3 explained:1 mckinnon:1 plenum:1 logical:1 replace:1 thought:1 anomalies:1 outcomes:1 univ:1 post:1 linearly:1 derivatives:1 projector:1 would:4 probabilities:4 contains:2 negative:1 ψt:2 france:1 sample:1 going:3 therefore:1 criteria:1 means:3 more:3 sort:2 τf:1 becomes:3 apparent:1 tiggelen:1 validity:1 berlin:1 everywhere:1 normalized:1 particular:6 known:1 actual:1 iii:1 opaque:3 must:2 md:2 account:1 valued:1 grant:1 postselection:3 equation:1 work:1 modified:1 mk:1 chamberlain:1 reproduce:1 remain:1 paragraph:1 values:7 following:1 example:1 unconditional:1 numbers:2 compare:1 weaker:1 give:1 process:1 introduces:1 cited:1 purposes:1 states:6 weighting:1 performed:1 sense:2 unphysical:1 hauge:2 occur:2 multilayers:1 ratio:1 information:2 kwiat:2 rather:3 divided:1 acts:1 feature:1 delay:4 how:3 varies:1 significance:3 instead:3 verlag:1 ensemble:1 product:1 de:1 description:2 superluminal:1 may:12 dτr:1 after:3 reflect:1 hence:4 plane:9 designed:1 multiplication:1 fi:2 fj:9 choice:2 sz:10 sx:1 natural:1 effective:1 light:2 counter:1 correspond:2 so:5 fundamental:1 subsequently:1 travel:1 holds:1 interpretation:4 reversal:1 developed:1 over:7 vary:1 satisfied:1 trade:1 paper:3 including:5 thesis:1 satisfies:1 integrands:1 pointer:23 its:10 tendency:2 before:1 regions:3 style:2 group:3 symmetry:2 decay:2 energies:2 interesting:2 τd:7 subensemble:1 mugnai:1 scully:1 fruitful:1 late:1 absence:4 parts:3 itano:1 constitutes:2 derivative:2 τt:18 main:1 τr:9 eur:1 correspondence:1 non:1 affected:1 heinzen:1 precess:1 repulsive:1 effects:1 they:2 acta:1 recap:1 rotation:6 now:1 eigenvalue:1 term:3 equality:2 university:1 loosely:1 hermitian:3 sin:1 orthonormal:1 magnitude:1 transmitted:8 found:9 entirely:1 side:5 referred:1 individually:1 weighted:4 energy:1 principles:1 related:5 constitute:2 onr:1 frequency:1 microscopy:1 measure:6 quantum:13 our:1 differ:2 eq:3 event:2 nonexistence:1 space:2 restricted:1 furthermore:1 since:9 interference:1 particles:13 re:9 dominated:1 internet:1 integrated:3 shows:1 earlier:1 theory:13 barrier:32 associate:1 given:3 quite:1 reason:2 york:2 might:2 additional:2 definition:1 interaction:12 derivation:1 transition:1 days:1 times:17 motion:1 length:1 enders:1 exponentially:1 chiao:4 barriers:1 app:1 flip:1 onto:1 suffice:1 first:2 initial:9 probability:7 stevens:1 wiesendanger:1 reflected:6 channels:3 clear:3 smaller:1 relations:1 another:2 comprises:1 reached:1 thick:1 precisely:2 electronic:1 aharonov:5 little:2 similarly:2 bears:1 leading:2 interact:1 construct:1 lagendijk:1 their:3 quadratic:1 truly:1 penetrates:1 dwell:14 postulate:1 perfectly:1 final:2 discussion:1 shifted:1 collapse:5 relationship:1 realization:1 albert:1 uttiker:8 part:10 translation:2 than:7 reflection:5 relative:3 determines:2 showed:1 princeton:2 was:2 imply:1 submitted:3 preparation:2 matter:1 determined:2 amplitude:1 were:1 outcome:3 treated:1 minus:1 disturbs:1 fashion:1 remained:1 unchanged:1 argument:1 generalization:1 summing:1 conjugate:2 need:2 seen:1 seem:2 vaidman:2 clearly:1 paths:2 strength:1 angle:5 zero:1 latter:3 maximum:1 predominantly:2 note:2 instance:1 ideal:1 potential:2 square:1 useless:1 provoked:1 n00014:1 channel:2 heisenberg:1 beyond:2 allow:1 opposite:1 measures:3 extending:1 detect:1 connor:2 phase:10 class:2 discarding:1 sala:1 calculated:3 later:2 implications:1 order:2 feynman:2 reflecting:2 principle:2 exp:9 mechanical:1 usual:1 physics:2 fact:4 dover:1 emerging:1 selection:1 particularly:1 show:2 supported:1 dependences:1 helv:1 relation:5 wigner:1 tempted:1 find:4 occupation:1 q2:1 resemblance:1 title:3 delays:2 histories:1 should:3 jan:1 only:5 explicitly:2 condon:1 muga:1 indeed:1 oscillate:1 2bc:2 pointed:1 do:2 dominant:1 goes:1 meanwhile:1 dependent:3 zurek:1 between:9 overall:2 expectation:11 adheres:1 criticized:1 joint:1 nearly:1 closely:1 collins:1 treat:2 evolution:1 precession:2 arxiv:1 baz:1 yield:2 roy:1 experiments:2 contain:1 through:2 nist:1 view:1 hκ:1 scanning:1 set:1 physically:1 violated:1 emergent:1 packet:3 stipulation:2 observed:2 essence:1 see:2 individual:1 result:3 arg:1 discussions:1 close:2 prototypical:1 points:2 phases:1 still:1 scattering:3 review:2 consequence:2 symmetric:1 state:16 various:4 simplest:1 approach:5 across:1 recently:1 ikx:3 weak:11 however:11 incident:4 nimtz:1 distribution:2 observable:1 last:1 many:2 region:8 hint:2 according:2 sensitive:3 manifestations:1 context:2 τg:1 contribution:2 argue:1 expression:3 asked:1 comes:1 detailed:1 timescale:1 point:3 steinberg:5 ca:1 others:1 corresponds:1 ce:1 except:1 dimensional:1 alone:1 simply:3 constant:5 testable:1 schleich:1 considering:2 better:1 rewrite:1 due:5 been:6 ai:8 much:3 combined:1 interest:1 ph:4 define:1 describe:1 corresponding:2 both:4 θb:6 wheeler:1 precision:1 traversal:1 observe:1 dirac:1 external:1 stems:1 bayesian:1 spin:17 former:1 those:3 applied:4 uncertain:1 unlike:3 pacs:1 indefinitely:1 defining:2 align:2 appearance:1 value:11 rectangular:1 will:7 while:9 suppose:2 kick:1 evaluating:2 squeezed:2 tunneling:13 mitchell:1 taking:1 walther:1 landauer:3 uncertainty:5 von:5 thus:9 equal:7 itself:3 im:4 binary:1 different:8 bollinger:1 verified:1 prior:1 perhaps:1 travelled:1 same:4 any:3 shifts:2 unity:1 complex:4 quant:3 split:1 several:4 grows:1 higher:1 independent:2 extended:1 trivially:1 trajectories:3 effect:4 average:7 portal:1 relies:1 off:1 center:1 whole:1 olkhovsky:1 well:5 spent:1 obviously:1 bohm:1 components:6 very:4 position:13 spend:1 left:6 proposed:1 appropriately:1 tip:1 baskin:1 press:1 clocks:1 questions:1 immediately:1 spatially:1 fertig:1 speed:1 eigenstates:2 alignment:1 preprint:2 generator:1 density:1 workers:1 scales:1 seems:1 emphasis:1 lett:7 easy:1 cb:2 untherodt:1 mod:4 eigenstate:2 momentum:7 take:1 real:10 depends:2 represents:2 subensembles:2 hartman:1 posed:1 possible:3 early:3 indicative:1 proton:1 vacuum:1 confined:2 using:3 unique:1 helpful:1 like:1 particle:23 follows:1 reduces:1 performing:1 serves:1 consensus:1 flux:1 continue:1 either:1 integrals:1 martin:1 served:1 stationary:2 parity:1 right:5 neumann:5 deal:1 conditional:5 some:5 back:6 understood:2 b0:1 respect:1 duration:2 broad:2 measurements:3 overlap:2 recami:1 does:7 decomposition:1 proj:7 semiconductors:1 proc:1 demonstrated:1 measuring:3 bc:2 perpendicular:1 although:2 become:2 imaginary:7 properties:3 bz:1 about:4 central:1 eaves:1 extension:1 most:1 instantaneously:1 discussed:5 o:1 remains:4 range:1 larmor:16 mean:6 projectors:2 automatically:3 soc:1 letters:1 presence:1 wineland:1 eisenbud:1 into:3 successive:1 accumulates:1 three:3 down:3 nothing:1 appropriate:1 because:1 sov:2 operator:8 proportional:1 unambiguous:1 van:1 classical:1 prepare:2 transfer:1 strictly:1 there:1 question:4 nucl:2 why:3 width:2 describes:2 low:2 way:2 conceivable:1 dx:4 bianchi:1 uncontrollable:1 ψr:1 function:3 lowe:1 complete:1 form:1 enough:1 becoming:1 but:12 hk:6 properly:1 irreversible:1 youssef:1 longer:1 made:1 portions:3 intuitive:1 whether:4 wish:2 up:4 us:3 considered:3 limit:6 ωl:2 demonstrate:1 problem:1 display:2 mechanics:2 proved:1 moore:1 defined:8 universal:1 measurement:25 general:8 oscillations:2 examine:1 formulation:1 intra:1 physical:7 compared:1 ideally:1 no:7 trials:1 when:6 vanishes:2 field:8 other:4 role:1 details:1 spatial:5 department:1 out:4 conclude:1 superposition:1 june:1 prepared:3 peak:2 generalized:1 decoherence:1 regime:1 faster:2 coulomb:1 typically:1 portion:2 ensuring:1 mass:1 presenting:1 time:40 signalling:1 rep:2
|
quant-ph9501016.txt |@word leighton:1 magnetic:2 four:1 controversial:1 anticorrelated:3 consists:2 whose:2 calculate:1 under:2 alternating:1 impinges:1 every:1 jack:1 summarized:1 affect:1 disturb:2 internally:1 cause:1 jeff:1 consistent:3 direct:3 unpolarized:1 approximation:1 second:4 even:8 errors:1 specification:1 above:7 new:2 consisting:1 simultaneously:6 notions:1 never:2 residual:1 here:4 atoms:1 represented:2 path:29 interpret:1 obtained:1 daughter:3 study:2 changed:1 controversy:1 changes:1 cancellation:9 explained:1 brought:2 stern:4 counts:2 total:2 would:19 handedness:1 arms:1 m1:1 therefore:3 m2:1 type:1 tell:1 mckinney:1 separated:8 populations:1 holt:2 odinger:3 glass:16 hold:1 must:6 md:1 ma:1 setup:3 work:4 theories:1 oxide:1 example:3 sinusoidal:1 indicated:1 relativistic:1 titanium:1 absolute:3 end:1 travel:9 hom:5 feature:2 far:5 answer:1 after:10 confirmed:3 diagram:2 law:1 third:1 green:1 ultimate:1 correlation:1 observability:1 order:11 interpretation:4 over:5 vary:1 frequency:5 thesis:2 burleigh:1 before:2 fit:1 exhibits:1 better:1 distinguishing:2 fig:54 persist:1 versus:4 them:5 combination:1 school:1 band:11 effects:8 they:9 eigenvalue:2 reflectivities:1 potassium:1 fringes:9 reasonable:5 each:12 interfering:4 side:1 mean:2 arrives:1 clauser:5 particles:18 sliding:2 linear:7 barrier:24 given:4 free:1 standard:1 measurable:1 universally:1 incorporates:1 filter:3 disturbed:1 chiao:13 already:2 features:1 another:4 revival:1 approximately:2 confirming:1 zeros:1 too:2 collapse:1 took:3 pulse:8 translating:1 princeton:6 zero:2 preparation:1 historical:1 contrasted:1 fashion:2 spectrum:3 seen:4 seem:2 relatively:1 strength:1 analyzers:1 latter:1 blue:1 though:5 bruce:1 involving:1 retaining:1 treats:1 calculated:1 partition:1 detectors:5 spend:1 points:1 principle:10 left:4 sum:5 incomplete:3 incorporate:2 labels:2 implying:4 disturbs:1 solutions:1 d2:12 d1:12 just:1 delays:4 adequate:1 chamberlain:1 do:2 erasure:3 reversal:1 despite:1 runs:1 traverses:3 fields:1 acknowledgments:1 twice:1 traverse:1 fair:1 detection:9 depends:1 decided:1 result:2 disturbing:2 limiting:1 brewster:1 away:1 symmetric:1 propagated:1 approach:2 terms:2 extend:2 nature:8 weak:3 however:11 suggested:1 essentially:1 chirped:2 uncertainty:4 adventures:1 exceeds:1 argue:1 disappears:1 appeared:1 character:1 factorize:1 wider:1 speak:1 conference:1 broadening:8 basis:1 equations:1 three:3 been:6 much:5 interest:1 expected:1 entered:1 helicities:1 concerning:2 krausz:1 coherent:1 spin:7 microns:5 air:7 employ:1 near:5 suppose:1 viii:1 ix:1 spacelike:2 iv:1 ii:1 cone:1 hong:6 perform:2 suggest:2 quant:4 several:2 independent:1 i1:1 i2:2 hand:1 kim:1 interferometers:6 immaterial:1 spacetime:1 epr:17 academic:1 materials:1 greatest:1 maxima:1 stringent:1 evanescent:2 proposed:4 rotated:1 photonic:2 farther:1 scattering:2 yet:2 han:1 had:6 innsbruck:2 possible:6 possibly:1 fusion:1 advanced:1 contradict:1 arbitrary:1 right:3 wavepackets:9 deal:1 born:2 einsteinian:1 jeffers:1 trombone:15 indirect:1 uncoated:1 fourth:2 electromagnetic:1 normal:6 microwave:1 heitmann:1 elucidate:1 shifting:1 properties:1 uncollapsed:1 anomalous:1 o:2 larmor:12 presence:3 maxwell:1 obtaining:2 down:9 r34:1 why:2 width:8 conservation:1 way:7 call:1 was:13 questionable:1 medium:5 offering:1 penney:1 differences:3 conclusively:1 removed:3 true:1 versions:1 inside:5 maximum:1 devices:3 until:1 crystal:8 phosphate:1 stages:1 shih:2 proved:1 evidence:1 conserved:1 exist:2 distributions:3 physical:5 vertical:2 nm:8 dotted:2 no:16 whereas:1 wavefunction:4 generally:1 vanishes:1 reality:6 role:1 papers:1 test:1 convincing:1 variable:1 faster:4 together:1 time:66 n1:1 measurements:8 varying:1 leads:3 extremities:1 displaying:1 layers:1 certainly:1 depend:1 technique:1 waveplate:4 compensate:1 analogous:1 advantage:1 orthogonal:1 frequencies:3 seemingly:1 choice:3 exact:2 level:5 did:3 standards:1 leave:1 coincidences:6 dip:20 findings:1 prediction:1 sign:1 lengthened:1 boyce:1 port:2 spectral:1 appear:1 assistance:1 satisfy:1 realizations:1 along:3 appears:2 change:1 institute:1 shift:4 studied:3 simultaneous:2 resonance:1 emerge:1 spatially:2 extra:1 traversing:1 operational:1 predictions:4 theoretical:7 eiφ1:1 eiφ2:1 apparent:2 cases:2 franson:8 labeled:2 values:7 following:2 making:1 arrive:2 thicknesses:1 heart:1 figure:3 mirrors:6 predict:4 december:1 sense:1 1980s:1 performed:4 allowed:1 distinguishable:4 occur:4 pure:2 parameter:1 product:1 may:6 applications:1 designed:1 destructive:4 data:13 stress:1 johnson:1 joint:1 whenever:1 so:13 typical:1 wavelengths:5 indeed:3 pointed:2 years:1 experiments:18 argued:2 tendency:1 paradoxically:1 thank:2 how:2 interesting:3 vicinity:1 window:1 decreased:1 correspondence:1 non:2 thereby:1 introduce:1 half:10 now:8 subluminal:4 discuss:1 developments:1 possess:2 term:3 podolsky:2 realistic:2 entirely:1 quarter:4 realism:1 individually:1 square:3 ed:4 gaussian:2 prisms:1 interferometer:23 gaps:2 begun:1 wavelength:2 shown:15 space:2 furthermore:1 interference:30 increase:1 bragg:1 investigation:1 etalon:1 squares:1 correct:1 shows:4 earlier:5 theory:16 possibility:2 quite:2 california:1 e1:8 e0:7 e2:5 motion:2 turn:1 place:4 invitation:1 first:12 symmetry:2 striking:1 variables:2 long:12 directly:2 onr:1 impossible:1 ring:1 angular:1 size:1 little:3 necessarily:1 checked:1 indicate:1 gives:2 holden:1 exploring:1 continuous:2 transverse:3 tapster:4 x2:8 x1:8 than:12 effective:2 transferred:1 delay:38 were:12 impinge:3 outcome:3 argument:2 alley:2 any:7 conversion:6 form:3 describe:2 violates:1 note:5 ideal:1 take:4 destroy:1 dips:1 begin:2 multiple:1 opposite:5 incidence:9 importantly:1 pair:2 inserted:4 latex:2 unknowable:1 especially:1 nonlinearity:1 considered:2 later:3 steady:2 feynman:6 nuclear:1 typically:1 quantity:2 precise:1 momenta:2 show:1 inconsistent:2 ratio:2 enough:1 only:7 hauge:2 viewpoint:1 get:1 between:15 expectation:3 cannot:6 conjunction:1 settings:5 yield:1 roger:1 predicted:2 rms:2 violated:4 relative:8 namely:1 nonlocality:5 inequalities:2 ways:1 review:3 pump:3 diamonds:1 reading:1 across:1 arrival:4 parent:3 screen:5 article:2 many:2 region:6 according:5 propagation:5 expression:1 minima:2 color:1 sampling:1 twin:4 anti:1 considers:1 workshop:1 direction:1 photon:54 traversal:5 observe:1 external:3 case:2 stacked:1 josephson:1 steinberg:14 squeezed:1 tunneling:24 orientation:4 characteristics:1 discrepancy:4 converts:1 motivated:1 technology:1 different:10 media:4 same:6 shifts:1 events:2 zehnder:2 driven:1 edges:1 entanglement:1 totally:1 relies:2 locality:4 roughly:1 vaidman:1 without:6 relied:1 model:2 summer:1 pakistan:1 when:7 rest:1 aspect:3 speed:4 thinking:1 photons:48 seems:1 except:1 improvement:1 wavevector:2 lett:16 samples:2 eigenstate:1 momentum:9 around:1 represents:4 rules:2 harmonic:1 early:1 experimentalphysik:1 vacuum:4 confined:1 using:7 accepted:1 ruled:1 vertically:1 particle:31 reduces:1 velocities:4 either:5 fully:3 served:1 stationary:2 conditional:3 erase:2 complementarity:2 piezo:1 matching:1 reasons:2 confirm:1 recorded:2 exit:2 propagating:3 measuring:6 destroys:1 process:8 nonclassical:2 comparison:1 central:2 fringe:1 discussed:2 mutually:1 greatly:1 shifters:2 ou:8 rising:1 determine:1 einstein:9 operator:2 factorized:1 assumed:3 there:15 dispersion:16 start:1 low:3 assumes:1 complete:2 delayed:1 longer:2 bandwidths:1 agree:2 detailed:2 certain:2 measurement:12 deep:2 general:1 scanned:2 controlled:1 spends:1 again:2 bluer:2 completeness:1 tradeoff:1 rosen:2 field:3 prism:17 cp1:3 cp2:3 separate:2 a1:2 commutator:1 a2:2 peak:6 hwp:6 remote:1 curve:5 mass:2 ultrafast:1 cps:1 resolution:5 original:2 represent:2 consider:3 lack:1 reasoning:1 nonlocal:8 removal:1 1930s:1 amplitudes:3 straightforward:1 very:8 superluminally:2 ultraviolet:2 difference:6 splitter:20 randomness:1 washing:1 accompanying:2 large:1 small:3 past:1 rate:15 design:1 pass:1 further:2 attributable:1 what:1 nonlinear:2 sub:2 section:1 brief:1 thickness:2 version:9 method:1 component:2 cylindrical:4 berkeley:7 directions:1 coupling:1 observing:1 legend:1 increments:1 colored:1 yablonovitch:1 allows:3 experience:1 amount:2 periodic:1 narrow:4 via:1 vii:2 polarizers:13 ask:1 takes:3 probabilities:1 de1:1 de2:1 taken:2 more:5 thus:15 emission:3 particular:3 known:4 mounted:1 producing:1 none:1 recall:1 equation:3 sweeps:1 superluminality:1 morgan:1 spontaneous:2 f1:3 f2:3 neglected:1 states:5 minimum:4 arise:1 sharp:2 axis:9 information:12 rather:1 maps:1 enders:2 influences:1 reject:1 fs:21 derived:1 waves:2 horizontal:3 response:1 short:12 fundamental:1 help:1 paper:3 through:18 filters:1 existence:4 avenue:1 its:13 energies:2 scully:2 actually:2 detected:4 travelling:1 might:1 kdp:9 skipped:1 return:1 number:1 englert:2 always:4 presented:3 labeling:1 factorizable:1 inequality:7 visibilities:1 found:2 universit:1 ports:2 heavy:2 tilted:1 generation:1 energy:18 idea:2 used:6 expect:1 sketched:1 quantum:40 beyond:1 event:2 travels:3 since:14 issue:2 occurs:4 belief:2 reason:2 acute:1 put:1 definition:3 pairs:1 imry:1 caption:1 conducted:1 consequence:1 configurations:1 exhibited:1 probability:11 reflected:6 done:2 reflectivity:1 differ:1 introduction:1 leading:4 least:2 assumption:2 passed:3 rates:1 scheme:2 shifted:2 uttiker:9 optical:7 jordan:2 differentiate:1 schr:3 translation:1 believe:1 reflection:8 polarized:4 determines:1 zachary:1 determined:2 intensities:1 polarizer:5 orienting:1 motivation:1 idler:2 conjugate:6 null:1 lie:1 depending:1 internal:1 analogy:1 experienced:1 reach:3 singlet:4 unused:1 most:4 position:17 nothing:1 measured:4 superlattices:1 deviations:2 clear:3 broadened:1 physica:1 part:2 electrons:1 reflections:2 velocity:10 physics:8 particularly:2 phenomenon:2 degraded:1 causality:7 parameters:1 factor:2 dominant:1 distance:1 dependent:1 zurek:3 combinations:1 freedman:2 arxiv:1 collapsed:1 investigate:1 apparatuses:2 scanning:1 set:1 dump:1 see:15 individual:3 sec:3 arm:4 analog:1 n00014:1 various:2 available:1 recently:2 complementary:1 initially:1 interfaces:1 incident:4 twophoton:1 interface:1 relying:1 both:15 reverse:1 quantization:1 connection:3 femtoseconds:2 experimental:4 point:6 simple:2 corresponds:2 coincidence:38 semiclassical:6 simply:3 throughout:1 ps:1 described:10 due:13 pc:1 describes:1 combine:1 ph:4 addison:1 flight:1 kronig:1 wheeler:4 precision:2 gap:6 understand:1 systematic:1 p2:12 p0:2 p1:12 solid:6 evaluated:1 precursor:1 while:9 behavior:3 mitchell:1 walther:2 landauer:6 itself:1 grant:2 lengths:2 attenuation:1 paths:5 appreciably:1 moment:1 appreciable:1 heterostructure:1 recent:2 lower:3 urgency:1 spent:1 analysis:1 solids:1 edge:4 parametric:5 stating:1 intervals:1 atomic:1 questions:2 world:2 zubairy:1 source:6 describable:1 mod:2 secondorder:1 entangled:7 helpful:1 rotate:2 stranger:1 signal:8 addressed:1 shapes:1 continue:1 translated:1 spins:1 cones:1 some:6 back:1 understood:2 towards:1 b1:2 b2:2 mirror:12 scale:1 describing:1 affects:1 shall:5 exceeding:1 per:1 prop:1 behave:2 eliminate:1 prog:1 prof:1 prob:1 inserting:1 agreement:4 kwiat:9 range:2 cutoff:1 into:10 within:3 integral:1 phase:15 appropriate:1 institut:1 classically:2 multilayer:4 extremely:1 question:2 fast:1 mach:2 sections:1 adjusting:1 line:4 collapses:2 directed:2 uv:6 up:1 us:3 ur:1 continuously:1 similar:2 called:2 bell:9 constant:1 defined:5 likewise:1 single:14 rainbow:1 paradox:3 dashed:3 application:1 department:1 elements:3 problems:1 prepared:1 lens:4 chirp:2 meaning:4 allowing:1 sides:1 structure:1 gedankenexperiment:1 correlated:5 implies:3 fluorescence:1 required:1 diffraction:2 notion:1 antireflection:1 nasa:1 presenting:1 once:2 partial:2 broaden:4 bandgap:5 results:4 broader:1 go:2 gaithersburg:1 leung:1 young:3 include:1 sent:1 random:1 wave:12 electron:1 entire:1 transmission:22 positions:6 underscored:1 optics:1 gerlach:2 concluded:1 smaller:1 imply:1 insertion:2 click:2 index:3 plays:1 unavailable:1 apparatus:5 experiment:31 twins:1 led:2 respectively:2 explore:1 others:1 consideration:1 great:1 contradiction:1 suggests:1 preferentially:1 resulting:2 makes:1 explain:2 composed:1 outcomes:1 austria:1 use:5 superpositions:1 remains:3 next:2 few:1 examination:1 simpler:1 sort:1 becomes:2 visibility:3 carrying:1 normalized:4 sharply:1 iii:2 ocs:1 sample:8 account:1 tunnel:4 erwin:1 infinitesimal:1 control:2 slid:1 plate:3 calculation:1 high:7 slit:4 assumptions:2 employs:1 triangle:1 winfried:1 varied:2 arrangement:1 regions:2 located:2 varies:1 instead:3 circular:5 profile:1 sommerfeld:1 superluminal:13 drop:1 light:12 counter:5 correspond:1 element:5 allow:1 horne:2 wigner:1 interpreted:1 produced:5 pulses:1 perfect:1 horizontally:2 revived:2 outer:1 decay:6 temporal:1 degrees:2 choose:1 lp:2 orange:2 derivative:1 greater:4 polarizations:2 practice:1 front:5 day:1 dielectric:6 university:1 sufficiently:2 magnitude:1 transmitted:10 mode:1 electrically:1 references:1 barnett:1 related:1 inverted:1 constitute:1 decays:1 sands:1 measure:9 our:30 out:10 rep:1 rev:33 electronics:1 supports:1 red:6 approaches:1 york:1 interaction:2 determining:1 could:5 diminished:1 times:14 length:11 hence:11 manuscript:1 possessing:1 reaches:2 reached:1 michelson:1 aharonov:2 dispersive:7 publication:1 unknown:1 system:4 relations:1 their:19 intermediate:3 travelled:1 perfectly:1 final:4 mandel:8 explanation:3 argon:4 observed:7 submitted:3 rarity:4 amplitude:6 projections:1 behaviors:2 function:5 curves:4 need:2 clearly:7 angle:10 studying:1 able:3 polarization:7 detector:3 accuracy:2 lectures:1 propagate:1 preliminary:2 device:1 intrinsic:1 class:1 consequences:1 face:3 proceedings:1 mechanical:2 shimony:3 fact:3 emerging:1 exclusive:1 violation:3 text:1 supported:2 rotating:1 nonfactorizable:1 µm:6 based:1 should:3 jan:1 dalibard:1 ambiguity:1 local:5 slows:1 means:6 beam:28 brillouin:2 words:2 timing:1 lossless:1 processes:13 precession:2 substrate:3 encounters:1 europhys:1 qm:4 temporarily:2 modulo:1 exists:1 acquired:1 national:1 correlations:11 packet:3 differs:1 phases:4 pattern:7 state:19 identification:1 tens:1 comparable:2 interfere:1 hypothesis:4 nimtz:2 group:23 observable:2 limits:1 equal:4 etc:1 admit:1 manifestations:1 passing:1 otherwise:2 splitters:2 adjusted:1 ch:1 cm:1 conclude:2 ca:1 narrower:2 cf:1 mugnai:1 respect:4 crystalline:1 cw:2 addition:1 arises:3 slowly:1 eraser:11 erases:1 compensating:1 senses:1 corresponding:2 coherence:3 cos:1 bulk:1 fsec:2 angles:1 mail:1 present:3 laser:11 discretely:1 brendel:2 align:1 appearance:1 value:7 choices:1 will:4 layer:1 vi:2 coating:7 instantons:1 surface:1 descriptive:1 indistinguishable:4 unity:2 strange:1 wavepacket:12 schematic:2 inch:2 difficult:1 conflicting:1 raymond:1 upon:1 effect:11 phd:2 ion:4 experimenter:1 sooner:1 infinite:1 off:1 center:6 nevertheless:1 well:11 bohm:4 comparisons:1 arising:1 latest:1 restore:1 less:2 spielmann:1 obtain:2 stored:1 distant:1 predicts:1 paul:1 sinusoidally:2 preprint:1 mohler:1 absorption:2 nonrelativistic:1 transparent:1 thermodynamics:1 add:2 slits:2 nor:1 identical:1 tests:2 disappearance:1 five:1 know:5 press:1 dimensional:1 necessary:3 like:5 lost:1 martin:1 become:3 therein:1 because:4 classical:12 discontinuities:1 neglecting:1 lead:1 broad:4 avoid:1 overlap:3 instantaneous:1 does:6 demonstrated:1 noise:2 coated:2 l1:1 wesley:1 although:3 fused:2 imaginary:3 periodically:1 stage:2 about:6 actual:2 carried:1 freedom:2 certainty:4 dependence:1 important:2 equally:1 previously:1 sharpness:1 mere:2 inner:1 uncontrollable:1 hz:2 femtosecond:4 but:12 hl:1 he:2 count:1 made:7 josh:1 micromaser:1 whether:7 smooth:1 placed:2 below:3 converted:1 limit:3 pumped:1 demonstrate:5 problem:2 piece:4 mechanics:14 inadequate:1 redder:2 compared:3 detail:1 virtual:2 other:14 clicks:2 conclusion:1 kinds:1 auxiliary:1 starting:1 rule:2 intentionally:1 portion:3 determination:1 silica:2
|
quant-ph9501017.txt |@word twistors:3 concept:2 consider:5 remarkable:1 rev:4 magnetic:2 results:1 four:13 roy:2 commute:3 hyperboloid:1 follow:1 denotes:1 contributions:1 scr:1 whose:5 calculate:1 tp:1 finally:2 those:2 p2:4 string:2 advantage:1 orthogonal:1 translations:1 noncommuting:1 seemingly:1 geometrical:1 electron:7 matrices:1 conserved:3 lefthanded:1 treating:1 leads:2 hamiltonian:7 irreducible:1 correct:1 large:2 vector:15 eigenvalues:8 warszawa:1 inertial:2 work:1 direct:2 lubanski:7 approximation:1 second:1 substituting:1 qualitatively:1 defines:2 odd:2 returned:1 linear:2 even:26 what:4 section:1 contracted:1 brief:1 helicity:11 agrees:1 version:1 belongs:1 above:2 lifshitz:1 new:3 body:1 edited:2 justification:1 simultaneously:1 notions:1 respectively:4 component:3 equals:3 here:3 agreement:1 met:1 groups:1 address:2 represented:3 standard:2 equations:1 appears:1 interpret:1 contraction:9 obtained:2 ultra:3 institute:1 leaves:1 completely:1 contradiction:1 suggests:2 resulting:1 pictorial:1 action:1 suitable:1 formulated:2 projection:3 classification:1 namely:1 explained:3 gordon:1 observation:1 neutrino:1 total:2 geometrically:1 unit:1 derivatives:1 discus:1 would:4 prove:1 covariant:3 positive:3 negative:1 therefore:3 m2:10 survive:1 means:1 ψa:1 type:1 more:1 introducing:1 formally:1 degeneracies:1 successful:1 becomes:2 operators:10 apparent:1 odinger:2 berlin:3 normalized:1 particular:1 known:5 cases:2 hold:1 iii:1 potential:2 must:3 springer:3 ma:3 room:1 quantized:2 equation:15 when:1 refered:1 mk:4 theories:2 values:1 following:7 root:1 example:1 def:1 cone:2 bell:5 stated:1 relativistic:19 choice:1 purposes:1 states:2 effectively:1 lorentz:7 o:7 sense:1 robinson:5 calculated:1 axis:1 motion:2 respective:1 requirements:1 klein:1 rather:2 discussion:1 get:3 opposite:1 answer:1 instead:1 ordinary:4 parameter:1 circular:2 description:1 algebra:19 may:3 sp1:5 sp2:5 sp3:4 applications:3 levi:1 plane:3 cambridge:3 representations:7 wave:3 concerns:1 constants:1 natural:4 imply:1 light:3 sp:18 explicit:5 correspond:2 su:1 element:1 extremal:2 sh:1 so:18 fundamental:1 sl:4 representation:9 sa:8 order:4 se:4 typical:1 wigner:1 indeed:4 satisfied:1 interpreted:3 symbols:1 course:1 iµj:1 motions:1 mentioned:1 existence:1 satisfies:3 still:4 its:9 boosts:1 effect:1 group:18 treat:1 decay:2 chosen:1 interesting:1 forms:1 permanent:1 degrees:1 choose:1 matematyki:1 2p20:2 might:2 deformation:2 shear:1 non:2 crucial:1 greater:3 noz:3 rotation:1 now:3 discuss:1 nor:1 term:1 dirac:19 fizyki:2 explains:3 university:1 identified:1 possibilities:1 pryce:1 inequality:2 l2:4 l3:4 reasonable:1 l1:4 found:4 soc:2 uniwersytet:1 mean:1 spinor:2 square:3 formulate:1 experiment:1 density:2 energy:8 idea:1 related:3 extended:6 measure:2 quantum:9 laboratory:1 gordan:1 xβ:1 commuting:2 shown:7 matrix:4 rs:3 restricted:1 since:4 squared:3 research:1 particles:12 investigation:1 mγ:1 reader:1 formula:3 electronics:1 occurs:2 shows:1 marek:1 theory:5 spinors:2 bayen:1 given:5 free:5 quite:1 difficulty:2 approaches:2 generate:2 andrzej:1 pairs:1 interaction:1 could:1 transition:5 times:2 counterpart:1 relativistically:2 massive:7 hence:1 adjoint:1 first:6 origin:1 xh:1 2p0:1 intuitively:2 spinning:3 smaller:2 another:2 electronic:1 angular:15 rs2:1 onu:1 little:9 reference:2 needed:1 introduction:1 leading:1 eqs:1 least:1 parallel:1 their:3 intermediate:1 structures:3 relationship:2 explanation:1 continuous:3 transverse:1 part:9 fuzzy:1 translation:2 sign:3 than:2 coefficients:1 kind:2 third:2 penrose:1 zero:4 limiting:1 project:1 contrary:1 were:3 radius:3 treated:2 result:4 twisting:1 symmetries:1 takes:1 footnote:1 lines:2 unchanged:1 argument:1 generalization:1 null:4 any:11 lie:9 generalizes:1 depending:1 latter:2 note:1 k2:1 k1:1 internal:2 generalized:1 timelike:2 modulus:1 moscow:1 heisenberg:1 formulas:1 begin:1 added:1 unless:2 though:1 trρ:1 object:1 singlet:3 algebraic:1 instytut:1 sb:2 multiply:1 intrinsic:2 why:1 enveloping:1 constructed:1 especially:1 dordrecht:1 bracken:2 clear:1 later:1 dimension:1 points:1 electrons:7 principle:1 mechanical:1 velocity:7 usual:1 physics:2 fact:9 phenomenon:2 show:1 angelopoulos:1 multicomponent:1 purely:1 radii:2 gauge:3 solutions:2 civita:1 interpretation:4 find:3 teoretycznej:1 spite:1 explain:1 state:3 should:1 jan:1 only:7 explicitly:1 generators:11 postulated:2 il2:1 nonzero:1 interested:1 do:1 his:1 goes:1 localizing:1 year:1 il1:1 twocomponent:1 cannot:1 closely:1 probably:1 during:1 αk:1 precession:3 podolsky:1 fields:11 arxiv:1 summary:1 twice:1 paper:2 contain:1 valid:1 view:1 satisfy:4 opposed:1 exists:3 physically:7 frame:8 testing:1 j1:1 j2:1 j3:1 differs:1 see:2 triplet:1 sec:1 projections:2 w0:2 kinetic:2 analog:1 ǫklm:2 instance:1 doebner:1 definite:2 tend:2 written:3 difficulties:1 various:1 between:2 invariant:1 neither:1 reading:1 approach:1 deforms:1 p20:11 notice:1 infinite:1 terms:3 twistor:3 wa:3 however:3 inertia:3 raczka:1 both:6 interpretations:1 last:1 candidate:1 limits:9 conclusions:2 equal:2 bispinor:2 hψ:1 pl:1 context:3 casimir:2 0k:1 expression:1 regarded:1 experimental:1 0m:1 point:2 corresponds:2 dimensional:7 directions:7 simply:1 constant:1 cp:1 considers:1 unusual:1 xα:1 described:2 transformations:3 basis:2 three:7 expressed:2 much:1 asymptotics:1 recognize:1 expected:1 ph:1 algebras:3 important:1 helicities:2 direction:6 contribute:1 corresponding:4 commutes:2 sufficient:1 subspace:2 collaborators:1 observers:1 understand:2 c3:1 c2:3 denote:1 spin:48 present:1 c4:2 case:5 extracted:1 p0:18 p1:3 nska:1 straight:2 definition:1 nski:1 will:4 euclidean:1 behavior:1 property:3 conformal:3 unitary:1 spacelike:2 played:2 vol:1 vi:1 iv:1 ii:2 ik:5 ij:1 im:3 il:1 vanish:2 technology:1 nonunitary:1 different:5 formalism:2 suggest:2 make:1 lett:1 same:4 poincar:7 parts:5 quant:1 pauli:14 uncertainty:1 units:3 finite:2 subalgebra:1 higher:1 used:4 localization:1 singapore:2 effect:2 hand:1 parametrized:1 average:2 moment:4 moving:4 kim:3 infinite:8 clebsh:1 identity:1 eigenvectors:1 schr:2 center:1 onedimensional:1 poland:2 well:4 analysis:3 bohm:3 barut:8 components:13 position:4 possesses:1 left:1 unified:1 less:1 rosen:2 obtain:1 rest:10 pwn:1 gda:6 transforms:1 facts:1 momenta:2 eigenstates:1 worldlines:1 polarization:2 enters:1 generator:4 application:2 localizability:1 photons:1 nonrelativistic:5 seems:2 book:1 treatment:1 versa:1 theorem:3 usage:2 transformation:1 momentum:45 identical:2 vii:1 iν:1 around:1 showing:1 possible:4 cf:1 increases:1 know:1 rescales:1 press:1 world:4 accepted:1 rotate:1 appearing:1 like:5 particle:14 follows:3 reduces:2 velocities:2 substitution:1 indication:1 either:3 zitterbewegung:1 always:1 become:1 spins:1 mathematical:2 circles:2 right:2 old:1 often:1 classical:8 some:4 somehow:1 self:1 understood:2 confusing:1 happens:1 provided:1 rarely:1 lead:1 electromagnetic:1 shall:4 davydov:1 does:4 decomposition:2 proc:2 bacry:1 equivalent:3 each:1 perpendicular:10 wesley:1 although:2 2m:2 cβ:1 cα:1 properties:1 superpositions:1 pβ:2 a1:1 pα:7 extension:1 freedom:1 discussed:2 generated:2 deduced:1 nonvanishing:2 remains:2 carrier:1 σw:1 uhlenbeck:1 propagate:1 introduced:2 thacker:1 exactly:2 sπ:2 nsk:3 reidel:1 measurements:1 into:7 rotations:6 isomorphic:1 phase:1 hermitian:3 because:2 wα:7 einstein:2 operator:29 proportional:1 a3:1 existed:1 additional:1 assumed:1 there:4 question:2 way:7 was:5 naturally:8 function:2 form:11 hp:1 but:8 contractions:4 pg:1 line:2 fry:1 he:1 made:1 flato:1 evident:1 characteristic:2 us:4 ul:1 limit:8 verification:1 continuously:1 problem:2 called:2 eigenvector:1 mechanics:6 associated:3 nauka:1 defined:5 czachor:2 abstract:1 congruence:8 meaningless:1 general:3 single:1 exist:2 our:4 kl:2 viewpoint:1 physical:10 again:2 paradox:2 no:6 generally:1 scientific:2 rewriting:1 field:5 other:4 role:2 sunrise:1 massless:26 picture:5 thaller:1 rindler:1 superposition:1 symbol:1 4i:1 problems:1 prepared:1 deriving:1 meaning:2 a2:1 flattened:1 massachusetts:1 additionally:1 structure:2 gedankenexperiment:2 implies:1 vice:1 assume:1 age:1 space:4 rule:2 having:1 factorizes:1 mass:9 time:3 observables:2 nuclei:1 strings:3
|
quant-ph9501018.txt |@word homomorphism:2 similarity:1 consists:4 whose:9 segments:2 aut:6 under:5 conjecture:1 amorphous:3 p1:4 hindman:2 supports:2 solution:3 admissible:4 vector:5 indices:2 shows:3 direct:10 empirical:17 feasibility:1 surrounding:1 second:4 eo:6 expressive:1 eigenspaces:12 even:8 specification:1 birkhoff:2 reconstruction:2 new:6 axiome:1 simultaneously:1 notions:2 here:5 atoms:17 met:1 represented:4 interpret:1 obtained:4 property:2 forum:1 leaves:1 characterizing:1 numerical:1 equivalence:7 projection:17 replace:1 univ:2 rω:1 unit:7 would:4 e1:2 motivate:1 negative:1 axioms:2 therefore:17 indiana:1 type:2 duals:1 hahn:4 th:2 holy:1 fraenkel:8 odinger:6 berlin:4 must:1 abundance:1 springer:4 join:1 permits:2 work:1 theories:3 erg:1 concepts:14 my:1 example:13 unilateral:1 indicates:2 end:4 carriers:1 provide:2 verify:1 feature:1 far:1 nontrivial:8 answer:1 symposium:1 description:1 monatshefte:1 adic:1 meaningful:8 attempt:1 effective:53 complexity:1 recursion:1 order:23 operations:3 restriction:9 interpretation:3 over:7 satisfied:2 london:2 thesis:1 satisfies:19 nets:2 ima:1 clh:1 fix:1 noninteracting:1 hidden:8 maximal:5 fragment:1 amenable:1 effects:1 they:2 represents:1 indeed:1 luce:2 arrow:1 each:33 choix:1 s1:19 series:2 principles:1 ru:1 restricted:1 content:3 newly:1 independence:3 perception:8 linear:34 associate:1 mω:14 standard:8 admits:6 onto:13 separable:8 already:1 thereof:1 system:22 restrict:2 philosophical:4 idealizations:1 another:3 illustrate:2 dedekind:24 needed:2 observations:1 hypothetical:1 postulate:1 eigenvectors:7 tool:1 serve:2 somewhat:2 peculiar:1 finitely:5 princeton:1 preparation:3 classes:1 powers:1 minus:2 modern:1 spectrum:5 kleene:4 seen:2 seem:1 relatively:2 noncontextual:1 latter:3 responsible:1 nonalgebraic:2 reals:3 effectiveness:2 shall:9 object:3 simplify:1 involving:1 retaining:1 acknowledgements:1 observation:8 dom:101 partition:14 principle:5 finitary:43 notion:12 heuristics:3 nonuniqueness:1 meetings:1 halpern:1 soluble:1 solutions:1 x1:2 proposed:1 implementation:1 situations:1 topological:4 specify:1 hamiltonians:6 axiom:18 continuity:1 do:7 mixture:2 above:7 dg:13 de:1 dc:4 cardinals:2 dx:1 despite:1 du:5 nλ:1 kochen:6 reference:2 observed:1 depends:10 projections:8 w1:3 w0:2 discussions:2 λi:9 tensor:2 symmetric:23 drawn:2 approach:4 terms:6 extend:4 nature:5 wo:1 wn:3 wk:3 however:12 wi:3 bose:1 improve:1 suggested:2 essentially:1 sierpinski:1 uncertainty:1 und:2 logic:19 logik:1 presumably:2 meaningfulness:3 applicability:1 polynomial:1 truss:1 gxy:4 conference:1 triviality:1 union:1 three:1 been:7 expected:5 algebras:2 families:1 concerning:3 coincides:2 spin:2 applied:4 applies:1 endpoints:1 procedure:2 ix:1 ir:15 ii:8 need:3 counterexamples:5 id:2 things:1 make:1 complex:3 quant:1 several:3 independent:2 pick:4 hand:2 zermelo:1 subgroups:2 mentioning:1 whereby:1 stimuli:4 academic:1 contact:1 simulated:1 just:2 identify:5 thanks:1 scattering:1 yet:1 previous:4 infinitely:2 character:2 cantor:10 polon:2 possible:5 possibly:1 brunner:14 unique:9 specific:1 arbitrary:4 heisenberg:1 acad:2 refinement:1 dense:22 unavoidable:1 comments:1 hauptstraße:2 linearly:3 cnk:2 constructive:10 atze:1 properties:1 o:96 nerve:2 soc:1 pelc:1 presence:1 preliminary:1 rotations:1 bound:2 lies:1 amsterdam:4 methods:2 compression:1 segment:1 support:9 initial:2 way:5 form:6 converse:1 analyse:1 idealized:3 failure:3 true:4 versions:2 supp:5 inside:2 dordrecht:1 fermi:1 jauch:3 proved:1 zeno:1 abstract:5 textbook:1 evidence:1 peres:2 proves:3 exist:6 hydrogen:1 commuting:2 constructed:2 nk:3 weakened:3 no:11 generally:1 reality:3 investigations:3 models:16 preceding:3 variable:2 lemmata:1 longer:1 assume:10 time:4 n1:1 laws:2 concept:16 mild:1 computation:1 depend:10 graph:3 environment:1 multilinear:1 orthogonal:20 choice:24 exact:1 partitions:6 dim:3 perceived:1 presented:1 solved:1 perceives:1 science:1 der:1 upper:2 measurable:1 riesz:2 specker:6 spectral:4 xω:13 appear:2 uniform:1 sequential:1 relational:2 satisfy:5 groups:2 alone:1 appears:4 change:1 bu:1 shift:1 vectors:5 krohn:1 domains:1 studies:6 transcend:1 compare:1 logical:1 additive:3 russell:13 working:1 lemma:86 predictions:1 live:1 suppt:1 scope:1 theoretical:30 inherited:2 appendix:1 everywhere:6 cases:1 cardinality:3 valued:2 sphere:2 avoiding:1 oscillator:2 modified:1 reviews:2 fock:3 values:1 9th:1 following:21 arrive:2 permutations:1 conversely:7 evidently:9 arbor:1 requirements:3 s2:4 discussion:3 orthogonality:1 rubin:2 cardinal:1 pure:9 allowable:1 parameter:2 map:7 product:10 isomorphically:1 mat:1 may:35 data:5 compatibility:1 natural:3 remember:1 correlate:1 whenever:3 lemmas:2 sw:3 su:1 st:1 sk:4 si:2 so:6 sn:2 sc:4 sb:1 sf:3 typical:1 joins:1 schwartz:2 constituents:1 pointed:1 professors:1 experiments:8 argued:1 still:1 τn:5 group:20 schachermayer:2 summands:1 interesting:1 decreases:1 forms:2 renaming:1 correspondence:6 prime:1 non:3 thereby:2 sω:7 sσ:1 now:5 nor:1 similarily:2 orthonormal:2 jech:5 em:1 domain:7 en:19 ei:7 ek:4 fixes:3 eg:2 ea:23 ec:13 eb:18 approximated:1 ev:52 ultimately:1 space:71 contained:2 investigation:1 dπx:2 theory:56 hull:1 qf:2 mechanisms:2 orbits:1 rendiconti:1 besides:1 nondecreasing:1 orb:11 inevitable:1 e2:2 benioff:9 language:5 question:5 hamel:1 suffice:1 first:7 xk:2 intuition:2 xi:5 xn:15 xm:3 clause:1 variables:3 symbolic:1 nested:1 mendel:1 impossible:2 open:5 given:8 necessarily:1 categorical:2 theoretische:2 realization:1 structures:6 continuous:4 pnk:1 copy:3 than:2 intrinsically:40 third:1 accordance:1 require:5 computes:1 ann:1 argument:2 say:1 any:8 converges:1 note:8 ideal:16 potential:2 resembling:1 coincide:2 gleason:5 multiple:4 normal:1 algebraic:12 automorphism:1 reducible:2 considered:6 average:1 implications:2 mrs:1 axi:1 typically:1 unster:1 precise:1 show:2 spaces:14 transfinite:2 ground:1 ferrand:1 only:11 aα:2 cannot:4 closure:3 reveal:1 yield:1 summary:1 scott:1 relative:3 namely:1 nonstandard:4 wonder:1 fails:3 eigenfunctions:1 review:1 definite:3 functionals:4 outside:2 between:4 αi:3 reading:1 αo:1 jp:3 gratefully:1 comm:1 ja:1 realizable:5 many:6 according:3 embedding:4 σp:8 jammer:3 characterization:3 assertions:1 ordered:4 submanifold:5 wien:6 skew:1 locally:28 wants:1 oω:3 restrictions:4 formed:3 photon:1 observers:5 observe:5 those:3 case:4 variances:1 situation:1 concatenation:3 dubious:1 supremum:1 helium:1 different:9 same:17 verifies:1 arguments:1 physical:9 events:1 status:1 investigated:1 assigns:1 maeda:5 titchmarsh:2 investigates:1 invariance:1 effectivity:9 without:7 model:51 dimension:1 isometry:13 manifold:3 being:1 when:3 rest:1 powerset:2 multiples:1 generator:1 conclude:3 seems:2 except:1 hyperreal:1 treatment:1 versa:1 momentum:2 real:14 eigenfunction:3 eigenvalue:1 rules:1 ruler:1 sums:1 harmonic:2 preference:1 world:13 vague:1 pitowsky:2 particle:2 automorphisms:6 either:2 moreover:16 complementarity:3 reasons:1 nonzero:1 conservative:1 decomposition:1 provides:1 o1:6 dimensionally:1 assembly:1 scientific:1 power:1 equivalent:18 prepared:1 svozil:3 oi:4 theorems:2 generated:11 whence:43 inclusion:2 unbounded:7 references:1 determine:1 einstein:1 elementary:3 technically:1 logics:1 her:1 assumed:3 strictly:1 there:62 lindstrom:1 complete:20 applying:1 embedded:2 multiplicity:1 eigenvector:2 ac:21 ab:4 hellman:4 ad:1 ag:1 af:1 ai:14 certain:1 describe:1 general:11 au:4 formulation:1 ay:1 ax:12 russel:1 incorrect:1 again:3 completeness:7 mathematik:1 graduate:1 field:1 valid:1 remarks:2 mathematics:7 incomprehensible:1 durations:1 representable:1 includes:1 a1:9 a0:1 important:1 bounded:37 observables:53 included:1 celestial:1 bertani:1 refutation:1 impossibility:1 original:1 represent:5 consider:7 splitting:1 scalar:6 commute:3 follow:2 reasoning:1 particles:3 tu:2 tr:16 tn:5 kα:3 preserved:1 kε:2 ti:1 stochastic:1 presentation:1 norm:9 straightforward:1 very:2 results:5 corollary:4 difference:1 condition:6 hamiltonian:12 t2:2 large:1 small:1 past:1 zero:1 further:1 canonical:3 what:2 section:11 version:2 abt:1 abu:1 subspaces:6 sup:2 method:2 contrast:2 gandy:2 ranges:1 modular:3 strong:2 equations:2 mostowski:7 experience:2 amount:1 permutation:27 action:4 provable:1 uniquely:1 via:1 family:6 texts:1 distinct:4 contains:7 almost:2 automata:2 taken:1 more:2 infima:1 zeitschrift:1 operators:26 constructs:2 particular:2 known:4 foundations:1 recall:2 equation:7 coalition:2 paragraph:1 den:1 f1:7 f2:1 states:10 contradicts:1 numbers:2 sense:16 exclude:1 species:1 information:6 needs:2 rather:2 maps:4 explains:1 intended:1 algebra:16 fx:3 notre:2 variant:3 mapping:27 fa:5 fe:4 fi:10 fk:1 concerns:2 fn:9 fo:1 spectra:3 departure:1 fundamental:1 help:1 schaller:1 paper:5 through:3 y1:1 existence:8 kinetic:1 its:26 systems:2 jacobi:1 might:7 yi:1 yh:1 yk:3 motivated:2 yn:15 propose:1 framework:1 motivates:1 rank:1 compound:1 oxford:1 easily:3 characterizes:1 assemblies:1 level:1 evade:1 iff:36 2m:2 2n:1 energy:2 reduce:1 idea:2 extended:3 measurement:10 quantum:104 psychology:1 discrete:3 nuovo:1 since:75 induces:3 induced:2 issue:1 reck:1 difficulty:1 base:19 definition:22 pairs:1 modularity:2 american:1 consequence:3 probability:2 encoding:1 relate:3 number:2 enlarged:1 construct:1 differ:1 introduction:1 least:8 seminaire:1 identity:4 kµ:7 bijections:2 scheme:1 ehrenfest:1 too:8 recursively:1 authors:3 kind:1 determined:4 pairwise:3 supposed:1 str:1 motivation:4 lie:1 generalizes:1 constructions:3 lim:4 speculative:1 k1:2 internal:3 generalized:1 analogy:2 orderable:1 towards:1 most:3 significant:1 kg:8 kk:2 ki:3 countably:1 countable:4 exp:13 usual:4 physics:7 bulletin:2 phenomenon:4 converge:1 multiplicities:2 relation:9 hereditary:1 completion:11 computability:3 absoluteness:1 parameters:4 assertion:5 annals:3 bernstein:1 abelian:1 his:4 notation:4 dependent:1 ϕh:5 closely:1 compass:1 resolve:1 disregarding:1 investigate:6 annalen:1 set:94 ser:2 plausible:1 sec:1 descriptions:2 close:1 sem:1 conditions:3 sageev:2 initially:1 complement:1 uω:6 distinguish:1 both:11 collaborators:1 improved:2 context:5 forgotten:1 experimental:4 arbitrarily:1 point:4 simple:1 corresponds:18 dimensional:35 bα:2 church:1 bλ:2 swi:1 pp:5 described:3 perspectives:1 due:13 hellmann:2 calculi:1 describes:4 pg:4 pe:5 collected:1 pk:2 ph:1 pi:4 meeting:1 empty:1 pm:1 surjective:5 addison:2 gap:1 representative:1 folklore:1 albeverio:1 p2:4 replaces:1 exponential:2 wiedner:2 bω:3 evaluated:2 forgetting:1 while:4 replaced:1 compactness:3 unitary:7 century:1 von:6 ruppert:1 vanish:2 read:1 modification:1 resulting:1 composition:2 higher:2 literature:1 assignment:1 usually:1 levels:1 purpose:1 pλb:1 clermont:1 analysis:6 obviously:2 concrete:1 consistency:1 chemistry:1 self:28 commensurability:1 λx:2 reviewed:1 abbreviation:1 λb:1 atomic:3 questions:1 alternative:3 λn:1 contradicting:2 kluwer:1 conclusions:1 informal:1 extra:1 hereditarily:3 empirically:7 source:1 rˆole:2 questioned:1 theorem:24 input:2 march:1 additivity:1 matters:1 subfamily:1 formal:3 modifications:1 continus:1 follows:26 translates:1 pointwise:1 essential:1 terminology:3 mathematical:7 neumann:6 some:59 back:1 added:3 examples:2 scale:1 measurements:5 isometrically:2 prof:1 minimal:1 ba:2 bn:7 restrictive:1 step:1 bp:1 universe:2 relating:1 bx:2 hilbert:59 pα:3 coexist:1 pλ:21 range:7 extensions:2 modal:1 into:7 within:9 isomorphic:12 diameters:1 statistics:2 span:43 sock:1 borel:4 vienna:1 linz:1 atom:5 padova:1 directed:1 consist:1 up:4 us:3 sum:10 similar:6 called:2 halmos:2 associated:2 defined:15 cover:1 single:1 formalism:1 defines:8 extensional:1 paradox:1 invalid:1 application:3 realizability:2 elements:13 problems:2 polynomials:1 helpful:1 meaning:2 structure:18 independently:1 implies:11 vice:1 speculations:3 weights:1 rigid:1 partial:4 illustrates:1 gz:1 gx:1 ga:2 gn:2 gi:6 rigidity:1 compact:26 uniqueness:2 stable:1 quarterly:1 g1:2 implicitly:1 electron:1 matrices:4 notes:1 tokyo:1 eigenvalues:3 zf:61 imply:4 zz:11 concludes:1 dynamics:1 index:2 expressed:1 lexicographic:1 experiment:1 body:1 focuses:1 led:1 degree:1 desired:1 objects:19 technical:1 involved:1 larger:1 contradiction:2 products:1 involves:1 boolean:11 names:5 apply:4 orderings:4 embeddability:1 use:3 gregor:1 next:1 few:1 exhaustive:1 reflects:2 hermitean:3 iii:2 definability:1 isomorphism:3 obvious:3 stabilizer:2 ishihara:2 proof:42 control:1 dn:2 calculation:1 reconstructed:2 kaplansky:7 assumptions:3 distinguishable:1 holds:7 pair:1 instead:2 philosophy:3 collection:1 scalable:6 abuse:1 inst:2 physik:1 multiplication:2 ultrafilter:1 λ2b:1 correspond:11 redundant:1 element:5 lλ:2 saturated:1 produces:1 interpreted:1 produced:1 including:1 banach:5 mentioned:1 la:3 ln:7 choose:5 wellknown:1 operator:35 functional:16 mention:1 autx:1 dirac:1 university:1 traced:2 identified:3 l2:4 mode:1 subset:3 arxiv:1 inputs:1 ergebnisse:1 related:7 bijective:7 our:12 shearing:1 shannon:1 out:2 category:4 respects:2 matrix:6 rev:1 chaos:1 lecture:1 suffices:4 math:19 diagonal:5 limε:1 completely:1 surely:1 york:4 hostile:1 dunford:2 could:2 conversation:1 hence:18 reflexive:1 manuscript:1 intuitively:1 πf:1 observer:10 ordering:4 adjoint:29 πn:8 πo:4 relations:4 πm:1 their:7 commutativity:2 explanation:1 exactly:2 constituent:1 holland:4 cimento:1 computations:1 distinguished:3 result:10 function:21 false:1 fail:1 kepler:1 disjoint:1 viewed:2 xrn:1 mappings:19 polarization:1 εn:1 sufficiency:1 calculus:11 unless:3 who:2 representation:8 intrinsic:11 class:12 stronger:1 mechanical:1 zfa:2 fact:1 perceptions:1 supported:1 hb:1 wigner:1 knowledge:7 eigenspace:4 rosenthal:1 jan:2 entities:1 bases:1 jai:1 equivalents:1 local:2 means:12 ones:1 words:1 richards:2 procedures:1 hyperfinite:2 evolution:3 qr:1 transposition:2 differential:1 expansions:3 ja1:1 qg:1 contain:2 aei:1 qk:6 fixed:3 qm:5 view:20 requirement:2 modulo:3 computed:1 exists:11 respect:3 finiteness:4 state:17 identification:1 closed:29 invariant:17 neither:1 counterexample:5 weak:2 physicist:1 hypothesis:2 configuration:1 ker:14 observable:22 interpretations:1 equal:3 attributed:1 chosen:1 admit:9 otherwise:15 unitarily:8 relevant:2 cn:11 cm:1 cl:1 ca:1 leipzig:1 cf:3 cx:1 sequences:3 ae:6 society:1 selfadjoint:4 addition:1 cauchy:3 topology:10 define:18 aj:2 corresponding:6 commutes:1 sufficient:1 subspace:16 informatik:1 zeilinger:2 bull:2 present:2 cofinite:3 subsets:7 value:4 choices:1 will:2 revisited:1 chaotic:1 thus:20 surprisingly:1 vo:1 helped:1 dual:6 sequentially:29 generic:1 parts:1 finite:112 infinity:3 interscience:3 functions:18 infinite:49 cµ:4 mech:1 schr:6 nevertheless:1 bohr:3 thought:4 mathematische:1 sets:17 position:3 arising:1 subgroup:1 less:1 obtain:1 allgemeine:1 density:2 bell:3 lattice:7 book:1 extends:3 diagonalization:4 semigroup:2 identical:1 increased:1 vα:2 vβ:1 know:1 press:1 intersection:1 like:45 qualitative:1 become:1 works:1 because:3 classical:6 sequence:24 phenomena:1 ideals:10 wider:1 choosing:1 proper:3 proofs:1 lead:1 nonempty:6 avoid:1 does:23 obey:2 journal:2 wesley:1 although:3 entirely:2 injective:6 simpler:1 about:9 extension:16 enlargement:1 column:1 freedom:1 basis:1 dependence:1 recognized:1 compatible:6 dependency:1 transitive:3 combinatory:1 equally:1 letters:1 attains:1 weyl:1 additional:3 appl:2 inner:2 hz:2 hx:2 hy:2 north:4 sequel:2 but:23 repeated:1 construction:9 hn:3 ho:2 convergence:1 partially:2 made:1 deficiency:2 pn:7 below:7 problem:10 dame:2 mechanics:14 intersects:1 linearity:2 meaningless:5 denote:1 teubner:1 barwise:1 inf:7 mutual:1 avoided:1 boos:2 hpt:1 other:3 conclusion:4 repeat:1 june:1 shown:1 hausdorff:1 stab:16 pincus:6 rule:4 coalitions:1
|
quant-ph9501019.txt |@word horne:3 customary:1 remarkable:1 violation:2 indeed:1 able:1 soon:1 notations:1 experiments:3 distant:3 supply:1 find:1 depend:1 violate:1 kluwer:2 representing:1 bell:3 written:1 nonlocal:4 actually:1 only:1 chapt:1 systems:1 theorem:1 include:1 swope:1 gave:1 opt:1 abundance:1 tests:1 supported:1 legitimate:1 means:1 kafatos:1 results:1 choice:1 test:4 effects:3 vacuum:4 own:1 using:1 respectively:2 now:1 conserved:1 instructions:1 restrict:1 processes:1 helpful:1 particle:11 did:2 january:1 erratum:1 alice:5 asher:1 inequality:2 predicted:1 contain:1 variant:1 side:1 apparatuses:3 arxiv:1 methods:1 classical:2 sep:1 ed:1 creation:2 some:1 zero:1 used:1 dordrecht:2 measure:1 quantum:7 greenberger:1 eq:2 nonlocality:2 theory:3 provided:1 shown:1 appear:1 space:2 commute:1 review:1 since:2 rev:2 detailed:1 research:1 particles:6 case:1 state:8 experiment:1 various:1 above:2 reader:1 new:1 numerous:1 consisting:1 refer:1 measuring:2 numerical:1 recently:1 linear:1 obscures:1 component:3 however:1 am:1 address:1 decision:1 detecting:2 singlet:1 bz:1 both:2 ref:1 actual:1 institute:1 universe:1 could:1 feasible:1 bob:5 makes:1 explicit:1 involves:1 first:1 origin:1 splitters:1 there:1 letters:2 projection:3 presence:2 reasons:1 namely:2 predictions:1 number:3 system:2 down:2 hardy:6 right:1 simply:1 long:1 operator:3 impossible:1 total:1 electronic:1 mere:1 gerard:1 given:2 superpositions:1 her:1 probabilities:1 create:1 contains:2 due:2 been:1 pb:13 their:1 pa:13 therefore:1 ph:1 was:2 final:1 more:2 israel:2 reinterpret:1 route:1 operators:2 photon:2 but:1 observers:1 fund:2 coherent:1 because:1 somewhat:1 known:1 technion:2 spin:2 than:1 coefficients:1 must:1 directed:2 states:4 none:1 quantized:1 pacs:1 equation:1 work:1 up:1 value:1 different:2 will:1 technical:1 below:1 fock:2 obvious:1 concepts:1 following:1 toward:2 similar:1 display:1 performed:1 mechanics:1 ac:1 do:2 process:2 likewise:2 abstract:1 thus:1 argument:1 encouragement:1 denote:1 peres:3 clauser:2 single:2 itself:2 initial:1 il:1 formalism:1 technology:1 occur:1 physical:2 conversion:1 mermin:1 locality:2 perform:1 latter:2 when:1 same:1 invoking:1 note:1 how:1 conceptions:1 quant:1 details:1 pure:1 department:1 ordinary:1 ignore:1 repeat:1 superposition:1 shall:1 may:2 who:1 convincing:1 effect:1 hand:1 simplify:1 involving:1 mechanical:1 pair:1 structure:2 zeilinger:1 independently:1 haifa:1 auxiliary:1 four:1 beam:3 considered:1 parametric:1 clear:1 no:1 detectors:1 obviously:1 without:2 expression:1 time:1 physics:2 discussion:2 choose:1
|
quant-ph9501020.txt |@word represent:4 limited:1 helstrom:1 magnetic:1 results:1 illustrated:3 consists:2 gaithersburg:1 whose:2 technique:1 contained:1 nonlocal:4 finally:1 efficiencies:1 device:1 sent:1 orthogonal:1 very:5 account:1 lecture:1 difference:1 splitter:6 school:1 solves:1 presented:8 transmission:8 positions:1 proposals:1 try:1 phase:2 originally:3 smaller:1 tel:2 φin:1 direct:1 osa:2 invention:1 pass:3 manipulating:1 implemented:1 d4:4 theory:2 even:4 what:1 plays:1 find:2 experiment:1 goes:1 shared:2 ever:1 method:14 degree:4 respectively:3 teleportation:26 here:1 atoms:1 intercept:1 others:1 directions:2 path:1 invented:1 obtained:2 sending:1 incoming:1 accomplishes:1 davidovich:1 technical:2 vectors:1 example:1 usually:1 implement:2 changes:1 involves:1 followed:2 private:3 contradictions:1 use:4 proceed:1 would:4 helvetica:1 few:1 therefore:1 encode:1 stage:1 type:6 until:1 more:4 israel:3 formally:1 initial:1 operators:1 particular:4 cases:2 must:2 md:1 none:1 ma:1 setup:1 modified:1 intercepted:1 flight:2 concepts:1 following:2 my:1 could:12 give:1 process:1 bennett:3 haroche:1 states:11 effectively:2 boldfaced:1 information:3 end:2 rather:1 s2:2 s1:2 acts:2 arrangement:1 shifters:2 opposite:1 significance:1 instead:4 brassard:1 product:1 after:6 applications:1 produce:1 designed:1 summarize:1 revealed:2 parallel:3 realized:1 third:1 light:1 departure:1 so:4 fundamental:1 verify:3 order:1 help:1 enter:1 indeed:2 despite:1 years:1 paper:7 through:2 signs:1 still:1 activating:1 its:4 digest:2 before:2 acknowledge:1 chosen:1 polarizing:3 subensemble:3 actually:2 destroyed:1 detected:1 degrees:3 fig:4 hidden:2 main:1 might:1 teleportations:1 happened:2 non:3 than:2 propose:1 practice:1 acta:1 nov:1 now:4 discuss:1 above:3 eigenvalue:1 transmitter:5 name:1 university:2 level:1 kerr:1 transmitted:4 each:2 schemes:2 directly:5 series:1 idea:3 sandu:1 measurement:12 quantum:14 eq:2 haifa:1 out:2 acknowledgment:1 since:1 rev:4 particles:9 acting:3 performs:2 denoted:1 got:3 receiving:1 common:2 sp3:1 linear:2 interactions:1 given:4 possibility:1 standard:5 difficulty:1 completely:1 jozsa:1 interaction:5 prepare:2 just:5 success:5 ups:1 thing:1 place:1 onto:2 first:7 already:3 probability:1 encoding:3 variables:2 reaches:1 parkins:1 done:2 fast:1 another:4 electronic:1 horizontal:6 passes:1 differ:1 similarly:1 unknown:2 system:1 their:2 station:5 passed:1 realization:1 scheme:8 exactly:1 wootters:1 optical:11 reverses:1 detection:2 polarized:1 unfortunately:1 crepeau:1 supposed:1 impinge:3 solely:1 pre:1 boston:2 randomly:1 say:4 need:2 weinfurter:2 any:2 relatively:1 conversion:4 depending:1 polarization:25 ideal:2 potential:1 generalized:4 transmit:2 new:1 detector:3 channel:4 allow:1 shall:1 who:1 reach:1 most:2 encodes:1 pair:3 measured:1 why:2 inequalities:1 technion:1 dordrecht:1 detectors:6 traditional:1 braunstein:1 part:2 left:1 physics:2 fact:3 emerging:1 random:2 rotating:1 registers:1 analogue:1 d2:1 d3:1 d1:4 based:2 proposed:3 implementation:1 outside:1 should:2 jan:1 being:2 only:4 bernstein:2 local:5 do:4 his:4 reconstruction:1 cryptography:1 beams:11 beam:10 cannot:2 altogether:1 reconstruct:1 runs:1 arxiv:1 she:7 brune:1 view:2 set:5 achieves:1 result:3 uncorrelated:1 nonlocality:1 analog:1 techniques:2 interacting:1 nondegenerate:2 eigenstates:4 symmetric:2 favor:1 state:27 between:7 progress:1 polarizer:5 august:1 vertical:2 jauch:1 implementing:1 succeed:2 sleator:1 faced:1 both:4 collaborators:1 last:1 efficiency:1 many:1 taking:1 according:2 etc:1 merging:1 raimond:1 receiver:1 passing:1 estimation:1 experimental:6 splitters:3 bell:8 simple:1 seems:1 dimensional:1 active:2 simply:2 aviv:2 pp:2 strong:1 described:2 transformations:3 cavities:1 three:2 been:2 povm:1 much:2 basic:1 ph:1 choose:1 wants:1 direction:7 arises:1 controlled:1 versa:1 photon:39 observers:1 finished:1 lives:1 c2:1 c1:1 spin:1 present:7 case:5 splits:1 will:6 institute:1 while:3 optimization:1 suppose:1 procedure:1 unitary:2 vol:1 thus:2 them:5 itself:1 cone:1 technology:4 different:7 verified:2 grant:1 same:7 data:1 member:2 quant:1 avoids:1 electro:1 difficult:4 independent:1 used:5 trivially:1 hand:2 phy:1 totally:1 bob:20 recent:1 task:3 kept:1 zagury:1 know:1 vaidman:2 academic:1 solve:1 comes:1 position:2 parametric:4 usual:4 bellow:1 popescu:2 among:1 transmitting:1 when:1 observed:1 rotated:1 obtain:1 actions:4 stored:1 aspect:1 mann:1 alternative:1 rotates:2 yet:3 previous:1 letting:2 rapid:1 preprint:1 kluwer:1 photons:12 had:1 day:3 source:1 setting:1 transformed:1 lett:2 easy:3 input:2 apart:1 eigenstate:1 identical:2 easily:1 possible:2 department:1 entangled:12 press:1 using:4 formal:1 desire:1 necessary:1 like:2 particle:5 reduces:1 alice:33 translates:1 facing:1 arbitrary:1 signal:2 because:1 methods:2 classical:1 sends:1 some:7 sight:1 proper:1 affects:1 measurements:4 does:3 measuring:3 run:1 reaching:1 equivalent:1 processing:1 conventional:1 simpler:1 helping:1 about:3 actual:1 carried:1 freedom:7 certainty:5 enters:1 o:7 deserves:1 nothing:1 own:1 communication:7 into:8 washington:1 isomorphic:1 nsf:1 down:3 lies:1 appropriate:1 activate:1 references:1 operator:10 rely:1 her:6 support:1 there:4 transform:1 long:1 start:1 workshop:1 low:1 way:4 analyze:2 was:3 piron:1 attempted:1 registered:1 but:9 encoded:4 line:1 proposal:2 he:3 made:1 rotation:1 wish:1 cells:2 up:4 us:1 tell:1 placed:1 limit:2 verification:8 problem:4 similar:1 called:1 mechanics:3 cirac:1 computing:1 devise:1 request:1 measure:5 doesn:1 peres:2 single:2 replica:1 exist:1 interchanged:1 corresponding:4 check:2 four:6 processed:1 dotted:1 no:2 storage:2 other:8 role:1 details:1 test:1 realize:3 conclusion:2 elements:2 models:2 describe:2 prepared:2 a1:1 meaning:1 important:1 astronomy:1 ago:1 implies:2 vice:1 changed:1 original:13 teleported:1 time:1 having:6 once:1
|
quant-ph9501021.txt |@word limited:1 consider:1 illustrates:1 caused:1 magnetic:8 varying:1 results:4 jawaharlal:1 shimony:1 consists:1 causes:1 whose:1 violate:1 deterministic:1 nonlocal:5 γt:1 environment:12 finally:1 th:1 under:1 stochastic:5 analogous:1 worth:1 applied:1 amplitudes:1 far:2 frequencies:1 rise:1 conditions:3 wave:5 reinterpret:1 τzz:1 condition:7 ρs2:1 school:1 hamiltonian:1 did:1 t2:2 iǫ:2 t1:2 vector:2 math:1 section:4 indices:1 equation:9 solutions:5 upper:2 averaged:2 force:2 consistent:1 sign:1 fold:1 zero:1 l2y:1 further:2 dynamics:1 l2z:1 odd:1 contingent:1 even:1 specification:1 celebrated:1 expressed:1 current:1 version:1 above:1 new:4 order:1 consisting:1 satisfy:1 degree:1 respectively:3 never:1 component:1 teleportation:1 here:2 bi:1 governing:1 separation:5 directions:5 ratio:1 along:4 equations:6 calculate:4 obtained:1 great:1 involved:2 study:1 larger:3 experience:1 suitable:1 involves:2 emerge:1 via:2 spatially:2 randomness:3 scales:2 marked:1 traversing:1 total:1 establish:1 unit:1 would:3 nehru:1 remains:1 positive:1 brittin:1 negative:2 next:1 classically:2 therefore:3 m2:1 taken:1 type:2 theoretical:1 more:1 separated:2 bennett:1 gyromagnetic:1 successful:1 india:1 operators:2 prog:1 excellent:1 known:2 iii:2 must:3 fly:1 kumar:2 account:1 evolution:1 science:1 setup:3 ρj:5 oscillator:3 theories:4 ρs:1 ρr:7 values:1 concepts:1 following:4 making:1 initial:10 transition:3 stated:1 predict:1 sps:1 share:1 states:1 mixture:1 sense:1 keep:1 axis:1 information:1 respective:1 monitoring:1 s2:7 travel:1 means:1 feature:1 id:1 positional:1 how:3 ig:2 pure:1 ensemble:2 brassard:1 simplicity:1 22b:1 description:1 may:2 oscillators:3 earlier:1 collection:1 ω2k:3 summarize:2 choice:1 natural:1 dynamical:1 correlate:1 σ1z:2 light:1 lost:1 σ1x:2 so:1 correlation:6 representation:1 s1:7 xj:11 indeed:1 over:5 p1k:1 lsj:1 soon:1 argues:1 experiments:2 through:3 statistical:1 signs:2 y1:4 existence:1 y2:4 its:2 envisage:1 markovian:1 perfect:1 write:2 x1k:2 rapidly:1 chosen:1 temporal:1 solving:2 coordinates:3 h2:1 absence:1 parts:2 degrees:7 systems:2 persist:1 hidden:4 main:1 τs:6 them:3 yj:12 integral:2 disturb:1 introduce:1 functional:1 obeyed:2 framework:1 p12:1 ls2:2 ls1:2 now:4 hall:1 pz:4 easily:4 university:1 pipkin:1 realistic:3 inequality:10 each:7 2m:3 2n:4 traces:2 side:1 realism:5 σ2z:2 ed:2 σ2x:2 σ2y:2 idea:1 related:3 solution:7 expect:2 measurement:5 quantum:33 our:3 summary:1 eq:12 ep:1 out:2 matrix:12 2m2k:1 space:3 tried:1 since:5 rev:5 denotes:1 particles:18 transforming:1 acting:1 race:1 mγ:5 m2k:2 rj:7 shows:1 theory:10 interscience:1 cre:1 diagonal:4 possibility:1 completely:1 york:3 conflicts:1 pairs:1 bates:1 kubo:2 computers:1 times:3 motion:1 place:1 due:2 first:2 origin:2 constantly:1 probability:4 variables:1 number:1 smaller:1 another:2 given:3 gpj:1 introduction:1 leading:1 system:15 their:3 underlie:1 leggett:3 gives:1 free:1 centered:2 exactly:1 wootters:1 environmental:2 part:7 simulate:1 authors:1 x2:7 x1:6 than:3 coefficients:1 cosθ:1 diffusion:1 kind:1 molecular:1 showed:3 princeton:2 modelled:3 were:1 wheeler:1 1n:4 well:2 exceeded:1 argument:2 manner:1 ω1k:3 ǫx1:1 seen:4 clearly:1 elsewhere:2 strength:1 angle:1 convenient:1 isolated:1 nonlocality:2 note:4 sciences:1 recognizing:1 take:1 forces:2 strengths:1 lectures:1 opposite:3 singlet:9 most:1 pair:5 measured:3 interacting:2 observation:1 τxx:1 considered:1 clear:2 detectors:3 physica:1 playing:1 feynman:1 principle:2 exp:10 mechanical:2 left:1 physics:3 notion:1 fact:1 quantity:1 2m2:1 particularly:1 show:2 violation:4 agreed:1 random:4 friction:1 attempts:1 rj2:1 inconsistent:1 substituting:2 longer:2 find:3 paradoxes:1 based:1 parameters:2 writes:1 state:13 jan:1 dalibard:1 only:1 hrj:1 satisfied:1 local:4 do:1 his:1 goes:3 cryptography:1 get:1 dependent:1 zurek:1 expectation:5 yielded:1 aσ2:1 σ1y:2 cannot:1 portions:1 dt:2 years:1 becomes:2 processes:1 podolsky:2 fields:3 arxiv:1 gbj:1 method:1 paper:3 roger:1 common:1 though:1 contain:1 analytical:1 d2j:2 intervening:1 conform:1 requirement:3 set:1 aspect:2 fascinating:1 hγ:1 mind:1 correlations:14 mentioned:1 see:4 individual:1 result:4 disturbing:1 violates:1 caldeira:3 satisfying:1 inequalities:7 ways:1 away:1 definite:1 written:6 various:1 between:8 conceptual:1 c2k:2 prentice:1 approach:3 venugopalan:2 terms:2 initially:1 n1x:1 weak:1 however:1 p2k:1 wj:5 vernon:1 distribution:3 σj:2 x2k:2 many:5 region:1 according:2 attributed:1 ln:2 context:1 attributes:1 expression:1 finds:3 experimental:1 con:1 among:1 bell:14 simple:1 character:1 acted:2 harmonic:3 path:1 respect:1 separable:1 described:1 addition:1 px:1 locally:1 three:2 been:6 combined:1 interest:1 basic:1 pj:2 ph:1 choose:1 direction:3 describe:3 corresponding:4 quantities:1 m1k:2 coherence:2 understand:1 external:5 angles:1 doubts:1 worked:1 spin:17 those:1 p2:7 p1:6 look:4 pacs:1 value:5 will:1 cast:1 ipy:1 situation:1 studied:3 coupled:5 vol:2 ip:1 thus:8 non:1 iv:2 ii:2 n2z:1 n2y:1 n2x:1 baths:1 everyday:1 disappear:1 biα:1 verified:1 propagation:1 lett:3 same:1 any:2 unity:1 strange:1 quant:1 pauli:1 iγ:1 difficult:1 literature:1 eds:1 upon:3 effect:6 hand:2 driven:1 average:1 moment:1 moving:1 implications:2 completeness:1 recent:1 mentioning:1 dunham:1 lower:2 off:1 reprinted:1 no:1 epr:4 bohm:2 academic:1 without:1 components:4 very:2 position:5 model:8 usual:1 secondly:1 proposed:1 being:2 when:2 obtain:1 vanishes:1 underlying:2 atomic:1 predicts:1 using:4 momenta:1 macroscopic:2 yet:1 move:1 polarization:1 disturbance:1 preprint:1 density:10 regarded:1 seems:1 noninteracting:1 source:1 interested:1 treatment:1 theorem:2 momentum:2 real:1 fluctuating:7 around:2 advances:1 couple:1 delhi:1 disagreement:1 deepak:1 know:1 press:1 world:1 emergence:1 apart:4 c1k:2 loss:2 counterintuitive:1 like:1 particle:9 reduces:2 isotropy:1 separately:2 continue:1 yields:1 become:1 reduced:3 spins:3 wavepackets:1 classical:5 some:1 back:1 b1:5 b2:5 provided:2 scale:2 represent:2 measurements:2 extensively:1 instantaneous:1 does:6 assuming:1 l2x:1 restoring:1 refer:1 process:2 obey:1 rep:1 freedman:1 agreement:1 bj:1 broken:1 exciting:1 bz:1 carried:1 freedom:7 certainty:1 prove:1 discussed:1 o:1 sake:1 obeys:3 act:1 recognizes:1 2x2:2 bloch:2 bath:1 firstly:1 previously:1 into:1 obtaining:1 bound:2 22a:1 predictions:1 down:3 determine:1 einstein:2 operator:1 classicality:2 there:2 way:2 was:3 assumes:1 ensured:1 function:5 arise:1 complete:4 form:5 analyse:1 but:4 gaussian:3 dissipative:3 coupling:5 made:1 arranged:1 intuitive:1 characteristic:2 up:2 us:1 record:1 liouville:2 limit:3 fluctuations:2 problem:4 called:1 mechanics:9 unrelated:1 proved:1 certain:1 measure:3 influence:1 life:1 general:1 peres:1 separating:1 exist:1 ǫx2:1 formalism:2 distributions:1 physical:7 functions:1 paradox:2 locality:7 wavefunction:1 rosen:2 detail:3 reality:4 field:13 other:4 role:1 spatial:11 test:1 interpretable:1 josza:1 2dj:1 elements:4 gf:1 superposition:2 calculating:1 xbj:1 inescapable:1 variation:3 prepared:1 important:1 additionally:1 variable:6 n2:3 gedankenexperiment:2 implies:1 faster:1 2d2:1 assume:3 requires:1 clauser:2 required:2 packets:3 calculates:1 incomplete:1 time:12 push:1 n1:3 decoherence:4 4e:1 ghosh:2 having:1
|
quant-ph9501022.txt |@word concept:2 partial:2 consider:6 remarkable:1 caused:1 magnetic:3 results:2 leads:1 jawaharlal:1 mild:1 consists:2 centers:2 issues:1 ρss:3 re:2 fokker:1 deterministic:1 γt:21 intensive:1 answered:1 av:1 those:1 γm:1 under:2 stochastic:2 circumstances:1 tc:2 summarizes:1 p2:1 mγ:40 kumar:2 very:1 rise:1 springer:1 choice:1 sons:1 figs:1 2γt:3 matrices:2 condition:4 paz:2 four:1 school:1 hamiltonian:5 ǫd:2 solution:10 occurs:1 large:12 solved:1 convenience:1 vector:4 small:3 optics:1 der:1 solutions:1 upper:1 smaller:2 construed:1 dealing:1 measurable:1 ornstein:1 sign:1 second:2 theo:1 further:3 dynamics:1 canonical:2 even:2 plays:1 appear:1 apparatus:29 section:2 selected:1 expressed:2 current:1 causes:2 above:1 new:4 method:2 coefficient:2 condensed:1 degree:2 component:1 here:7 understanding:1 behaviour:2 desired:1 relaxation:1 path:2 equations:10 obtained:5 great:1 ǫx:1 shift:1 study:2 studied:1 allows:2 leaving:1 dewitt:1 γr:4 fourier:3 examining:1 via:4 inference:1 scales:2 plenum:1 scaled:1 stern:6 viz:1 ipx:2 barchielli:1 planck:1 environment:17 superpositions:1 would:1 nehru:1 remains:1 contains:2 hilbert:1 classically:1 characteristics:1 taken:2 type:3 today:1 eiωj:1 initiated:1 becomes:3 apparent:1 validity:1 dissipatively:1 berlin:1 appendix:3 iii:3 potential:1 must:1 evolves:2 account:2 ρd:25 science:1 equation:10 work:5 ρr:1 values:2 three:1 freedom:10 following:5 making:1 root:1 example:1 figure:3 give:2 process:5 sps:1 india:2 states:10 sense:4 david:1 dk:1 goal:1 provide:2 zhang:1 ghirardi:1 feature:1 write:1 dρd:1 pure:1 significance:1 answer:1 ordinary:1 verlag:1 establishment:1 ensemble:1 coarsegrained:1 product:2 intended:1 may:3 oscillators:2 after:2 eighty:1 orbits:1 wave:4 gaussian:2 short:1 dynamical:2 third:1 whenever:1 correspond:2 beyer:1 so:4 allow:1 correlation:3 representation:7 acknowledges:2 order:2 interpretation:2 john:1 zeh:3 move:1 years:1 paper:2 through:3 signs:1 mentioned:1 its:9 decay:3 susceptible:1 interesting:2 τd:1 coordinates:2 actually:1 degrees:9 systems:4 quant:1 τs:1 weber:1 correspondence:1 them:1 affected:1 entire:1 h6:1 fig:1 they:1 ys:1 bath:1 hall:2 wiley:1 easily:3 term:1 2r:1 always:1 university:3 traced:1 prosperi:1 theory:5 each:1 2m:1 organized:1 cliffs:1 mean:3 domain:1 differential:2 ei:1 dichotomy:1 energy:1 enables:1 reduce:1 idea:1 inhomogeneous:2 decays:2 measurement:23 quantum:30 our:3 summary:1 eq:1 monitors:1 out:1 matrix:33 space:6 gradient:1 furthermore:1 since:4 rev:12 denotes:1 looking:1 iλr:1 contained:2 investigation:2 dxdy:1 emerged:1 issue:1 integrated:1 shows:1 earlier:1 linear:2 mσ:1 interactions:1 derived:1 diagonal:27 quite:1 difficulty:1 surely:1 york:3 incorporates:1 interaction:14 derivation:1 r2:2 english:1 success:1 times:2 motion:1 turn:1 length:2 hence:1 dekker:1 first:4 initial:6 features:1 probability:1 feel:1 variables:1 number:5 3m2:3 4i2:1 directly:1 xs:1 given:8 necessarily:1 temperature:2 introduction:1 behaves:1 system:26 unruh:1 needed:1 master:1 observations:1 calculations:2 realization:1 scheme:3 gives:3 rimini:1 i22:1 collapse:4 centered:2 exactly:1 environmental:6 part:2 authors:2 x2:3 translation:1 than:3 diffusion:1 leggett:2 accordance:1 cimento:1 zero:2 matter:1 determined:3 ber:1 outcome:1 result:2 exhibit:1 m2:5 nuovo:1 spectrum:1 sae:1 manner:1 seen:1 seem:1 obviously:1 any:1 viewed:1 bohm:3 realm:1 partly:1 studying:1 latter:1 able:2 ideas:1 mechanism:1 sciences:1 high:1 without:1 generalized:1 singh:1 hq:7 though:3 object:2 joos:1 simplify:1 preliminary:1 pair:1 hu:1 measured:1 considered:2 average:1 drive:1 physica:1 feynman:1 accounted:1 principle:1 exp:19 justify:1 physics:2 notion:1 reprinted:3 2m2:2 dr2:6 spaced:2 show:2 friction:1 purely:1 iǫ:7 gerlach:6 goes:1 substituting:2 d2:1 find:2 q2:3 aτ:1 written:1 should:1 jan:1 only:5 going:1 postulated:1 local:1 over:5 do:1 establishes:1 means:2 dependent:1 zurek:7 ones:1 closely:2 dw:1 dt:2 dr:5 ds:7 dq:1 evolution:6 resolve:1 conditions:2 arxiv:1 consisting:1 predicted:1 including:1 set:6 decides:1 achieved:3 hγ:7 correlations:2 packet:2 observed:1 habib:1 see:6 w2:3 w1:3 discussions:1 nonlocality:1 incorporating:1 situation:1 caldeira:2 gravitation:1 interacting:4 ways:3 definite:1 state:7 various:1 between:5 invariant:1 prentice:2 approach:1 venugopalan:2 terms:3 debroglie:1 nature:1 weak:1 however:2 vernon:1 demonstrate:1 problem:2 both:1 contrasted:1 last:2 many:2 taking:1 according:2 σz:1 whole:1 regarded:1 comes:1 relevant:2 conclude:1 simple:1 harmonic:2 grants:1 scully:1 moreover:1 ae:2 considers:1 considering:1 described:1 basis:3 arbitrary:1 due:2 been:6 commission:1 reduction:2 combined:3 interest:1 basic:1 ph:1 choose:1 2ǫt:7 describe:1 corresponding:4 influence:1 wheeler:4 implied:1 observe:2 understand:1 prescription:1 denote:1 spin:23 spirit:2 present:1 case:3 look:1 pacs:1 quantenmechanik:1 transformation:1 while:2 investigating:1 drives:1 property:1 versus:1 larger:1 coupled:3 vol:1 ip:5 von:3 ir:1 thus:5 probabilistically:2 ii:3 examined:1 im:2 vy:1 vanish:2 around:2 different:4 inc:1 perform:2 acknowledgments:1 make:2 same:1 clearly:5 princeton:10 inquiry:1 arguments:1 dimensionless:1 several:2 independent:1 calculation:1 literature:2 eds:5 dǫ:1 i1:13 everett:1 i2:9 upon:1 effect:2 driven:3 moment:1 levels:1 potentials:1 recent:2 early:1 lower:1 suitable:1 off:8 recurrence:1 expression:3 variety:2 analysis:2 bohr:4 thought:1 mathematische:1 contact:2 solve:3 experimental:1 components:1 convenient:2 coordinate:1 position:9 model:4 arising:3 dimension:1 usual:1 proposed:1 being:4 identify:1 aspect:2 world:2 momenta:3 macroscopic:7 eigenstates:1 now:4 preprint:1 density:35 workers:1 ipe:2 setting:1 lett:1 mod:2 remaining:1 momentum:18 take:1 real:4 iλ:1 spinless:1 aspects:2 definitive:1 worlds:1 delhi:1 possible:1 corresponds:1 deepak:1 increases:1 press:1 using:1 debatable:1 englewood:1 like:2 particle:14 identifying:1 follows:1 invariants:2 essential:3 spins:5 mathematical:1 a15:2 satisfactory:1 because:1 neumann:3 classical:14 discrete:1 translational:2 some:2 understood:1 2rq:6 respect:3 a11:2 a10:1 happens:2 scale:2 measurements:3 langevin:1 does:2 grundlagen:1 prog:1 who:1 obey:1 plot:1 drift:1 equivalent:2 wavefunctions:1 found:3 refers:1 dictated:1 properties:2 bz:1 about:1 tracing:1 idr:1 dependence:1 o:2 reduced:5 probabilities:2 uhlenbeck:1 a5:1 efforts:1 financial:1 markovian:1 presence:1 h2:11 into:2 within:1 integral:2 astronomically:1 dissatisfaction:1 down:6 lies:1 appropriate:2 determine:1 operator:1 factor:1 reducing:1 a16:1 methods:1 72b:1 deal:1 support:1 there:2 question:1 transform:3 long:1 width:3 way:2 was:2 assumes:1 function:5 considerably:1 form:6 enough:2 hr:1 pe:2 but:1 principles:1 heat:1 illuminating:1 line:2 dissipative:3 collapses:1 made:1 ux:1 characteristic:1 up:9 us:1 iqr:1 ωj:1 limit:7 sum:2 iqd:1 distribution:11 more:1 called:1 mechanics:5 ab:1 associated:2 aj:1 linearity:1 general:1 single:1 wavelength:1 ax:1 formalism:1 distributions:1 physical:2 courant:1 no:4 wavefunction:4 when:2 detail:1 ǫt2:1 field:4 other:1 role:1 details:1 interpretable:1 really:1 poor:1 a14:1 draw:1 elements:10 kinds:1 superposition:4 a13:1 a12:1 potentialities:1 a1:1 a3:1 a2:1 a9:1 a4:1 a7:1 a6:2 variable:4 a8:1 ballentine:1 meystre:1 rq:32 correlated:1 implies:3 coupling:2 requires:1 packets:1 dq2:1 lanz:1 2im:1 mass:1 time:17 decoherence:4 4e:3 ghosh:1 rep:1
|
quant-ph9501023.txt |@word limited:5 consider:6 represent:1 forbidden:1 leads:1 commute:1 gk:2 hole:1 causes:2 whose:2 depend:2 calculate:1 tr:1 ts:39 tp:2 anglin:1 environment:32 finally:5 th:1 under:3 must:2 norm:1 applied:2 protective:1 straightforward:1 very:2 continues:1 induce:1 wave:2 putting:1 difference:1 exact:3 condition:15 arrange:1 exits:1 hamiltonian:6 issue:1 conceive:1 t2:33 solution:7 t1:31 hartle:1 convenience:1 eigenvalues:1 force:1 occurrence:1 direct:1 l2n:1 approximation:3 second:5 substituting:2 further:3 dynamics:1 even:6 ˆs:43 sub:4 ˆw:2 fine:1 section:4 selected:14 near:4 expressed:6 agrees:1 reminiscent:1 issues:1 above:1 new:2 satisfy:2 ibid:1 respectively:3 modify:3 protection:1 equations:1 extreme:1 obtained:4 study:1 studied:2 resulting:1 published:1 usually:1 verri:1 suitable:1 composed:2 via:1 projection:3 extra:1 σln:1 apply:2 total:2 unit:1 use:6 would:3 probabilities:5 laflamme:1 next:1 ψk:3 nucl:1 ψi:2 call:1 therefore:11 taken:1 cαβ:1 ψf:2 reflects:1 more:3 ψout:3 operators:3 ti:1 odinger:1 validity:1 basically:1 known:2 cases:6 circumstances:3 me:1 evolves:3 ρe:1 integrating:1 equation:25 work:1 accumulated:1 modified:6 ρs:1 values:1 rewritten:1 freedom:4 following:6 drops:1 example:5 heart:1 compare:1 process:2 arise:1 generically:1 states:16 effectively:1 sense:1 every:1 absolute:1 information:3 rather:1 s2:28 s1:20 acts:1 necessary:1 vancouver:1 pure:24 simplifies:1 ordinary:6 preferable:1 ensemble:3 ψin:5 exemplify:1 simplicity:2 product:4 description:4 may:3 after:1 derived:5 corrections:3 ρef:4 choice:1 constants:1 realized:1 short:1 dynamical:4 effective:11 computations:1 correspond:2 st:1 σzk:1 verify:1 representation:3 first:1 order:7 se:2 s0:2 closely:1 reservoir:2 developed:1 over:11 satisfied:2 interpreted:1 htot:2 paper:1 through:1 tqj:1 during:1 agricultural:1 satisfies:2 still:3 derive:2 thank:1 la:1 chosen:1 interesting:1 lm:1 lj:2 li:7 lw:5 degrees:4 systems:2 mail:1 lz:1 setting:2 non:9 contributions:1 half:3 now:9 postselected:2 2t:12 easily:2 term:4 tro:1 january:1 university:1 traced:1 appropriate:1 possibilities:1 davydov:1 l2:1 l1:1 2n:1 side:1 subsystem:5 inserts:1 square:1 ek:1 independent:6 tre:3 reduce:2 cushion:1 inverted:1 expect:1 measurement:4 quantum:10 our:4 eq:5 es:1 out:2 canada:1 shown:1 matrix:29 space:7 rep:1 since:2 rev:6 rd:1 re:2 iλt:2 induced:1 ref:1 correct:1 math:1 stat:1 linear:1 free:7 trˆ:1 nth:1 completely:1 ρin:4 nonunitarity:1 eih0:2 e1:7 e0:1 e2:7 λhi:2 interaction:23 r1:2 r2:2 transition:1 british:1 times:8 motion:5 hence:7 βk:6 initial:17 probability:16 variables:2 iht:1 peculiarity:1 intuitively:1 open:11 angular:1 aharonov:4 ihe:3 given:16 necessarily:1 reference:1 introduction:1 unknown:2 system:34 construct:2 unruh:2 intermediate:10 1e:2 observations:1 scheme:1 final:25 ih0:5 albert:1 b239:1 part:3 focusing:1 schr:1 coefficients:1 determines:1 nonreversible:1 approximations:1 see:7 limiting:1 determined:1 contrary:1 amplitude:2 interacts:2 powers:1 perturbative:1 pre:13 λqi:1 kossakowski:1 rewrite:1 dynamically:2 measure:1 invalidated:2 say:2 conjugate:1 need:2 seen:1 cumbersome:1 vaidman:3 any:11 traditionally:1 zero:2 depending:1 convenient:2 latter:3 ideas:1 note:2 amusing:1 analogy:1 δnm:1 completed:1 spectral:1 play:1 unless:1 trace:3 shall:8 object:2 most:2 significant:1 device:1 measured:1 class:4 stands:2 special:1 into:1 later:1 principle:2 exp:5 mechanical:1 usual:1 physics:2 specification:1 fact:1 selection:15 particularly:1 show:3 nτ:3 solutions:1 reznik:3 trivial:1 find:4 q1:1 boundaries:2 aχ:5 situations:3 written:1 should:2 jan:1 analytic:1 only:16 black:1 factor:1 hamiltonians:1 zeh:1 do:1 notation:1 get:3 dependent:1 zurek:3 words:1 hii:6 dt:1 boundary:1 evolution:7 arxiv:1 factorization:1 tuned:1 investigate:1 mapped:1 qi:5 qj:1 valid:1 set:8 computed:1 exists:3 lnz:1 spohn:1 lnw:2 correlations:1 operates:1 depends:3 result:2 discussions:1 terms:21 interacting:1 review:3 symmetric:2 state:39 closed:6 between:3 αk:6 conditions:16 available:1 notice:3 recently:1 nature:3 initially:4 component:1 weak:10 however:5 fluctuations:1 analyzed:1 article:1 problem:4 suggested:2 both:2 last:4 hint:13 according:2 σz:11 σy:1 σx:2 expended:1 contribution:1 expression:9 otherwise:1 aa:1 relevant:2 simple:5 ca:1 each:3 corresponds:5 cs:1 respect:2 slots:1 described:9 tuning:1 basis:1 due:6 describes:1 hawking:2 ph:2 ann:1 choose:1 grqc:1 observable:1 suppress:2 coherence:2 generalization:2 general:6 spin:3 former:1 case:19 bχ:5 bill:1 appearance:1 examine:2 value:2 will:4 while:2 situation:1 property:1 elaborate:2 generate:1 unitary:1 gorini:1 coupled:1 almost:1 1z1:1 ih:1 ij:3 fn:6 vanish:1 ie:1 different:1 verified:1 etc:1 generic:16 suggest:1 paz:1 same:1 clearly:2 quant:2 factorized:3 uncertainty:1 higher:1 evolve:1 used:4 columbia:1 unconventional:1 sudarshan:1 effect:4 hand:2 ρout:2 uˆ:4 normalization:2 expend:1 joos:1 shortly:1 well:2 obviously:2 without:2 ow:1 thi:3 model:1 left:1 λt:1 when:10 v6t:1 eigenstates:4 λl:1 density:29 regarded:1 mediator:1 mathematically:1 add:1 other:6 lett:1 versa:1 usage:1 mod:1 solvable:2 momentum:1 sˆk:2 identical:1 iλ:7 reexpress:1 advances:1 possible:4 possibly:1 b59:1 entangled:8 using:1 unique:1 helpful:1 phenomena:1 imposed:1 like:2 particle:3 follows:4 reduces:4 separately:1 yields:4 always:4 become:1 reduced:13 spins:4 right:2 often:1 decoheres:1 shen:1 some:14 back:5 polynomial:1 examples:1 happens:1 factorizable:1 apa:2 measurements:2 does:3 assuming:2 greenberger:1 particles:5 prob:11 measures:1 ba:1 bb:1 selecting:2 arbitrary:2 expansion:1 step:2 although:4 post:30 hilbert:5 extension:1 constraint:1 tracing:5 o:11 remains:1 mixed:9 frigerio:1 h0:2 bound:1 measurments:1 accommodate:2 reducible:2 hermitian:3 references:1 determine:2 sov:1 operator:13 proportional:3 conceptually:1 additional:1 assumed:1 there:6 question:1 long:1 pa:19 inner:1 way:4 ed:1 was:5 function:4 considerably:1 complete:6 form:11 hs:7 but:5 hi:18 hn:4 he:4 compute:1 prevents:1 practically:1 up:2 us:7 ur:1 perturbatively:1 liouville:11 simplifying:1 sum:3 demonstrate:1 distribution:1 define:2 called:1 mechanics:4 ab:2 constant:3 ln:3 defined:3 abstract:1 describe:1 denote:1 single:2 circum:1 taup:1 formulation:1 formalism:4 distributions:1 proceeds:1 regime:1 effected:1 compared:1 paradox:1 nm:4 nn:1 no:3 fixing:1 generally:7 vanishes:1 tim:1 interested:1 role:1 details:1 department:1 igk:1 naive:1 nonzero:1 briefly:1 elements:2 generates:1 problems:1 deriving:1 scale:1 ubc:1 acknowledgment:1 d28:1 implies:1 coupling:4 vice:1 assume:4 typically:1 d24:1 governed:1 d26:1 time:14 observables:10 decoherence:8 requires:1 external:1
|
quant-ph9502001.txt |@word secondly:1 represent:2 rev:15 magnetic:17 global:1 amplifier:1 results:5 leads:1 computation:1 consists:1 relationships:1 whose:3 depend:1 calculate:1 subjected:2 technique:1 braginsky:1 environment:2 critical:1 wmn:1 weakening:1 tb:5 tc:5 ta:5 case:7 confirmation:1 t12:4 far:1 splitting:1 every:1 experimentally:1 legnaro:2 condition:1 squids:2 level:2 solution:1 t0:1 small:1 eigenvalues:7 mahler:1 measuring:1 grateful:1 periodicity:5 direct:1 second:1 evaluated:1 insertion:1 dynamics:2 estimated:1 odd:1 theory:3 spectral:1 what:1 nonlinear:2 appear:1 incompatible:1 giving:1 expressed:1 experiment:1 above:1 reply:4 method:3 satisfy:1 edited:2 condensed:1 respectively:1 understanding:1 behaviour:3 sandberg:1 selective:1 relaxation:2 represented:1 path:8 observing:1 implicit:1 galilei:1 obtained:5 study:4 studied:1 allows:8 trial:1 resulting:1 action:1 hospitality:1 makes:1 t26:4 via:1 mensky:3 collected:1 namely:1 outcomes:2 hardy:1 aimed:1 depicted:1 predicted:1 tn:1 use:1 feb:1 takes:1 would:1 remains:1 positive:1 predictions:2 next:1 ψj:3 few:1 magnification:1 foster:1 therefore:2 ψm:1 taken:1 type:1 cited:1 more:3 introducing:1 wkb:1 becomes:2 odinger:2 validity:2 instrumental:3 particular:6 central:2 cases:3 hold:1 must:1 high:1 account:1 quantized:1 intrawell:1 equation:1 oscillator:1 theories:1 macroscopically:2 values:1 following:2 strategies:2 modifies:1 example:3 decoupled:2 grassi:1 control:1 compare:1 tab:3 give:3 process:4 choice:1 mohanty:1 states:6 minimum:2 performed:5 degenerate:1 sense:2 distinguishable:2 occur:1 verify:1 enj:1 holds:1 ghirardi:2 pure:3 noninvasive:1 optimal:11 parameter:1 simplicity:1 circuit:2 replacing:1 numerically:1 after:5 impulsive:3 barriers:1 verified:1 wave:1 meaningful:1 short:1 dynamical:2 effective:13 whenever:1 thorne:2 extremal:1 complexity:1 ones:1 so:3 fundamental:1 correlation:2 observability:1 restriction:1 help:1 meter:2 interpreted:1 report:1 experiments:4 through:6 still:2 its:5 manuscript:1 acknowledge:1 chosen:2 temporal:5 khalili:1 writing:1 systems:2 spreading:1 overcome:3 maximal:1 good:1 affected:2 greater:1 views:1 ya:1 obtaining:1 outlined:1 framework:1 effects:1 they:1 half:4 now:1 discuss:1 eigenvalue:1 february:1 several:1 overdamped:1 always:2 university:3 realistic:4 magnitude:1 φn:8 each:1 found:3 universit:1 realism:2 lasting:1 lie:1 domain:2 schemes:1 ei:2 weight:2 ej:3 laboratori:1 energy:6 journ:1 reduce:1 related:1 interferometer:1 measurement:26 quantum:27 our:2 differ:1 eq:1 projections:1 shown:5 matrix:1 space:1 furthermore:1 since:1 crucial:3 rf:4 dominated:1 drever:1 get:1 induced:1 evaluation:1 shows:1 mullen:1 linear:1 barrier:5 fisica:1 possibility:1 standard:1 besides:2 put:2 intermediate:1 iop:1 finite:1 interaction:2 could:3 bistability:1 times:11 appearing:1 nondemolition:2 unknown:1 consequence:1 neglect:1 first:1 already:3 features:1 probability:2 segre:1 number:3 reaches:1 caves:1 given:2 perturbation:2 checked:1 integrals:1 leading:1 dipartimento:1 system:14 approximately:1 their:1 assumption:2 statement:1 scheme:1 structures:2 gives:1 testing:1 way:5 relationship:1 trapped:1 centered:1 continuous:2 contribute:1 speakable:1 authors:1 peculiar:1 kind:3 leggett:9 double:1 roberto:1 depends:1 submitted:1 preparation:1 matter:1 determined:1 were:2 tion:1 outcome:1 trento:1 result:9 exhibit:1 argument:2 null:1 any:4 collapse:2 paths:3 attributable:1 tommaso:1 instance:2 potential:9 square:4 measurability:1 φac:1 accuracy:1 heisenberg:2 even:1 play:1 unless:3 shall:1 wells:2 most:3 letter:1 quantitative:1 device:1 analytically:3 intrinsic:1 class:1 probable:3 observation:1 considered:1 calculated:3 opaque:1 typeset:1 symmetrically:1 principle:3 exp:3 mechanical:1 presilla:6 notion:1 quantity:2 spaced:1 show:5 calculable:2 individuated:1 based:2 parameters:2 φeff:11 written:2 topological:1 than:1 analytic:1 only:2 corresponds:1 commensurable:1 nj:1 do:2 di:4 between:6 assumed:2 criticized:1 cannot:1 negative:3 words:1 combinations:1 dt:3 lahti:1 evolution:3 resolve:1 arxiv:1 acknowledgments:1 twice:1 paper:2 tbc:3 common:1 contain:1 including:1 requirement:1 set:3 computed:1 violated:1 correlations:1 packet:1 observed:1 see:6 quantitatively:1 discussions:1 close:2 forthcoming:1 subject:1 detect:1 mechanically:1 inequalities:9 subsequent:1 review:1 symmetric:1 state:6 future:1 hopefully:1 affecting:1 consecutive:1 reading:1 approach:4 ire:1 available:1 publishers:1 comparable:1 terms:3 extend:1 initially:2 however:1 hypothesis:1 analyzed:1 atoms:1 both:5 last:2 limits:1 uncertainty:15 equal:1 involve:1 figures:1 bristol:1 whole:1 arbitrarily:1 mechanics:10 anti:1 bell:9 sullivan:1 period:4 height:2 instants:1 simply:4 sequences:1 clifton:1 pp:3 described:3 basis:1 due:7 been:10 strategy:1 interest:1 privilege:1 ph:1 territory:1 e4n:2 fig:14 direction:1 arises:1 corresponding:2 mazenko:1 quantities:1 bml:2 spectrum:1 coherent:1 understand:1 external:2 demand:1 maximally:1 spirit:1 present:3 applied:1 being:1 expanded:1 calarco:1 value:2 rectangular:1 will:4 error:3 situation:1 tunneling:4 benatti:1 versus:2 linked:1 squid:4 thus:2 according:1 middle:2 superconducting:5 obstacle:1 properties:1 different:2 unaffected:1 italy:3 paz:1 same:4 orders:1 quant:1 arguments:1 nanopoulos:1 regime:3 conflict:2 independent:1 used:1 singapore:2 numerical:1 upon:7 effect:3 haus:1 v0:5 levels:2 potentials:2 completeness:1 schr:2 center:2 minimize:2 well:7 analysis:1 magnified:1 peculiarities:1 without:2 firstly:1 position:1 model:2 plotted:1 proposed:2 cj:1 increasingly:1 reformation:2 identify:1 atomic:1 predicts:1 using:5 macroscopic:9 eigenstates:8 mittelstaedt:1 previous:4 monitored:1 cl:1 instrument:1 other:3 lett:16 relevance:1 violations:2 mod:2 5a:1 5b:1 identical:1 around:2 optimality:1 showing:1 possible:2 harmonic:1 vacuum:1 press:2 world:4 unique:1 like:6 insert:2 bistable:1 imposed:1 marzolo:1 schematized:1 specific:1 flux:18 sezione:1 arbitrary:1 output:3 topologically:1 therein:1 classical:9 sequence:10 minima:1 back:1 suppl:1 duration:2 multiple:2 chakravarty:1 happens:2 provided:1 scale:1 ellis:1 collapses:2 measurements:34 t15:1 does:1 expressing:1 unavoidably:1 prog:1 whitaker:1 proc:2 limitations:1 vitale:1 manifesting:1 noise:4 scientific:2 bc:2 problems:1 equivalent:1 onofrio:5 fed:2 qnd:1 symp:1 revtex:1 although:1 2m:1 zimmermann:1 dictated:1 predictability:2 bz:1 asymptotic:9 actual:1 impenetrable:1 constraint:1 am:1 discussed:4 dependence:6 distinct:1 introduced:2 equally:1 cambridge:4 presence:1 garg:6 into:3 integral:4 functional:3 three:2 extending:1 references:2 determine:1 operator:1 uncertainties:1 measured:5 initial:2 philadelphia:1 dispersion:1 width:2 squires:1 editor:1 abovementioned:1 mesoscopic:1 propagator:2 collapsed:1 differences:1 but:2 failure:1 repeated:10 quiescent:13 repeatedly:1 delta:1 proposal:1 padova:3 infn:2 evident:4 circuits:2 characteristic:3 us:4 below:1 limit:7 spectroscopy:1 problem:1 define:1 called:2 detailed:1 ac:1 associated:1 zeno:1 defined:2 abstract:1 measure:1 influence:5 general:3 peres:1 nazionali:1 home:1 exist:1 physical:2 functions:2 compared:1 discriminate:1 no:2 wavefunction:8 when:3 detail:2 reality:1 valid:1 role:1 tij:1 papers:1 test:2 theor:1 expected:1 elements:1 models:1 describe:4 includes:1 important:1 allowing:1 heffner:1 prepares:1 ballentine:1 structure:3 algorithm:1 physics:1 having:2 equivalently:1 time:17 observables:2 dϕ:1 requires:1 original:1 unspeakable:1 once:1
|
quant-ph9502002.txt |@word represent:2 consider:2 switched:2 rev:11 magnetic:2 unique:1 results:19 existing:3 leads:3 fig1:3 go:1 devoted:1 whose:4 const:1 violate:2 graph:2 concerned:1 behave:1 γb:2 γa:2 presentation:1 outside:1 very:1 eckmann:1 choice:2 ρb:2 ishikawa:1 condition:3 did:1 ref:2 t0:4 magnet:1 convenience:2 vector:2 phase:5 recall:1 small:2 economically:1 neighborhood:4 ten:1 consistent:1 prediction:1 sign:2 zero:2 further:1 dynamics:1 even:2 what:5 plays:1 apparatus:22 clock:1 section:11 expressed:1 uniform:1 equidistance:2 version:1 above:3 new:2 satisfy:1 respectively:5 component:9 here:3 following:4 objects:20 represented:3 along:5 equations:7 appears:1 change:6 obtained:2 remark:1 rigorously:1 oxford:1 study:2 completely:1 suggests:2 professor:3 action:8 changes:4 plotted:5 appropriately:1 pxy:3 inference:1 diffusion:1 outcomes:8 ask:1 boolean:7 stern:1 viz:1 angle:9 unit:2 use:5 feb:1 indicated:1 neighborhoods:2 probabilities:2 positive:1 contains:1 negative:3 properties:2 phenomenological:1 call:3 therefore:4 taken:1 scope:1 type:3 more:1 introducing:1 schematic:1 becomes:6 operators:1 pairs:3 known:3 must:4 ρa:2 sample:1 account:4 stabilized:1 concretely:2 quantized:1 science:1 equation:1 insists:1 modified:1 theories:2 reproduce:1 values:1 believed:1 making:1 closing:18 my:1 example:4 initial:5 heart:1 figure:5 stated:1 process:5 suggestions:1 states:15 effectively:1 performed:2 sense:2 counting:14 occur:1 axis:11 information:4 available:3 lacks:1 captions:1 rather:1 discussion:4 six:2 feature:1 arrangement:1 write:1 how:2 answer:2 ordinary:1 sin:1 simplicity:1 product:1 beyer:1 may:10 after:2 different:6 diagram:1 applications:1 plane:1 faculty:1 fits:1 summarize:1 grangier:2 data:4 parallel:1 sz:23 sy:2 sx:2 dynamical:2 correspond:1 lengths:1 so:6 decreasing:1 sb:4 sa:5 order:5 selleri:1 horne:1 least:2 interpretation:1 help:1 produces:2 uchiyama:2 argues:1 hokudai:1 experiments:4 statistical:1 mentioned:1 japan:1 satisfies:1 sapporo:1 before:4 du:1 chosen:1 interesting:2 solving:1 τb:13 coordinates:1 τa:13 detected:3 degrees:5 systems:2 redhead:1 mail:1 hidden:11 defining:1 marshall:1 versus:3 eventually:1 non:10 good:1 greater:3 yn:5 evolution:5 its:3 they:3 accumulate:1 rotation:4 now:2 hall:1 nor:2 eigenvalue:1 february:1 hereafter:2 always:1 university:1 identified:3 labeling:1 ensemble:18 inequality:10 each:8 characterized:1 mean:1 subset:7 ruelle:1 arxiv:4 independent:1 journ:1 idea:2 related:1 measurement:10 quantum:34 our:31 beyond:1 eq:5 shown:2 matrix:1 space:8 restricted:1 nuovo:3 since:13 crucial:1 ry:3 rz:3 roger:2 supports:2 math:1 shows:3 wiley:1 theory:7 fluctuates:2 monotone:1 approaches:1 complicated:1 york:1 members:2 put:2 org:3 estimate:1 earliest:1 beginning:6 θab:1 r6:1 interaction:9 r3:2 pascazio:2 times:8 motion:4 place:2 hence:8 origin:4 already:2 features:1 probability:12 variables:4 number:3 xy:1 done:2 approximately:5 directly:1 comprises:1 given:5 necessarily:1 introduction:2 system:6 construct:1 their:2 assumption:5 brevity:1 too:1 calculations:1 speaking:2 gives:2 relative:6 ishigaki:1 direct:1 mech:1 authors:1 than:7 png:6 begins:1 distance:9 showed:1 accordance:1 cimento:3 depends:1 preparation:1 matter:1 incompleteness:1 were:2 outcome:2 distinguished:1 exhibit:1 generality:1 contradict:1 fluctuation:1 measure:1 say:2 seem:1 border:1 clearly:2 escapes:5 nonlocality:1 note:1 concerns:1 take:4 encyclopedia:1 detector:2 modulus:2 accuracy:1 shall:10 object:48 reach:1 singlet:1 most:1 locality:4 position:3 remarks:1 acknowledgements:1 measured:7 why:2 give:1 especially:1 tθ:10 considered:1 neighboring:1 calculated:5 later:1 flow:1 χe:3 principle:1 mechanical:14 velocity:4 treats:1 physics:2 fact:3 quantity:1 show:2 violation:1 detection:3 random:1 rotating:2 spaces:4 gerlach:1 threshold:1 hokkaido:1 find:3 ensembles:1 duncan:1 explain:2 less:6 distributed:11 behind:2 institution:1 only:5 experiment:2 thompson:1 local:13 do:3 gains:1 means:3 express:3 beltrametti:1 unacceptable:1 cannot:2 during:1 dt:4 years:1 ds:2 freedman:1 contextual:5 processes:4 settings:2 differential:7 summary:2 rotationally:1 paper:7 stead:1 predicted:1 though:1 characteristic:1 finishing:14 cycles:1 kochen:1 apparatuses:3 guessing:1 set:1 human:4 exists:6 violated:2 correlations:9 maximum:1 observed:1 see:5 result:7 existence:2 violates:3 subject:3 inequalities:2 dipole:1 yet:1 specker:1 state:24 ua:3 rephrase:1 simplest:1 invariant:4 neither:2 approach:1 knowing:1 terms:4 jp:1 however:3 reproduces:1 no:9 modeling:1 come:1 holds:1 observable:1 cos:6 many:3 taking:2 according:5 against:2 agree:3 83b:1 connection:2 logic:4 argue:1 whole:1 comes:3 otherwise:6 among:1 point:2 corresponds:1 coincidence:17 dimensional:1 directions:2 addisonwesley:1 respect:1 comprehend:1 gratitude:1 ps:3 due:3 been:3 pc:3 describes:1 prentice:1 expected:1 ph:4 hardly:1 fig:5 direction:2 describe:4 corresponding:8 finishes:2 both:2 santos:1 sufficient:1 finished:1 understand:5 external:4 angles:1 general:1 spin:27 present:1 instructive:1 case:3 attractors:7 stolen:1 solid:4 ǫi:2 chap:2 value:4 aim:1 while:1 suppose:3 behavior:1 situation:3 property:1 procedure:1 almost:1 thus:7 them:3 sy2:2 itself:2 vanish:3 d14:1 containing:3 d10:1 perform:2 things:5 make:5 format:3 same:5 any:1 member:1 quant:4 emphasize:1 widely:1 several:3 evolve:1 calculation:1 used:2 http:3 trajectories:2 effect:1 hand:2 v0:5 usually:1 purpose:1 satoshi:1 task:1 nevertheless:1 modeled:1 epr:17 roughly:1 evolves:1 bohm:18 without:7 components:1 coordinate:1 organization:1 model:42 just:3 attractor:3 being:3 generally:1 obtain:2 valuable:1 press:1 intervals:1 identify:3 aspect:3 world:4 eigenstates:2 previous:2 enters:1 thinking:1 photons:3 bell:15 character:1 except:1 source:5 setting:1 lett:11 samples:3 propositions:2 reason:5 violations:1 mod:2 spin1:1 eigenstate:5 real:1 represents:8 judge:1 using:2 sampling:5 apart:2 loss:1 like:1 particle:2 follows:4 either:1 characterizes:1 become:1 stationary:1 reduced:1 spins:4 exceed:1 because:3 often:1 classical:1 some:4 vol:1 measurements:11 instantaneous:1 arranged:1 does:4 assuming:1 refer:1 measuring:33 γab:4 equivalent:1 perpendicular:1 clarendon:1 step:1 although:2 98a:1 between:9 gained:1 comparison:1 about:2 actual:5 would:1 extension:2 freedom:5 certainty:2 theorems:1 meaning:1 o:2 realism:1 insufficient:1 slightly:1 considerations:1 into:9 numerically:2 down:1 pair:5 appropriate:4 right:1 references:1 next:3 mere:1 devices:2 fluctuate:1 strictly:1 there:9 question:1 width:3 accordingly:2 way:4 was:1 function:6 something:1 phenomena:5 regard:1 delayed:1 but:3 approximates:2 line:1 fry:1 he:1 uy:4 ux:4 uz:5 whether:2 wish:3 inside:1 up:4 us:5 placed:4 limit:1 similar:1 called:1 ub:2 mechanics:16 ac:1 partition:1 associated:1 defined:8 detectors:1 abstract:1 ez:12 influence:1 deep:1 denote:5 fujii:1 clauser:2 single:6 exist:2 correlation:4 constructed:2 compared:1 sˆz:7 sˆx:2 sˆy:2 when:16 reality:1 field:1 other:3 role:2 details:2 department:1 mathematics:1 conclusion:1 superposition:1 models:2 uniformly:11 variation:1 helpful:1 replace:1 sx2:2 important:4 variable:7 sides:1 watanabe:1 ago:1 gedankenexperiment:11 implies:1 dψ:1 assume:3 interval:3 curve:4 governed:2 satisfied:1 time:47 far:2 observables:1 inc:1
|
quant-ph9502003.txt |@word limited:2 roj:8 partial:1 consider:7 remarkable:1 extremes:1 hint:2 lack:1 bandgap:8 results:7 chiao:9 leads:4 eds:3 commute:1 comments:1 controversial:1 edu:1 gaithersburg:1 expressions:3 gk:1 localized:1 reluctant:1 layers:3 particles:19 measurable:1 depend:2 calculate:2 wavepacket:2 concerned:1 similarity:1 presents:1 answered:1 behave:2 those:7 weakening:1 under:2 arranged:1 analogous:2 worth:1 maximum:2 alternating:1 division:1 supported:1 shielding:1 advantage:1 orthogonal:1 far:4 could:8 impart:1 translations:1 none:1 wigner:1 wave:30 electron:20 wishes:1 interpreting:1 sensitivity:1 overcomes:1 affect:4 little:3 entire:3 disturb:2 reciprocal:1 beam:6 presented:2 transmission:31 ref:8 notes:1 hopping:1 mirror:9 standards:1 large:10 shielded:2 detected:1 phase:6 rj:4 recall:2 small:9 eigenvalues:3 unconditioned:1 optics:1 noted:2 added:1 unexpected:1 force:5 b27:1 dealing:1 prediction:4 pulse:1 split:1 approximation:4 surrounding:1 itself:6 a41:1 timescales:1 perspective:1 further:1 bandgaps:1 choices:1 odd:1 extremities:1 linear:2 even:10 δr:1 what:9 sub:2 apparatus:2 clock:6 contributions:1 sum:3 near:18 expressed:2 thickness:4 current:1 experiment:4 sokolovski:6 new:3 order:2 ever:2 contrast:2 satisfy:2 justification:1 evanescent:6 behavior:1 whose:5 κd:4 respectively:2 never:2 modify:1 here:5 atoms:1 june:1 desired:2 velocity:3 operating:1 possibility:1 sinh:3 berkeley:3 active:1 consideration:4 along:4 quite:1 appears:1 change:2 violate:1 great:1 hamiltonian:1 crystal:1 suitably:1 technical:1 shift:16 popescu:1 studied:2 allows:1 reason:1 experience:3 leaving:2 significantly:1 prior:2 amount:4 periodic:1 resulting:1 suggestion:1 action:10 chain:1 devices:2 makes:2 relation:1 plotted:3 examining:1 positions:1 projection:1 scales:1 barker:1 app:1 explained:2 plenum:1 outcomes:3 put:1 boolean:2 ml:1 issue:1 resonant:2 apply:1 total:1 differ:1 post:2 linearly:1 multilayer:1 conventional:1 feel:1 feb:1 projector:3 would:19 probabilities:12 positive:1 transmissivity:4 negative:6 ψt:17 france:5 distinct:1 ψk:4 nucl:2 ψi:29 call:1 therefore:3 taken:1 survive:1 themselves:2 type:2 reflects:1 more:10 separated:3 introducing:3 entrance:7 th:2 initial:13 operators:1 infinitesimal:1 ascribe:2 conducting:2 interplay:1 berlin:1 normalized:1 particular:2 known:4 cases:1 iii:1 opaque:4 must:3 logarithm:2 md:5 k02:2 valued:1 springer:1 skipping:1 tunnel:4 decay:4 averaged:1 protons:2 modified:1 chamberlain:1 reproduce:1 regions:5 values:7 indicating:1 making:1 trans:19 my:1 example:6 history:2 claim:1 figure:11 plate:1 predict:1 allowed:5 purposes:1 dxp:1 states:6 indicates:4 minimum:1 caused:1 numbers:2 want:1 sense:3 unphysical:1 hauge:2 times:23 yet:1 multilayers:1 charged:1 inherent:1 information:3 vanish:1 straightforward:2 decaying:1 pure:1 rather:7 discussion:1 holds:2 feature:1 entangled:1 delay:18 how:8 r34:1 opposite:1 significance:3 opt:1 instead:3 absolute:1 ensemble:6 massive:1 product:2 fs:2 agresti:1 undergoing:1 superluminal:2 may:17 watch:1 office:1 after:10 differing:1 barriers:2 plane:4 structure:3 waves:2 fi:1 choice:1 meaningful:1 parallel:2 constants:1 curve:3 natural:1 effective:9 phases:1 negligibly:1 light:7 grant:1 explicit:1 yielding:1 st:1 provide:1 so:9 fundamental:2 pay:1 definitions:2 increase:1 imply:1 divided:1 eikx:7 nearly:2 packets:2 interpretation:1 help:1 evident:1 essence:1 over:9 move:1 find:7 soc:1 years:1 held:3 kwiat:2 already:1 through:9 statistical:1 experimentally:1 argued:3 existence:1 kinetic:1 still:3 pointer:24 its:10 before:3 unruh:1 write:1 style:1 longitudinal:1 symmetry:1 termed:1 τf:1 interesting:4 τd:2 translation:2 mugnai:3 scully:1 late:7 attraction:2 absence:4 parts:7 choose:1 constitutes:1 persist:1 derivative:2 τt:7 freely:1 might:7 image:1 coincidental:1 versus:1 them:1 good:1 affected:1 greater:1 gets:1 integral:1 material:1 ye:4 fig:9 sooner:1 reflected:25 obeyed:1 repulsive:2 effects:7 they:9 identically:1 accumulate:1 1b:1 rotation:2 now:9 discuss:2 temporal:1 eigenvalue:4 term:2 several:3 perot:2 intuitively:1 occasions:2 reasonably:1 level:5 arrows:2 grows:2 orthonormal:1 applied:1 magnitude:4 transmitted:24 mode:3 each:9 found:9 entirely:5 quarter:2 side:7 mean:6 subset:1 domain:1 square:2 directly:1 series:2 energy:5 sov:2 gaussian:1 related:9 manifests:1 constitute:1 martin:2 frequency:2 travelling:2 expect:2 connor:4 measure:3 quantum:17 our:4 beyond:1 eq:7 event:1 special:1 out:6 respects:1 shown:8 dominates:1 matrix:1 borderline:1 space:3 restricted:1 furthermore:2 since:10 rev:33 projected:1 tolerated:1 research:1 looking:1 re:2 anywhere:1 vector:3 dominated:3 recently:1 internet:1 suffices:1 integrated:5 independence:1 shows:3 earlier:2 turning:1 theory:9 barrier:65 interactions:1 diagonal:1 free:2 standard:3 causally:1 assures:1 approaches:1 advantages:1 bayes:2 dx:2 imagine:1 ask:2 detecting:2 falck:1 e2:1 definition:4 represents:2 interaction:10 r0:1 argument:1 reexamined:1 penny:1 feasible:2 rohrlich:1 turn:2 length:7 enders:2 exponentially:3 tempting:1 transfer:2 hence:6 portal:1 onto:4 think:3 first:5 suspend:1 features:1 probability:38 stevens:1 rydberg:1 variables:1 thesis:1 wiesendanger:1 number:11 clear:3 smaller:2 reflectivity:4 another:5 wavevector:1 impossible:1 xp:2 precisely:2 electronic:1 aharonov:9 fire:1 passes:5 given:11 perturbation:6 decrease:3 their:5 leading:5 system:3 approximately:2 grow:1 anyone:1 indicate:3 assumption:1 calculations:2 articles:1 dwell:18 final:9 speaking:1 low:6 shifted:3 collapse:2 relationship:1 ratio:2 centered:1 completed:1 acquire:2 serve:1 wisdom:1 leavens:1 part:27 blindly:1 quasiclassical:1 x0:5 stipulation:1 representing:1 than:8 coefficients:2 reflection:22 begins:1 according:1 succeeded:1 princeton:1 suppressed:1 double:1 collins:1 typically:1 zero:6 submitted:1 preparation:1 determined:1 contrary:1 amplitude:8 were:6 identical:1 design:1 outcome:2 treated:1 minus:1 displays:1 exhibit:1 fashion:1 better:1 calculation:1 ann:2 turned:1 spectrum:2 attenuation:8 correspond:2 gentle:1 lowe:1 manner:1 conjugate:4 need:5 seen:10 constrained:1 any:5 relatively:3 absorber:5 strength:3 angle:1 noncontextual:1 tends:1 latter:5 aside:3 predominantly:1 note:4 instance:2 ideal:3 potential:11 take:1 schematically:1 negligible:2 n00014:1 channel:1 begin:2 towards:1 multiple:1 scripta:1 anandan:1 though:2 albert:1 object:1 dial:1 falls:1 mimics:3 most:4 experiences:1 significant:11 successive:1 device:9 transverse:1 measured:4 interacting:1 constancy:1 deny:1 constructed:2 observation:1 considered:2 sala:2 average:4 later:2 implications:1 physica:1 face:8 vanishingly:1 graphs:1 proceedings:1 points:2 electrons:18 principle:5 exp:6 mechanical:2 quadratic:1 usual:3 physics:3 came:1 quantity:1 precise:2 emerging:1 selection:1 unimportant:1 index:1 show:4 absorbing:2 text:3 doped:1 uttiker:4 disturbs:1 curves:4 subtle:1 consequent:2 july:1 faces:1 impact:2 stored:1 q2:1 causality:2 knowledge:1 parameters:5 favor:1 true:1 explain:1 written:2 incidence:1 should:9 analytic:1 only:24 asking:1 condon:1 muga:2 indeed:4 acknowledge:1 identification:1 reminiscent:1 pointed:1 demonstrated:1 meant:1 do:7 dominant:1 dk:7 compounded:1 means:1 dependent:5 vary:1 de:1 stop:1 expectation:9 mirrors:2 yielded:1 joint:2 feels:2 ones:1 preparing:1 words:4 despite:2 kurizki:1 during:4 dt:2 becomes:5 evolution:3 traverses:2 intuitive:2 die:1 course:2 conditions:1 büttiker:1 arxiv:1 baz:1 violent:1 microscopy:1 appear:3 paper:1 cf:2 predicted:1 shots:1 characteristic:1 albeit:1 distant:1 interference:3 voltage:1 hκ:2 rms:1 traverse:3 set:3 constructing:1 physically:1 undergoes:2 national:1 hypothetical:1 packet:20 transferred:1 relative:1 see:13 individual:2 full:2 result:5 captions:2 discussions:2 close:4 heavy:2 connected:2 eaves:1 nonlocality:3 best:1 seems:3 closer:2 reconstructing:1 fails:2 suffer:1 mechanically:1 give:1 record:2 speed:2 away:1 heading:1 symmetric:2 originated:1 state:20 future:1 various:2 chosen:1 between:23 without:7 theta:1 approach:5 across:4 multiplied:1 attention:1 terms:3 statistically:1 extend:1 complementary:1 rolled:1 ikx:5 weak:18 however:8 interfere:1 incident:16 comm:1 percent:1 group:7 understanding:2 come:1 thank:1 suggested:1 observable:2 essentially:8 garrison:1 prescription:1 contemplate:1 many:5 region:31 density:2 equal:7 against:1 flipped:1 sensitive:5 figures:4 context:1 τg:1 distinction:1 contribution:2 regimes:1 expression:3 asked:1 experimental:2 grounds:1 arbitrarily:1 strongly:1 anti:2 relevant:1 fields:1 timescale:2 point:5 simple:5 cb:2 ca:1 address:3 period:1 proton:33 height:2 semiclassical:1 variety:1 simply:8 scanning:1 losses:5 constructively:1 sees:1 rep:2 testable:2 schleich:1 considering:3 sensible:1 pp:1 strong:1 agree:1 addition:3 trajectory:1 create:1 exceeded:1 due:12 been:5 much:7 treat:1 beams:1 pe:1 expected:3 ph:5 anomalously:3 hardly:1 empty:1 define:2 stopped:1 describe:3 corresponding:3 inspecting:1 kronig:1 both:11 θb:1 mind:1 propositions:1 photon:1 traversal:4 krausz:1 offers:2 coherent:1 observe:3 understand:2 external:1 angles:1 thick:1 careful:4 spin:3 former:1 present:4 naval:1 case:6 uncertain:1 look:1 unlike:4 pacs:1 solid:2 τr:2 single:4 value:16 rectangular:1 will:13 institute:1 while:18 steinberg:9 kick:5 shall:1 involved:1 situation:1 tunneling:38 mitchell:1 yablonovitch:1 walther:1 landauer:6 unsatisfactory:1 layer:17 uncertainty:10 spacelike:2 characteristics:3 von:2 wkb:3 thus:10 non:1 discrepancy:2 conditioned:2 middle:2 examined:1 im:3 controversy:1 technology:1 different:5 unaffected:1 tra:2 propagation:4 perhaps:1 suggest:1 make:2 shorten:1 indistinguishable:1 same:11 clearly:2 shifts:1 unity:1 complex:9 quant:4 arguments:1 units:2 plates:13 finite:2 events:1 exponential:2 independent:4 outside:3 used:3 peaks:1 closest:1 again:1 numerical:3 upon:1 effect:14 dimensional:1 hand:8 mandel:1 edges:3 arrived:1 dielectric:6 expand:1 vaidman:5 break:1 argue:1 least:1 proceed:1 scenario:1 nevertheless:2 whole:2 nonetheless:1 well:9 spent:8 analysis:1 obviously:2 thought:5 off:1 edge:6 components:1 dashed:2 very:5 position:30 model:1 nearby:3 arising:1 dimension:1 left:6 unified:1 fast:1 just:1 being:3 when:7 observed:4 half:1 resolution:1 rest:1 distinguishing:1 bandwidth:4 lossy:6 fact:6 atomic:1 questions:1 advertised:1 regardless:1 momenta:3 fertig:2 scattering:1 eigenstates:3 verlag:1 york:1 rapid:1 preprint:4 generator:1 conclusions:1 absorption:11 photons:1 extra:1 had:1 except:1 iω:6 reasons:1 k0:4 extends:1 attractive:3 theorem:2 eur:1 untherodt:1 mod:4 reversal:1 eigenstate:2 momentum:26 real:29 stingl:1 insensitive:1 around:1 depends:1 easily:1 rules:3 subensembles:2 hartman:1 corollary:1 possible:5 corresponds:3 early:2 department:1 indicative:1 know:1 support:1 confined:1 using:2 τbl:1 loss:10 necessary:1 like:8 particle:51 follows:5 reduces:1 lett:11 extremely:1 unrealistic:1 serves:3 femtosecond:1 flux:1 continue:1 yields:1 either:6 always:1 completely:1 become:5 conclusion:1 continuation:1 university:1 therein:1 parity:2 exceed:1 because:3 neumann:2 classical:2 smoothly:2 mostly:2 conditional:29 some:6 back:12 proportionally:1 self:2 experiments:1 understood:2 broglie:1 acad:1 traversing:2 oscillations:6 indirect:2 neglecting:1 happens:1 provided:1 scale:1 describing:4 lead:3 bottom:1 poorly:1 broad:2 measurements:6 overlap:2 recami:1 useful:1 does:9 exit:3 assuming:1 greenberger:1 indication:1 semiconductors:1 propagating:2 closely:2 displayed:1 measuring:13 conference:1 process:1 measures:1 meanings:1 obey:1 indicated:2 bc:2 performed:1 selecting:2 equivalent:2 wavefunctions:1 oscillating:1 use:2 overall:1 who:1 step:2 olkhovsky:1 although:5 2m:2 additive:1 imaginary:29 obscured:1 properties:2 bz:1 asymptotic:1 comparison:1 about:10 weighted:1 extending:2 discussed:5 location:1 o:1 practical:2 remains:4 range:1 plus:1 obeys:1 larmor:7 importantly:1 ou:1 fabry:2 lowering:1 individually:2 equally:2 contains:1 presence:3 eisenbud:1 into:3 within:6 probabilites:1 sol:1 predictions:3 down:1 pair:5 hermitian:2 right:2 references:1 einstein:1 operator:1 proportional:4 baskin:1 nimtz:3 utility:1 unambiguous:1 statistics:1 hep:1 additional:3 spending:2 assumed:1 strictly:1 there:6 question:7 approximate:1 long:5 width:5 ruggeri:1 describes:4 physicists:1 way:6 conceivable:1 was:13 ψr:2 function:16 medium:2 arise:1 complete:2 form:3 enough:4 understandably:1 becoming:1 three:2 tailored:1 but:17 idea:3 hk:5 lowered:1 gain:4 spielmann:1 implies:1 optical:1 irreversible:1 youssef:1 shutters:1 reset:1 made:6 applying:1 builds:1 consist:1 whether:4 wish:3 inside:1 smooth:2 flip:1 us:4 work:3 placed:1 possesses:1 decays:1 limit:8 demonstrate:1 distribution:10 similar:2 calculated:3 recalling:1 mechanics:6 intents:1 diverges:1 constant:3 reconcile:1 factor:1 up:3 defined:7 certain:4 measurement:30 am:2 general:4 ch:1 duration:2 examine:2 exist:1 wavelength:1 formalism:2 distributions:9 spends:3 physical:7 high:2 functions:2 compared:2 dotted:1 no:4 amounts:1 trials:1 redrawn:1 generally:2 vanishes:2 reality:6 field:2 other:12 ocs:1 details:1 spatial:3 test:5 borne:1 reflections:1 elements:2 calculating:1 emerges:1 center:9 problems:2 ultimately:2 prepared:5 meaning:6 important:1 peak:4 photonic:3 variable:1 dielectrics:1 sci:1 sides:2 vein:1 gedankenexperiment:4 regime:4 coulomb:7 spend:4 imprecise:1 confirm:1 holes:1 rule:2 portion:6 presenting:1 time:93 determination:1 decoherence:2 requires:2 having:3 evenly:1
|
quant-ph9502004.txt |@word concept:1 consider:2 remarkable:1 caused:1 results:1 localized:1 particles:1 send:1 finally:1 sent:1 orthogonal:1 very:4 wave:1 fall:1 exact:1 condition:1 school:1 level:1 did:1 knight:1 applicable:2 large:4 small:1 round:1 concluded:1 tel:2 past:1 second:2 machines:1 even:4 what:7 selected:4 experiment:8 ever:1 placing:1 component:1 here:1 lev:1 coupling:1 appears:1 change:1 ensembles:1 obtained:1 popescu:1 larger:1 allows:1 accomplished:1 usually:2 narrow:1 makes:2 criticism:1 elaborated:1 explained:2 rarely:1 feb:1 would:2 next:1 classically:1 call:1 therefore:2 themselves:1 hulet:1 more:1 israel:1 successful:1 elec:1 particular:2 known:4 setup:3 work:4 modified:1 labeled:1 claim:1 plate:1 states:2 effectively:1 slit:1 performed:7 want:1 requirements:1 travel:1 feature:1 machine:21 far:1 speeding:1 instead:3 parameter:2 ensemble:1 description:2 after:1 waves:5 end:1 effective:1 light:1 correspond:1 so:2 operate:2 granted:1 restriction:1 indeed:3 interpreted:1 experiments:8 through:2 statistical:1 argued:1 still:1 pointer:1 its:4 before:1 actually:1 aviv:2 differently:1 might:3 easier:2 interference:2 weakness:1 polarizations:2 spell:1 mention:1 effects:2 they:3 ritchie:1 easily:1 always:1 university:1 realistic:1 mode:1 each:1 found:1 heavy:1 energy:1 interferometer:1 measurement:9 quantum:15 our:1 operation:2 out:1 shown:2 since:2 rev:6 looking:1 formula:1 correct:1 shows:2 theory:1 localization:1 story:1 besides:1 put:3 beginning:1 definition:1 suter:12 just:1 filter:2 massive:1 speeds:1 first:4 there:3 features:2 succeeds:2 variables:2 faculty:1 number:1 another:2 aharonov:4 given:1 necessarily:1 sackler:1 system:14 too:1 realization:2 final:2 shifted:1 shell:1 explanation:3 nobody:1 albert:1 task:1 part:1 translation:8 believe:1 than:2 center:1 future:1 contrary:1 supposed:2 were:4 result:2 pre:5 spectrum:1 distorted:1 seen:1 seem:1 any:2 genuine:1 latter:1 polarization:5 sciences:1 shall:1 device:8 measured:2 class:2 mach:1 considered:1 flow:1 optical:1 mechanical:1 physics:1 fact:3 quantity:1 saying:1 selection:6 anandan:1 indicator:1 slow:1 rocket:1 implementation:4 explain:1 should:1 only:6 achieve:1 do:2 his:1 beam:2 cannot:2 evolution:7 arxiv:1 yield:1 requirement:2 lasers:1 achieved:2 correlations:1 packet:1 molec:1 achieves:1 us:1 close:1 analog:4 fails:2 heteronuclear:1 state:8 various:1 between:2 conceptual:1 nuclear:2 neither:1 terms:3 gedanken:2 weak:16 however:7 article:1 suggested:1 both:1 taking:1 according:1 fulfilled:2 ernst:4 experimental:4 point:1 simple:1 had:1 period:1 moreover:1 considers:1 unusual:1 described:1 three:1 been:2 defined:1 much:3 basic:1 ph:1 systems:8 direction:1 restrictions:1 readings:1 external:1 doubts:1 spin:1 present:1 value:3 will:2 near:1 property:6 procedure:3 almost:1 itself:2 claimed:2 different:5 perform:5 make:2 radiation:3 same:4 quant:1 universality:1 evolve:1 used:4 raymond:1 zehnder:1 effect:7 purpose:1 recent:1 birefringent:4 modes:1 changes:1 well:6 analysis:1 vaidman:7 without:1 components:1 proposed:3 less:1 sources:2 predicts:1 speed:1 photons:2 seems:1 lett:4 remaining:1 identical:1 tests:1 around:1 know:4 using:1 necessary:4 like:1 follows:2 specific:2 yields:1 arbitrary:2 beverly:1 works:1 spins:1 because:2 classical:18 successfully:2 some:1 deflection:1 calculating:1 undisturbed:1 measurements:7 does:4 demonstrated:1 measuring:6 evolutions:2 post:7 practical:1 discard:1 previously:1 down:1 appropriate:1 references:1 operator:1 initial:4 question:1 fast:1 start:1 way:2 was:10 form:2 but:7 proposal:1 he:3 made:1 inside:4 up:3 devices:5 lead:2 placed:1 below:1 unusually:1 distribution:1 called:1 mechanics:3 fulfills:1 boundness:1 certain:2 abstract:1 general:4 single:2 aw:1 trip:1 regime:1 no:8 when:1 field:4 prism:1 other:3 superposition:4 accidental:1 variation:1 prepared:1 chance:1 important:1 variable:3 astronomy:1 longer:1 together:1 time:31 retardation:3 having:1
|
quant-ph9502005.txt |@word partial:1 consider:6 lack:1 results:8 illustrated:1 commute:1 go:1 follow:1 whose:1 violate:1 subjected:18 nonlocal:6 answered:1 finally:1 unpleasant:1 dramatically:1 applied:1 orthogonal:1 far:1 every:1 anonymous:1 difference:1 matrices:10 four:2 school:1 presented:1 turns:1 list:1 deals:1 solved:1 eigenvalues:3 shows:1 rohrlich:2 tel:2 consistent:1 direct:5 zero:1 perspective:1 situated:2 eigenspaces:1 even:1 what:2 incompatible:1 sum:2 selected:3 while:4 expressed:1 subspaces:1 selecting:1 new:2 nakamura:1 pioneering:1 led:1 respectively:5 teleportation:3 here:2 understanding:2 behaviour:1 lev:1 address:1 along:2 appears:1 change:1 obtained:5 remarks:1 institute:1 larger:2 contradiction:1 suggests:1 products:1 usually:2 projection:2 classification:1 explained:1 highly:1 put:1 contradictions:1 stern:1 apply:1 select:1 use:1 feb:1 prove:2 remains:1 positive:1 chooses:2 properties:1 noting:1 therefore:2 taken:1 type:4 decomposable:1 more:10 separated:6 yes:1 dλρ:4 becomes:1 operators:6 holt:2 particular:1 known:5 cases:1 must:1 me:1 states:15 account:1 valued:1 khalfin:1 recall:1 work:2 values:1 learn:1 following:1 my:1 example:7 proof:1 compare:1 give:1 involve:1 performed:11 degenerate:1 arise:4 information:4 means:1 very:3 vital:1 pure:8 answer:1 sij:6 ensemble:8 product:4 superficially:1 ancilla:2 after:6 santos:2 revealed:1 revzen:3 light:1 correspond:1 ones:1 so:2 correlation:1 pleasure:1 subsequently:1 horne:2 indeed:8 over:1 years:1 course:2 paper:3 through:1 still:3 its:1 before:1 thank:1 chosen:2 exact:1 solving:1 subensemble:6 actually:2 aviv:3 systems:11 hidden:21 might:5 maximal:1 non:5 good:1 they:7 instead:2 now:2 eigenvalue:2 dirac:1 university:2 2d:5 inequality:7 each:26 found:1 side:2 mean:1 another:2 sandu:1 literature:1 measurement:34 quantum:16 beyond:2 eq:2 special:1 out:1 living:1 shown:2 rw:1 matrix:7 space:12 rev:7 particles:8 acting:2 suffices:1 independence:1 predicted:1 state:17 commits:1 standard:1 completely:1 complicated:3 ask:1 beginning:1 generate:1 pairs:6 could:6 place:1 onto:1 think:2 first:9 there:3 probability:2 variables:16 powerful:2 intuitively:1 directly:6 precisely:1 open:2 given:3 reference:1 similarly:2 system:11 relations:1 their:1 attack:1 normalization:1 scheme:4 gives:2 imperfect:1 option:1 completed:1 part:1 simulate:4 probably:2 than:4 second:1 matter:1 were:2 outcome:4 say:2 manner:1 seem:1 vaidman:1 clearly:1 mermin:2 depending:2 violates:2 note:1 ideal:23 take:1 forces:2 detector:1 channel:1 singlet:2 most:3 letter:4 pair:3 measured:6 class:1 haifa:1 considered:1 tsirelson:2 sometimes:1 braunstein:1 principle:2 mechanical:3 left:2 physics:3 fact:1 son:1 show:6 violation:1 random:3 boojums:1 analogously:1 discovered:1 bring:1 spaces:2 gerlach:1 carefully:1 d2:1 postulates:1 implementation:1 situations:3 enough:4 should:2 only:9 going:1 factor:1 local:24 do:3 above:3 get:1 dependent:2 simplest:1 yielded:2 famous:1 feels:1 cannot:5 consecutive:2 qp:1 qw:1 arxiv:1 yield:12 experiments:4 common:1 valid:1 revealing:1 questions:3 observer:2 violated:1 correlations:16 observed:1 see:2 result:2 discussions:1 nonlocality:4 subject:2 said:1 inequalities:6 nondegenerate:2 subsequent:4 shimony:2 outside:1 between:5 incompatibility:1 progress:1 knowing:1 recently:1 however:3 efficiency:1 answers:2 distribution:2 both:2 last:1 avoid:1 many:2 according:5 interesting:1 asked:1 mann:3 among:1 bell:11 others:1 corresponds:1 dimensional:7 werner:17 sequences:1 considers:1 considering:4 better:3 described:5 three:1 been:4 strategy:1 povm:1 much:2 basic:1 ph:1 choose:1 direction:1 referee:1 corresponding:6 subjecting:1 subspace:3 zeilinger:1 understand:1 general:6 spin:4 extensive:1 present:1 case:12 explicitly:1 p1:14 splits:1 value:1 will:12 near:2 suppose:3 behavior:2 situation:1 property:1 procedure:1 detailed:1 almost:1 von:1 thus:1 characterize:1 itself:2 cone:1 aspects:1 technology:1 different:3 perform:1 things:1 belong:1 same:3 any:4 strange:1 quant:1 mixtures:4 resulting:3 status:1 independent:1 used:6 hand:4 uses:1 identity:2 simulates:1 nevertheless:1 no:3 well:5 obviously:2 without:2 simulated:1 model:16 dimension:2 usual:5 popescu:3 less:1 being:1 obtain:1 rest:2 aspect:1 using:1 alternative:1 density:6 point:2 had:1 setting:1 lett:7 violations:1 remaining:1 identical:2 march:1 depends:1 easily:1 subensembles:4 decomposed:1 possible:3 test:5 entangled:1 press:1 immediately:1 outcomes:3 necessary:1 success:1 particle:29 hardy:1 imposes:1 yields:1 either:2 arbitrary:1 essential:1 spins:1 because:2 neumann:1 classical:10 sequence:4 some:8 supplementary:1 examples:1 proofs:2 happens:4 decision:1 measurements:27 cirel:1 does:3 refer:2 measuring:1 s12:5 although:3 hilbert:5 about:5 anything:1 freedom:2 probabilities:2 mixed:3 raised:1 cambridge:1 into:3 predictions:1 pps:1 included:1 hermitian:1 references:1 operator:5 behaving:1 initial:4 question:6 start:1 way:5 analyze:1 was:1 himself:1 complete:1 form:4 registered:1 but:12 sophisticated:1 illuminating:1 technion:1 ramat:1 true:1 raising:1 he:1 made:1 whether:2 flip:1 us:4 below:1 problem:3 similar:1 called:1 gisin:1 mechanics:5 ab:4 defined:1 certain:1 abstract:1 measure:3 israel:3 proven:1 denote:1 peres:1 clauser:2 single:12 locality:1 when:12 ny:1 other:6 role:1 department:1 conclusion:1 conclude:1 apparent:1 models:3 nonclassical:2 prepared:1 deriving:1 meaning:1 important:3 variable:4 astronomy:1 bases:1 correlated:1 longer:1 together:1 remarked:1 observables:1 chsh:5 original:11
|
quant-ph9502006.txt |@word represent:2 code:22 customary:1 consider:2 lagrangian:2 magnetic:1 global:1 results:3 existing:1 leads:5 eds:1 rˆ:1 commute:1 entropy:7 grateful:1 perturbations:3 remarkably:1 research:1 forget:1 devoted:1 whose:3 inverse:3 lawrence:1 physiological:3 iii:1 umezawa:16 nonlocal:2 γt:2 environment:6 finally:6 monotonically:1 squeezing:10 stable:1 presentation:1 activities:2 conjecture:2 labels:2 nski:1 evolves:1 very:1 memories:4 translations:1 springer:3 induce:1 wave:3 spoiled:1 replication:5 electron:1 interpreting:1 remarks:1 ma:1 difference:3 condition:6 transformation:1 pre:1 reciprocal:1 hamiltonian:4 stimulus:2 turns:1 shock:1 proposals:1 solution:3 t0:10 damped:3 large:2 discrete:1 vector:1 recall:3 rev:3 biological:5 shows:3 optics:3 configurations:4 unconscious:2 holography:1 celeghini:2 thermo:1 cosh:5 past:1 surrounding:1 itself:2 26b:1 zz:1 further:1 dynamics:30 functioning:4 machines:1 avoiding:1 even:3 plays:3 appear:1 section:5 selected:2 both:1 expressed:1 guaranties:1 cell:2 consistently:1 sequential:2 above:7 tachiki:1 3c:2 new:8 3a:2 contributes:1 ricciardi:10 implementable:1 pioneering:1 condensed:2 full:2 interfacial:1 exchange:1 respectively:6 presence:2 never:1 here:2 understanding:1 behaviour:3 objects:1 focused:1 free:4 sinh:2 making:2 represented:8 observing:1 appears:2 change:4 obtained:4 remark:1 algebra:1 splitting:1 institute:1 spontaneous:5 study:4 studied:3 allows:1 suggests:2 amount:1 simultaneous:3 resulting:1 situations:1 action:6 unwanted:1 changes:3 cancellation:1 sci:2 uniquely:1 named:1 useful:2 j32:1 elaborated:1 contrarily:1 deals:1 brought:1 aimed:1 marcel:1 carry:1 literary:1 virasoro:1 discuss:2 use:2 feb:1 proceed:2 would:8 recalling:6 positive:3 h0:7 quasi:1 anatomical:1 thermofield:2 linear:1 going:1 therefore:7 bender:1 memory:54 conservation:1 means:2 type:2 reflects:2 more:6 beyond:1 formally:2 neurophysiology:1 operators:5 under:11 occurred:1 instantons:2 glass:2 berlin:3 carrying:1 intermediate:2 labelled:6 microtubules:2 eκ:5 known:3 central:3 conditioned:1 producing:2 glad:1 eβ:1 high:1 account:5 rotational:6 defines:1 quantized:1 languages:1 tunnel:1 mentary:1 work:2 oscillator:1 london:4 theories:1 macroscopically:1 printing:19 values:4 rewritten:1 concepts:1 following:6 dea:3 specialized:1 example:1 stimulating:2 initial:7 exchanged:1 del:10 hyperplane:1 stated:1 process:9 introduces:3 choice:2 sense:1 organized:1 belonging:2 generically:1 states:34 minimum:2 numbers:5 degenerate:2 allowed:1 interpreted:1 quasistationary:1 times:1 distinguishable:1 occur:2 verlag:3 information:39 needs:1 redundancy:1 carriers:1 rather:1 discussion:3 acts:3 feature:7 regions:1 dekker:1 classifying:1 giudice:10 pure:1 answer:1 instead:1 expresses:1 parameter:9 simplicity:1 fr:8 fs:2 undergoing:1 huge:12 may:34 oscillators:1 after:4 derived:2 different:20 collection:3 fa:2 dwq:12 emperor:1 water:6 cambridge:2 representations:6 summarize:1 destructive:5 revealed:1 grow:1 realized:1 short:2 natural:2 dynamical:10 effective:3 light:1 eliminated:1 summing:1 su:5 think:1 provide:1 complexity:1 cannot:4 so:3 specifying:5 fundamental:1 decreasing:1 representation:6 sa:15 order:16 triggering:1 typical:1 neglect:1 reversal:7 produces:2 constituents:3 thresholds:2 eqs:3 find:1 satisfied:2 years:1 stability:6 brain:69 thermal:5 paper:8 through:7 statistical:1 mentioned:2 existence:5 rasmussen:1 nets:1 its:8 vacua:15 solitary:3 group:5 thank:2 decay:1 ln:4 interesting:5 solving:1 actually:1 resorting:2 absence:2 parts:1 microscopic:2 systems:11 persist:1 mail:1 scripta:1 main:1 defining:1 image:5 non:8 good:1 affected:1 greater:1 obtaining:1 rasetti:3 processes:2 introduce:3 b275:1 framework:3 hold:1 effects:5 they:1 focus:1 oxford:3 rotation:1 now:3 realize:1 developments:2 biomolecular:3 represents:1 term:3 finite:12 cognition:1 university:4 presented:3 annals:1 identified:1 inequivalence:2 grows:1 realistic:5 davydov:4 mode:21 arrow:3 each:17 found:1 universit:1 cliffs:1 2i:1 characterized:2 referred:1 goldstone:5 successively:1 significantly:1 map:1 generation:1 ed:8 energy:16 sov:1 ea:2 related:6 manifests:1 constitute:1 operator:5 frequency:1 ezard:1 quantum:34 our:3 transitions:7 eq:17 special:1 nonexistence:1 living:9 shown:9 network:1 space:5 nuovo:2 since:6 crucial:4 denotes:1 particles:2 similarly:1 write:2 hill:1 conjectured:1 print:2 illustrate:1 ref:6 occurs:2 mκ:2 benjamin:1 sinh2:5 perception:1 theory:8 normalized:1 interactions:1 mechanisms:1 fisica:1 possibility:1 treatments:1 takahashi:3 clarify:1 completely:3 formation:2 york:1 besides:1 put:1 equipped:1 1t:1 diffused:1 interaction:6 tilde:7 could:3 transition:2 moment:1 used:2 local:2 motion:1 introduction:4 act:1 produce:3 atp:1 consequence:4 neglected:1 degeneracy:3 condensate:8 destruction:3 first:4 origin:1 informations:7 already:5 features:2 symmetry:30 question:1 variables:6 waves:2 coding:7 number:18 dsa:3 cybernetics:2 biol:3 another:6 blank:1 dt:1 difficulty:1 noticed:1 open:6 size:3 received:1 given:7 necessarily:1 temperature:6 glauber:1 ordering:3 dipartimento:1 phenomenologically:1 amsterdam:1 system:51 relations:4 response:3 anyone:1 their:4 confirming:1 assumption:2 observations:1 realization:1 quanta:2 recent:2 dfa:1 recovered:1 too:1 commutativity:2 warmly:1 reversed:3 continuous:5 foliation:2 neurodynamics:1 part:2 biomolecules:1 fall:1 focusing:1 translation:2 dissipativity:1 representing:1 than:5 coefficients:2 approximation:2 kind:4 critically:2 holland:1 penrose:4 sections:4 require:4 cimento:2 see:13 optimism:1 limiting:1 recording:7 matter:7 determined:2 contrary:1 were:1 separate:1 providing:1 treated:1 exhibit:1 bridge:1 fashion:1 symmetries:5 dynamically:2 modern:1 mind:2 few:1 discussions:1 say:2 electrochemical:2 b251:1 close:2 need:1 seen:2 seem:1 turn:1 any:3 viewed:1 complete:1 uncertainty:4 zero:3 ohlich:8 convenient:1 self:4 responsible:2 able:1 mechanism:2 polarization:2 fundamentals:1 internal:1 take:1 supply:2 destroy:3 canonical:3 mit:1 play:6 exactly:1 unless:1 electric:5 replicas:2 who:3 reach:1 suffix:2 boltzmann:1 involving:1 printed:3 successive:1 phase:9 accepting:1 future:1 extremely:1 class:3 sub:1 kb:2 observation:1 considered:8 milani:6 intrinsic:2 flow:1 drive:1 physica:1 points:1 qbd:1 principle:2 exp:23 mechanical:1 duplication:1 physics:3 fact:11 show:7 random:1 radford:2 hh:1 spaces:1 relation:7 superradiant:2 threshold:5 magnons:1 trivial:1 d3:2 ground:9 slow:1 based:2 simulating:1 spite:1 nonequivalence:1 irreversible:1 written:1 controls:1 only:11 difficulties:1 intrinsically:1 molecules:2 indeed:7 constant:5 thousands:1 over:4 hope:1 lim:2 his:1 notation:1 di:2 dependent:1 express:2 expectation:1 truly:1 feels:2 ones:5 conjugate:1 words:2 3b:1 during:1 aλ:1 aκ:39 ds:1 dq:2 produced:1 evolution:17 de:1 densities:1 course:2 yuen:1 reintroducing:1 arxiv:1 doubled:1 acknowledgments:1 whether:1 nκ:2 underlying:1 cf:5 inputs:1 activity:11 including:1 remains:1 consciously:2 satisfy:1 requirement:1 set:10 hagan:1 ser:1 fascinating:1 achieved:2 correlations:4 emergent:1 ables:1 j3:4 observed:5 opposite:1 namely:9 sec:1 result:2 separately:1 inequivalent:6 nonlocality:1 subject:2 hilbert:1 phases:5 capacity:13 commutation:1 pattern:2 missing:1 dipole:8 artificial:1 label:2 boundaries:2 state:45 classes:2 between:2 invariant:5 neither:1 before:2 approach:4 preserve:1 gives:1 nambu:1 terms:4 relative:1 nature:2 confusion:2 attention:2 weak:2 however:10 interfere:1 probe:1 spoil:2 macro:1 bose:2 ferromagnet:1 distribution:2 originates:1 minimizing:3 observable:1 essentially:1 instant:1 keep:1 qft:7 many:20 taking:2 density:2 according:4 against:3 quantization:1 propagation:3 connection:3 protection:1 casimir:1 whole:2 regarded:1 jersey:2 unitarily:6 among:6 relevant:1 key:1 point:7 simple:1 guaranteed:1 harmonic:1 running:2 na:17 maintained:1 simply:2 stationarity:1 modeling:1 associated:13 writing:1 factors:1 filippo:1 conference:1 better:1 ensures:1 configuration:1 described:3 transformations:3 basis:1 addition:1 trajectory:3 due:7 been:16 much:1 eigenstate:1 recognize:2 degrees:2 ph:1 unchanged:2 empty:1 differently:2 field:14 direction:2 lived:1 corresponding:8 easy:1 reaction:1 drugs:1 quantities:1 sufficient:1 coherence:4 excite:1 coherent:17 observe:7 recalled:1 external:16 consecutive:1 worked:2 denote:2 spin:4 diffuse:2 present:7 case:9 macromolecules:1 exponential:2 tanh:2 frozen:2 variances:6 rigorously:2 conserved:2 value:8 spontaneously:2 will:12 while:2 suppose:1 behavior:3 squeezed:10 nonstationary:1 property:2 characterizing:1 stoler:1 iy:1 aa:1 unitary:6 coupled:3 riv:1 refs:1 neuron:2 thus:36 them:7 encouragement:1 equal:3 ii:1 reads:1 neurons:5 orthogonal:1 finds:1 ig:4 sequentially:2 damaged:1 recover:1 italy:1 parisi:1 acquire:1 coexisting:1 radiation:1 lett:5 same:6 clearly:1 shorter:1 complex:4 quant:1 positively:1 largest:1 units:2 dimensionless:1 several:1 privileged:1 breakdown:12 independent:1 extended:3 infinity:2 watt:1 singapore:1 stressed:1 nondissipative:2 sudarshan:1 effect:5 hand:1 domains:3 vitiello:14 levels:1 purpose:2 infinite:12 protected:3 concluding:1 subgroups:1 eigenvectors:1 kept:1 modes:30 scenario:1 neural:2 expression:3 stimuli:10 no:1 well:5 analysis:3 ccr:8 academic:2 directly:1 without:6 feshbach:1 matsumoto:1 sets:2 model:18 chemistry:1 arising:1 usual:2 comment:3 26a:1 magnetization:2 cosh2:1 proposed:6 when:5 klauder:1 actions:1 assigned:1 manifestation:1 stored:2 spread:1 using:3 macroscopic:10 eigenstates:3 previous:3 adv:1 note:6 like:1 signal:4 generator:1 infinitely:10 decayed:1 conclude:1 character:4 ele:1 thermodynamics:1 add:1 rˆole:10 association:3 versa:1 electrical:3 ruled:2 excited:3 momentum:1 generalized:2 shadows:1 amit:1 2j3:1 around:1 depends:2 replaced:1 breaks:1 possible:2 corresponds:3 possibly:1 know:1 vacuum:15 press:5 world:4 moreover:1 advanced:2 mod:1 phenomena:3 englewood:1 replacing:2 lost:1 obvious:1 collective:9 specific:7 mirror:6 either:1 neuronal:1 alternatively:1 output:1 giuseppe:1 sˆa:6 stationary:5 reduced:1 gauge:1 accessible:8 shed:1 interference:5 methods:1 sequence:3 creation:2 some:12 back:1 alive:1 experienced:1 acad:1 refresh:1 specified:3 proper:1 root:1 recognition:2 forgotten:1 nonzero:2 provided:3 scale:2 describing:1 dimensions:1 lead:1 micro:1 electromagnetic:2 shall:1 recorded:7 comments:1 does:7 dipoles:3 provides:1 assuming:1 gapless:2 propagating:1 chains:2 lowest:1 biology:1 algorithmic:1 obey:1 reaching:1 performed:1 equivalent:4 srinivasan:1 broken:6 projection:1 reduces:1 although:3 become:1 relating:2 properties:4 tanh2:1 integers:2 actual:1 ensured:1 mcgraw:1 coexist:3 freedom:2 consciousness:3 theorems:1 discussed:4 meaning:1 recognized:3 practical:1 sake:1 range:6 jept:1 nothing:1 yasue:8 stuart:5 introduced:2 specifies:1 computational:2 inclusion:1 previously:3 into:8 rotations:1 functional:5 negative:1 variable:2 zuber:1 references:1 determine:1 hanson:1 elementary:2 factor:1 bosonic:2 graziano:1 ole:1 definiteness:1 assumed:3 strictly:1 there:2 available:1 nucl:2 long:6 symmetron:5 start:1 trigger:4 bosons:2 way:7 salerno:2 forward:1 preparata:1 scientific:1 was:3 damping:1 function:3 washed:1 north:1 irreversibility:1 triggered:1 constancy:1 metastable:1 constantly:1 a13:1 but:7 volume:15 insured:2 heat:2 hi:8 might:1 elimination:1 ha:3 dissipative:24 infn:1 made:3 circuits:1 characteristic:3 cells:2 variations:1 up:4 us:10 international:1 limit:12 continuously:1 fluctuations:2 problem:9 define:1 similar:7 called:6 mechanics:2 storing:1 interval:1 ordered:5 ad:1 nka:1 int:1 certain:4 abstract:1 describe:2 am:2 life:1 general:3 globally:1 oscillations:1 single:3 replica:1 exist:1 operatorial:1 journal:1 controlled:1 cytoskeleton:1 formalism:2 anesthesia:1 interferences:1 physical:3 again:4 functions:4 codes:3 ingredients:1 allow:2 commutes:1 storage:3 treatment:1 virtual:2 occasional:1 application:1 other:16 coded:6 details:1 spatial:1 dipolar:1 you:1 out:5 itzykson:1 conclusion:3 picture:1 briefly:1 elements:2 kinds:1 superposition:2 excitation:4 emerges:2 models:1 behavioral:1 kluver:1 variation:1 generated:3 important:2 restore:1 allowing:3 serious:1 dissipation:9 erlbaum:1 cooperate:1 structure:2 independently:2 condensation:5 coupling:7 vice:1 thermalization:2 american:1 required:4 holes:2 theor:3 together:1 implied:1 mass:2 biosystems:1 time:60 95a:1 observables:1 inc:1 original:3 once:2
|
quant-ph9502007.txt |@word replacing:2 represent:3 iǫ1:1 concept:2 consider:9 iǫ2:1 separates:1 results:4 leads:2 proposition:21 generalize:2 computation:9 consists:1 follow:1 denotes:3 contributions:12 reasoning:5 compact:2 contributing:1 preserves:1 const:3 calculate:1 ac03:1 graph:12 show:10 tr:1 recurrence:1 finally:4 program:1 indicate:1 those:3 weakening:5 stable:1 tg:1 td:1 include:2 divergent:2 division:1 labels:1 deforming:1 distorting:1 straightforward:2 very:1 continues:2 translations:1 none:1 distort:1 liability:1 replaces:1 every:4 fall:2 exact:1 encounter:1 four:5 immediately:1 level:2 suffices:3 integrating:1 vertex:3 solution:1 integrated:2 large:8 ρi:56 convenience:1 vector:7 dealt:1 small:4 study:2 exhibits:1 accumulation:1 disclaimer:1 application:2 ρj:38 neighborhood:4 ten:2 dealing:1 japanese:1 sign:2 approximation:1 go:1 imply:1 diagrams:1 dρj:11 insertion:1 pass:1 ρn:3 residue:2 established:1 what:2 adds:1 combined:1 apparatus:1 dr1:8 trivial:3 sum:19 dr2:3 while:1 expressed:2 find:23 version:1 poles:4 above:11 boundary:1 international:1 consisting:1 satisfy:1 counting:1 full:2 simultaneously:1 degree:1 respectively:1 applies:1 commercial:1 here:13 behaviour:3 them:1 will:7 berkeley:5 represented:4 path:1 along:16 strong:1 equations:4 implicit:1 logarithmic:3 obtained:4 remark:8 rdr:2 institute:1 shift:2 employees:1 studied:1 cut:1 dri:1 p2:7 drj:8 products:1 advertising:1 drn:7 usually:1 complicated:1 ctn:2 makes:2 ctj:1 york:1 emerge:1 via:1 convolution:1 ii2:1 technique:1 dλi:1 replace:3 brought:1 addressed:1 weaker:5 privately:1 apply:4 establish:1 rω:20 linearly:2 tn:5 use:12 graphs:3 feb:1 asymptotic:1 would:2 prove:2 remains:1 beginning:3 stated:1 rω2:4 negative:9 next:1 comparing:1 examination:1 therefore:4 totality:1 m2:27 taken:1 tj:3 simpler:2 type:2 entails:7 possible:3 more:3 separated:1 mm:4 th:1 definition:2 becomes:3 operators:2 dressing:2 validity:1 appendix:2 loss:1 cases:4 hold:5 iii:6 keeps:1 must:1 high:2 account:1 extension:1 rights:1 deformed:1 science:1 equation:8 work:3 theories:1 itself:2 values:5 henry:1 following:34 under:4 example:6 lhs:1 proof:14 f1:2 f2:2 f3:1 figure:5 give:5 process:3 introduces:1 allowed:2 purposes:1 dependence:5 states:4 collision:1 performed:2 arise:1 dominant:10 nonnegative:2 occur:2 weaken:1 normalize:1 information:1 needs:2 united:4 requirements:2 lemma:10 ij:4 verify:5 discussion:1 holds:15 write:1 how:2 opposite:2 endorsement:2 instead:2 ordinary:5 axis:1 parameter:4 dσ0:5 dσ1:6 product:10 express:1 singular:8 may:8 rm:4 after:1 singularities:10 dx2:9 tied:1 diagram:7 fa:1 fb:5 plane:2 distortions:1 coming:1 between:1 end:13 constants:14 dσn:11 induction:6 effective:1 computations:1 slightly:2 dhh:1 lines:9 correspond:1 λdλ:3 interpolates:1 rather:1 complexity:1 responsibility:1 sm:3 enter:2 taking:1 integrand:5 m1:1 order:7 xj:12 s0:3 played:1 help:1 office:2 produces:3 λi:24 developed:1 over:17 satisfied:3 making:1 trade:1 held:2 ing:1 through:3 motions:1 omitting:1 japan:1 satisfies:3 its:16 before:2 ima:1 bridges:3 supplemented:1 ln:6 continued:1 lm:6 coordinates:1 actually:3 harmless:1 complex:3 distortion:5 disclosed:1 ǫ2m:2 potentially:2 main:1 defining:3 setting:1 correspondence:7 eventually:2 non:21 views:1 gets:1 weakness:2 fig:5 introduce:5 landau:13 scaling:2 disrupted:1 cutting:1 thereof:3 they:2 half:2 singularity:47 now:8 definedness:4 nor:3 suppose:1 easily:1 february:1 finite:11 name:1 lies:1 dσ2:4 university:5 classified:1 form3:1 sufficiently:3 each:29 contours:3 identifies:1 side:12 subset:2 domain:10 differential:4 dωj:4 independent:3 lm0:2 mesoscopic:1 energy:6 hard:1 reduce:1 principles:1 applicable:1 constitute:1 extended:1 yield:3 combining:3 quantum:9 laboratory:4 avoided:1 explicit:3 orient:1 special:1 out:8 leave:1 shown:7 divide:1 matrix:1 space:8 gradient:4 furthermore:4 since:14 rev:2 denote:12 research:4 particles:2 re:8 report:2 xt:1 formula:5 rn:17 dominate:1 ref:17 ri:14 rj:29 shows:5 occurs:1 earlier:1 theory:3 lawrence:4 8b:2 dx3:3 discontinuity:3 divergence:1 cℓ:11 reason:1 necessarily:2 california:5 residues:2 usual:1 intermediate:1 companion:1 remainder:5 e0:2 e2:3 reflect:1 qj:4 r0:104 r1:29 r2:4 ministry:1 aλ:3 pertains:1 could:1 similarly:4 times:2 length:1 place:3 incorporated:1 hence:30 uses:1 analyticity:1 onto:1 first:23 separable:3 cǫ:4 xh:4 xn:1 upper:3 third:2 variables:26 number:10 owned:1 nested:1 nonnegativity:1 ranges:1 2p2:2 done:2 another:2 xp:4 open:2 several:3 stage:1 passes:2 given:8 perturbation:1 e1:6 ctα:1 service:1 needed:3 introduction:1 leading:4 behaves:1 least:5 their:2 assumption:2 identity:1 eqn:1 structural:1 1j:1 final:1 iδ:1 denominators:2 shifted:4 holomorphic:22 exactly:4 contribute:2 employ:1 part:25 authors:1 x2:9 x3:3 close:2 representing:2 than:5 coefficients:10 finitely:1 distance:3 kind:4 dtn:1 showed:1 sections:3 rate:1 submitted:2 dtd:5 claim:2 determined:1 amplitude:1 represents:4 dx1:14 similarily:1 gives:4 treated:4 distinguished:5 decompose:1 perturbative:3 bridge:17 nonleading:2 sees:1 entail:1 generality:1 electrodynamics:6 correction:1 argument:4 generalization:3 say:1 manner:2 distorted:3 disjoint:1 seen:1 null:2 lbl:3 eq:1 zero:9 min:4 lim:6 latter:2 agency:3 proportional:1 si:2 nonseparable:1 converges:1 note:12 sciences:1 stapp:4 absorbed:1 generalized:1 analogy:1 so:12 acquires:1 accuracy:1 even:1 begin:1 continuous:1 shall:3 rhs:4 denominator:5 fails:1 most:2 said:2 sponsored:1 plan:1 pair:2 plays:1 segment:6 why:1 δr1:1 singled:1 takes:2 consequences:1 hk:4 accord:1 kj:14 clear:1 later:1 upset:2 kn:7 km:9 tα:3 feynman:2 points:9 engendered:1 principle:7 nuclear:1 left:2 physics:2 section:24 fact:6 quantity:2 hyper:1 opinions:1 reductions:1 retains:1 supported:1 dr0:9 infrared:2 obtains:1 ki:21 relation:2 supplied:1 decompositions:1 possibilities:1 substituting:2 d4:6 uniform:2 fine:3 agrees:2 d0:7 d1:1 q1:34 q0:2 q3:28 q2:9 spite:1 amplitudes:1 series:1 written:1 topological:1 employer:1 analytic:10 only:13 explicitly:2 subsection:1 indeed:1 integrate:1 employed:1 constant:13 local:1 interested:1 columns:1 dn:4 do:7 cube:1 triangle:14 establishes:1 dh:19 means:5 dependent:4 dg:12 de:1 wiggly:1 iagolnitzer:1 cannot:3 dx:15 new:9 combinations:2 dw:7 dt:18 multiplied:2 dr:9 geometric:1 holland:1 analysis:1 runs:3 roles:1 arxiv:1 factorization:4 method:5 double:1 qi:3 including:1 fixed:4 favoring:1 2p1:2 coefficient:4 requirement:1 set:15 modulo:3 computed:2 reference:1 notational:1 respect:2 notice:2 relative:1 culture:1 namely:4 p21:4 usefulness:1 p23:2 p22:3 fail:3 contains:2 contour:5 analog:1 techniques:1 preparation:2 αs:3 evaluation:1 exponent:1 ways:2 macroscopic:3 away:2 nature:1 label:1 state:1 smallest:3 various:2 chosen:1 closed:4 simplest:2 affecting:1 neither:1 conditions:1 across:2 quantities:1 meromorphic:21 milder:1 ends:7 attention:1 terms:31 complementary:1 dxj:3 component:2 were:3 however:4 vanishing:3 concentrate:1 hypothesis:1 p2s:1 article:1 both:10 essentially:3 last:1 repeating:3 limits:1 powers:5 region:4 equal:3 contract:1 etc:2 collection:3 smearing:1 contribution:18 extracting:1 expression:2 action:1 comes:1 otherwise:2 ck:4 cj:15 key:1 point:17 simple:6 meaningfulness:1 pole:12 simply:5 adaptation:1 numbers:1 consideration:1 polynomial:2 moreover:1 transformations:1 dj:3 ps:26 combines:2 described:2 reversal:1 second:9 locally:2 trademark:1 due:2 been:2 balian:1 reduction:1 much:2 dρ0:2 dρ1:10 dρ2:7 expected:2 ph:1 pi:1 pn:2 summable:2 define:3 direction:1 arises:2 corresponding:5 efficacy:1 σj:2 am:3 concerning:1 propositions:2 photon:25 coincides:1 depend:1 finished:2 external:4 derivative:2 c2:5 c1:4 weierstrass:2 present:1 σn:36 case:27 p3:18 p1:9 critical:1 dρn:2 suitably:1 appearance:1 single:2 value:3 remaining:4 ǫs:2 near:29 replaced:6 many:1 cancelled:1 aid:1 property:3 couplings:5 loop:3 exclude:1 unitary:1 existence:1 orientation:3 coupled:5 almost:1 vi:2 thus:15 herein:2 surface:12 according:5 ii:21 need:4 examined:1 im:5 demanded:1 dual:1 turns:1 claimed:2 0x:1 vanish:3 solutions:3 result:9 different:7 education:1 verified:2 grant:1 perform:2 dhf:4 make:4 belong:1 same:18 any:13 unity:2 parts:8 quant:1 arguments:7 modification:1 resulting:2 proved:2 document:1 bring:1 meets:1 used:12 see:3 i1:1 i0:134 numerical:1 upon:2 effect:3 flows:2 hand:4 director:1 v1:2 v2:2 v3:2 moving:1 purpose:2 infinite:2 changing:1 opportunity:1 circumvented:1 normalization:3 keep:2 numbered:1 prescribed:1 task:1 off:2 takahiro:1 changes:1 vertices:1 well:11 deal:2 finds:1 without:2 components:1 coordinate:1 position:1 arising:1 self:2 charged:5 kawai:3 distances:4 just:6 appropriately:2 being:4 x1:14 numbering:1 obtain:6 intervals:4 identify:1 using:9 λj:11 momenta:1 scattering:3 λm:1 cn:2 oriented:1 enters:3 conclusions:2 photons:7 extra:2 character:1 except:2 add:1 internal:2 combine:1 theorem:3 guarantees:1 disrupt:2 transformation:4 momentum:2 take:1 real:7 increased:1 government:4 rules:2 evaluate:1 couple:1 term:19 cf:5 increases:1 ej:17 excluded:1 confined:1 integer:13 unique:1 heaviside:1 occurring:2 insert:1 76sf00098:1 nakanishi:2 pertinent:1 like:3 particle:4 follows:11 reduces:2 performing:2 acts:1 δs:1 noted:1 specific:1 index:6 either:6 integrals:8 arbitrary:1 leaves:1 works:1 soft:5 reduced:2 replacement:3 mathematical:3 pertaining:1 because:6 often:2 classical:4 smoothly:1 tells:1 maintained:1 some:25 back:1 added:1 evaluated:2 choosing:3 recommendation:1 kinds:1 repeated:1 nonzero:6 separately:1 scale:2 lead:1 confirm:2 electromagnetic:2 rℓ:1 xg:2 integration:21 legal:1 flow:4 does:7 decomposition:1 eliminate:1 tends:4 cnm:5 tk:1 refer:1 particular:2 run:4 scientific:2 power:4 kyoto:2 tail:4 aj:3 expansion:4 disappeared:1 step:2 although:1 qˆ:1 imaginary:2 ignored:1 properties:2 manufacturer:1 integers:6 actual:1 anything:1 impose:1 column:2 domains:4 completing:1 discussed:2 a3:3 important:2 plus:1 positive:13 connected:1 introduced:3 consequently:2 other:15 allowing:1 warranty:1 computational:1 letters:1 decreased:1 formerly:1 assignments:2 jn:4 into:28 within:2 integral:36 three:12 multiply:1 appropriate:1 en:9 references:2 operator:5 factor:13 log:157 prepare:1 strictly:4 there:5 question:4 specifically:1 way:3 labelling:2 flowing:1 subsequent:1 was:11 assumes:2 m0:9 function:47 head:3 north:1 interest:3 form:70 ed:1 hp:3 trivector:2 but:14 mm0:3 change:2 pj:1 hh:4 integrations:2 repeatedly:1 justify:1 convergence:2 mln:1 line:50 conventions:1 true:1 auxiliary:1 kℓ:2 made:1 improved:1 formulas:1 whether:1 up:3 us:14 ωi:6 placed:1 below:5 ωj:20 limit:1 verification:1 problem:5 similar:4 called:2 care:1 regimes:1 originating:1 sort:1 required:6 associated:19 separability:1 introducing:1 defined:17 likewise:1 abstract:1 specified:4 condition:11 remove:1 covers:1 general:10 examine:3 exist:2 dλ:13 our:10 formalism:1 proceeds:2 constructed:2 again:6 functions:14 completeness:1 weakened:1 no:9 dressed:1 whereas:1 when:6 vanishes:4 scaled:3 field:3 regents:3 role:2 papers:2 department:1 electrodynamical:1 polar:1 formed:2 star:6 completes:2 separate:4 become:1 problems:4 polynomials:1 prepared:1 a1:1 generated:2 a2:3 bounded:4 a4:1 variable:14 sides:4 structure:9 interval:2 implies:1 coupling:16 assume:3 factors:5 changed:2 accumulations:1 together:2 having:3 ments:1 implied:1 procedure:3 demonstrates:1 failures:1 applied:1 starting:1 original:3 provided:5 once:1
|
quant-ph9502008.txt |@word urbana:1 customary:1 consider:4 leads:1 eds:1 concept:1 philosopher:1 computation:2 go:2 liar:2 mccarthy:1 depend:1 subjected:1 deterministic:1 ts:2 nonlocal:2 passage:1 does:1 permanently:1 marks:1 tb:6 sent:1 ta:10 case:1 finkelstein:2 very:3 than:1 rise:1 seemingly:1 handling:1 anonymous:1 randomness:4 unlike:1 level:3 transmission:1 ref:1 solution:2 ossler:3 wolfram:1 yale:1 eigenvalues:1 solutions:1 des:1 deutsch:4 consistent:5 barendregt:1 tex:1 crete:1 zero:1 perspective:1 anton:1 dynamics:1 implemented:1 situated:1 machines:1 scientific:3 even:1 what:3 stands:2 apparatus:1 giving:1 diag:1 uniform:1 henceforth:2 consistently:1 experiment:1 above:6 capital:1 new:8 method:2 paradoxical:6 margolus:1 ibid:2 exchange:1 respectively:3 here:1 objects:1 others:2 represented:1 path:5 appears:1 extrinsic:1 arena:1 operational:2 search:2 bible:1 singapore:3 cbit:9 allows:1 contradiction:1 analogon:1 resulting:2 real:1 opinion:1 studies:1 via:4 merwe:1 requiring:1 plenum:1 logical:2 outcomes:8 austria:1 names:1 total:1 unit:1 solovay:1 use:5 feb:1 figure:2 would:5 remains:1 contains:1 toffoli:1 classically:2 automata:2 overhead:1 telegraph:3 taken:1 themselves:1 type:5 theoretical:3 more:3 sessions:1 heijenoort:1 berlin:3 controlling:1 labelled:1 particular:6 foundations:3 cases:1 must:2 springer:2 tokyo:1 science:1 setup:2 work:1 remain:3 publications:1 concepts:1 following:3 europhysics:1 il:1 control:4 indicated:1 stated:1 discussed:1 inaccessible:2 agent:4 pieces:1 states:12 contradicts:1 performed:2 allowed:2 unphysical:2 verlag:1 information:27 recursive:1 syntactic:1 rather:1 s2:1 s1:1 feature:3 how:1 nontrivial:1 weibel:1 opt:1 gate:1 parameter:7 94a:1 inputs:1 description:2 monatshefte:1 may:1 turing:1 after:1 applications:1 produce:1 physik:2 society:1 gdansk:1 natural:1 effective:1 whenever:1 register:1 lines:2 correspond:1 st:4 switch:1 fundamental:1 lambda:1 order:2 talk:1 produces:1 indeed:1 pointed:1 interpreted:1 symbols:4 experiments:2 london:1 signs:1 japan:1 its:4 before:2 perfect:3 controllable:2 probability:4 send:3 cbits:1 actually:1 undecidability:4 systems:5 inconsistencies:2 mail:1 hidden:3 might:1 versus:1 them:1 incompleteness:2 thereby:3 schilpp:1 universality:1 processes:1 kamefuchi:1 they:1 oxford:3 subluminal:1 hall:1 eigenvalue:1 february:1 several:1 always:1 university:9 mode:2 arrow:1 die:1 universit:1 cliffs:1 side:1 constraints:1 combinatory:2 house:1 revised:1 stronger:1 related:2 operator:6 computable:1 sketched:1 quantum:30 shannon:1 out:3 living:1 shown:2 space:2 nuovo:1 since:6 rev:8 research:1 particles:4 re:1 mediated:2 hill:1 denoted:1 cause:1 independence:1 common:1 foundation:1 perception:1 theory:19 diagonal:1 reason:1 base:1 formation:1 york:6 put:2 van:1 jozsa:1 pairs:1 backwards:2 benioff:1 language:4 english:1 prophet:1 could:2 computers:3 british:1 thing:1 technische:1 davis:2 onto:1 stimulate:1 first:2 initial:1 features:1 manuscript:1 martin:1 combinator:1 variables:1 coding:1 reflected:1 theoretische:1 another:3 impossible:2 angular:3 aharonov:1 city:1 given:3 cartesian:1 fair:1 their:1 cambridge:8 top:1 amsterdam:3 system:5 construct:1 indicate:1 assumption:3 hypothetical:1 postulate:3 scheme:1 discussion:1 a32:1 statement:2 relationship:1 brains:1 exactly:1 albert:2 took:1 immediate:1 speakable:1 regards:1 off:1 eliminated:1 haven:1 kind:1 perfectly:2 holland:4 penrose:1 cimento:1 second:3 submitted:2 preparation:1 defense:2 amplitude:2 were:2 letters:2 vienna:1 solely:1 result:2 pre:1 minds:1 epr:5 topics:1 argument:4 curves:1 already:1 say:2 manner:1 kleene:1 sentences:1 need:1 north:4 any:8 paths:1 centennial:1 angle:3 mermin:1 self:1 able:1 note:1 instance:1 cantor:1 timelike:3 transmit:1 channel:1 calculus:1 pain:1 opposite:1 who:1 singlet:1 most:1 regular:1 locality:1 letter:2 device:1 coin:1 measured:1 inconsistency:1 rogers:1 exo:1 professor:1 later:1 flow:4 physica:1 tph:1 feynman:2 accounted:1 principle:1 hamming:1 databases:2 d44:1 physics:10 review:1 fact:2 bell:2 paul:2 phenomenon:1 neumann:1 fifty:1 halting:4 registers:1 inconsistent:3 fuzzy:1 translation:1 paradoxes:4 computability:1 unther:1 based:1 popescu:1 implementation:1 less:1 outside:1 universal:1 should:3 only:6 annals:2 postulated:1 isham:1 local:1 do:2 means:1 overall:1 truly:1 beam:6 cannot:2 closely:1 despite:1 compute:1 evolution:1 continuum:1 titus:2 arxiv:1 tuned:1 scientist:1 processed:1 fixed:6 discussing:1 valid:1 view:3 reveals:1 requirement:1 potentiality:1 observer:6 achieved:1 physically:3 tossing:1 correlations:4 lazy:1 operates:2 relative:2 edition:3 namely:1 computer:3 devices:2 existence:1 close:1 theoretic:3 alternative:1 philosophy:2 realizable:1 seminars:1 said:1 mechanically:1 expert:1 shimony:4 artificial:1 eigenstates:1 state:8 identification:1 closed:3 between:1 qbits:2 drawn:3 prentice:1 notice:2 terms:1 gedanken:1 citation:1 however:1 jr:1 blame:1 news:1 rohrlich:1 suggested:2 both:2 outcome:15 tractable:2 many:2 ill:1 uncertainty:1 against:4 und:1 receives:2 logic:6 reply:1 argue:2 confronted:1 jersey:1 otherwise:1 comment:1 among:1 ch:1 point:8 cf:4 active:1 maintained:1 non:1 evanston:1 throughout:1 moore:3 macdonald:1 described:1 krenn:1 basis:3 wien:1 due:1 been:5 strategy:3 defined:1 odel:8 96b:1 recognize:1 collected:1 ph:1 formalized:1 fig:2 elitzur:1 obtained:1 direction:2 contribute:1 corresponding:8 received:2 coherence:1 remark:1 zeilinger:1 coherent:4 observe:1 spin:1 applied:2 novel:1 exponential:1 wiedner:1 appearance:2 will:6 properly:1 procedure:1 resolved:2 unitary:1 dictum:1 orientation:1 phenomenological:1 von:1 epistemological:1 thus:4 coffee:1 encountered:1 ii:3 itself:2 tuwien:1 partner:2 containing:1 d10:1 atmanspacher:1 author:2 journal:4 recursion:9 make:1 intrinsic:5 lett:6 same:1 princeton:2 stimulated:1 quant:1 arguments:1 pauli:1 gets:1 events:1 ac:1 used:5 see:2 undecidable:3 evil:1 hand:1 uses:1 implements:2 task:4 shortly:1 database:1 nonetheless:1 well:2 without:1 components:1 consistency:2 just:3 sentence:1 transmitting:1 when:2 rest:1 unary:1 stored:1 questions:1 yes:2 yet:3 qbit:6 contradicting:2 preprint:1 sciences:2 percent:1 mirrored:2 passive:1 instrument:1 setting:4 treatment:2 innocent:1 theorem:1 diagonalization:7 input:1 mod:2 eigenstate:1 momentum:3 raven:1 identical:1 pitowsky:3 sequential:1 alternatively:1 read:1 phenomenology:1 possible:3 corresponds:1 entangled:3 press:11 world:6 bit:7 formal:4 generated:1 englewood:1 necessary:2 particle:4 identifying:1 follows:2 signal:1 johann:1 specific:1 either:2 arbitrary:3 translated:2 output:2 works:1 reduces:1 accessible:1 because:1 methods:1 classical:15 obliged:2 phenomena:1 back:1 convey:1 mirror:1 complementarity:2 universes:1 proofs:1 happens:1 delivered:1 informationtheoretic:1 lead:2 bottom:1 tasks:2 prison:1 avoid:1 shall:4 comments:1 recami:1 hauptstraße:1 proc:4 refer:1 measuring:1 algorithmic:2 truth:1 power:1 idealistic:1 nonclassical:1 equivalent:2 processing:2 clarendon:1 symp:1 refers:1 svozil:7 chapter:1 about:1 propositions:1 theorems:2 introduces:1 dependence:5 o:3 nonvanishing:1 reproducing:1 curry:1 block:1 considerations:1 soc:3 own:2 dilemma:1 into:1 within:2 implications:1 references:1 einstein:2 elementary:2 versions:1 technically:1 acknowledgements:1 institut:1 few:1 assumed:2 there:6 question:1 lond:3 anderson:1 ed:10 forward:1 conceivable:2 was:1 uncontrollable:1 therefore:2 arise:1 complete:3 form:4 some:1 registered:1 but:2 chaitin:1 volume:3 mechanistic:1 construction:1 atom:1 true:1 arranged:1 embedded:1 deterministically:1 whether:1 inside:1 us:2 ur:2 international:3 below:1 rothstein:1 problem:2 similar:2 called:3 mechanics:5 bearing:1 controllability:6 choosing:1 computing:1 int:1 certain:2 abstract:3 measurement:7 general:3 peres:2 referee:1 exist:2 controlled:1 dawson:1 computational:1 physical:5 again:1 functions:1 paradox:11 no:7 mathematik:1 claiming:2 illinois:1 application:1 other:3 role:1 details:1 revisions:1 arithmetic:3 conclusion:1 superposition:5 resembles:1 inescapable:1 deriving:1 chance:1 important:2 variable:1 structure:1 relativity:1 feferman:2 correlated:1 individual:1 algorithm:4 vigorously:1 d27:1 impossibility:3 reprinted:3 time:16 popper:1 signalling:5 backward:7 requires:3 unspeakable:1
|
quant-ph9502009.txt |@word consider:3 rev:2 results:1 leads:1 comments:1 expressions:1 whose:1 depend:1 kλ:1 analogous:1 include:1 divergent:3 applied:1 very:1 wave:3 putting:1 experimentally:1 gkλ:8 hamiltonian:3 cause:1 solution:1 vector:2 warszawa:1 zk:3 consistent:1 direct:1 sign:1 approximation:3 rate:1 even:2 aim:1 sum:1 brief:1 d3:3 experiment:1 spacing:1 equals:1 here:1 atoms:2 address:1 represented:1 based:3 z0:4 appears:1 obtained:3 institute:1 shift:4 vectors:2 resulting:1 stressed:1 makes:2 golden:1 unit:2 conventional:1 feb:1 would:6 therefore:1 theoretical:1 more:1 knows:1 operators:1 emission:5 given:3 must:2 valued:1 ma:1 mc:2 equation:3 obvious:1 following:1 spontaneous:3 compare:1 calculation:1 discussed:1 occur:2 lamb:1 rather:2 feature:1 pure:1 instead:1 ordinary:2 simplicity:1 fw:1 ow:1 centrum:1 choice:1 constants:3 light:2 order:1 wigner:1 over:1 spectral:1 nsk:1 through:1 argued:1 kinetic:1 its:2 before:1 thank:1 chosen:1 interesting:2 permanent:1 matematyki:1 greater:1 introduce:1 now:6 bigger:1 represents:1 term:12 fizyki:2 level:1 found:2 heavy:1 significantly:1 ek:2 dωk:1 ed:3 energy:1 frequency:1 laboratory:1 shown:1 matrix:1 robert:2 since:2 interference:1 rz:2 research:1 electronics:1 evaluation:1 shows:1 marek:1 doppler:3 theory:1 divergence:1 ewski:2 standard:4 divergency:3 difficulty:1 reason:1 put:2 beginning:1 βt:2 interaction:9 could:1 consequence:1 moving:2 neglect:1 first:4 already:1 probability:4 rank:1 done:1 akλ:2 differ:1 leading:1 system:1 ekλ:3 too:1 calculations:5 part:2 authors:1 eliminated:1 than:2 zakowicz:1 spectrum:2 strength:1 physique:1 polarization:2 ˆp:4 electric:1 opposite:1 denominator:2 involving:1 considered:1 stronger:1 velocity:1 fact:2 solutions:1 d2:3 find:3 teoretycznej:1 weisskopf:1 should:1 only:2 explicitly:2 summarizing:1 emitting:1 do:2 his:1 dependent:2 report:1 arxiv:1 twice:1 investigate:1 hβ:1 hα:1 packet:2 observed:1 see:1 result:1 terms:3 αt:1 pattern:1 dipole:7 state:3 fermi:1 approach:1 recently:1 modify:1 wm:1 emitted:2 however:2 both:2 essentially:1 last:1 infinitely:1 dγp:2 quantization:1 contribution:3 expression:1 otherwise:2 reasons:1 directions:1 pole:1 kazimierz:1 simply:1 polynomial:1 hω0:7 criticised:1 been:1 much:1 basic:1 pj:1 pk:2 ph:1 wants:1 direction:4 corresponding:1 photon:2 c2:6 present:2 p2:2 nska:1 value:1 spontaneously:1 will:4 eik:1 hωk:7 procedure:1 vk:1 ii:1 pathology:1 technology:1 radiation:3 same:3 shifts:1 quant:1 wavepacket:2 modification:3 wilkens:4 pan:1 moment:3 uses:1 infinite:3 schr:3 center:2 poland:2 gda:2 shape:2 atomic:13 momenta:2 rapid:1 density:1 seems:1 haf:2 mathematically:1 usage:1 momentum:5 identical:1 ωk2:2 like:1 follows:4 martin:1 because:1 growth:1 neglecting:1 provided:2 lead:2 per:1 does:3 eliminate:2 assuming:1 formfactor:2 who:1 equivalent:1 perpendicular:2 2m:11 properties:1 stage:1 reappear:1 numerator:2 dependence:5 patern:1 trustworthy:1 mixed:1 seeing:1 cambridge:1 inclusion:2 integral:2 operator:1 proportional:1 additional:3 initial:2 way:3 opposed:1 lotnik:1 form:1 hv:1 but:5 volume:1 hk:1 recoil:5 atom:4 elimination:1 line:1 ha:2 hf:2 absent:1 2πc:1 ωk:5 limit:3 distribution:2 czachor:1 describe:1 single:1 lifetime:1 az:2 physical:1 again:1 nk:8 field:3 role:1 problems:1 odinger:3 massachusetts:1 additionally:1 included:1 coupling:7 assume:1 rule:2 mass:6 time:2
|
quant-ph9502010.txt |@word ibid:1 partial:3 consider:8 illustrates:1 squared:1 magnetic:4 reversibility:1 extensively:2 leads:1 commute:1 entropy:22 consists:1 follow:1 contributions:1 dα:1 whose:2 depend:1 technique:2 tr:2 preserved:1 under:6 include:1 norm:2 prigogine:6 far:1 induce:2 wave:8 lyapunov:1 electron:1 every:2 mixing:8 experimentally:6 emphasized:1 exact:1 condition:8 school:1 hamiltonian:9 proc:3 erratum:1 t2:1 large:1 au0:1 vector:1 small:1 eigenvalues:1 degeneracy:3 tel:2 consistent:5 measurable:4 second:3 evaluated:1 defines:1 implemented:1 canonical:1 even:6 what:1 appear:4 apparatus:1 section:1 version:1 localized:1 above:5 lifshitz:1 new:5 method:1 satisfy:1 evolving:1 full:4 degree:1 excludes:1 respectively:1 component:6 here:3 desired:1 possibility:1 opposite:1 concluding:1 appears:1 change:6 obtained:2 remark:1 weisskopf:1 rigorously:1 study:2 changed:2 resulting:3 therein:1 suitable:1 sci:3 uniquely:1 equivalence:7 useful:1 projection:2 classification:1 app:1 convexity:1 regeneration:1 stern:1 meson:1 univ:1 linearly:1 use:3 98a:1 feb:1 asymptotic:7 would:2 positive:2 contains:2 properties:1 call:2 therefore:18 fonda:2 taken:1 theoretical:2 reflects:1 more:2 israel:2 operators:5 validity:1 reversible:1 normalized:3 particular:3 known:3 foundations:2 iv:1 iii:1 must:1 involve:1 springer:2 ρe:2 khalfin:1 integrating:2 work:1 dokl:1 taup:1 itself:1 values:3 ρt:1 ρˆe:5 following:1 koopman:2 example:10 purity:7 defer:1 rosenfeld:1 process:1 choice:1 states:27 effectively:34 performed:1 degenerate:1 sense:1 keep:1 namiki:1 axis:1 information:4 unmeasurable:2 requirements:1 provide:1 discussion:3 holds:4 ghirardi:2 deµ:1 a173:1 pure:48 acta:2 verlag:2 sin:2 simplicity:2 description:4 may:13 wiley:1 ρˆt:1 lax:1 fe:2 faculty:1 multiplication:1 law:1 constants:1 realized:1 short:2 natural:4 dynamical:4 effective:16 explicit:1 correspond:1 element:2 rather:3 so:3 specifying:1 fundamental:2 sudarshan:1 representation:7 eisenberg:1 order:1 se:1 acts:2 wigner:1 over:9 dek:1 years:1 course:2 through:2 looks:1 statistical:6 argued:1 existence:3 satisfies:1 still:1 its:3 before:1 phillips:1 thank:1 decay:3 chosen:1 extract:1 scully:1 li:8 aviv:3 degrees:2 systems:8 schmidt:2 into:2 weber:1 arguments:1 correspondence:1 factorizability:2 non:10 horwitz:4 propose:1 processes:1 framework:3 they:1 oxford:2 singularity:1 now:4 dede:1 term:2 university:2 level:1 b3:2 factorizable:5 l2:1 l0:8 each:6 found:2 2n:1 subset:7 domain:1 formulate:1 evolve:4 experiment:1 tre:3 energy:13 principles:1 related:1 sinha:1 decays:1 obtains:4 measure:2 quantum:19 our:1 operation:1 eq:6 out:4 shown:9 matrix:14 space:30 restricted:2 furthermore:1 since:9 induces:2 george:2 increase:1 contained:1 europhys:1 induced:2 ref:1 occurs:2 math:2 shows:2 theory:7 interactions:2 dξdξ:1 diagonal:3 free:12 trˆ:2 admits:1 necessarily:1 york:3 jour:1 interaction:2 pascazio:1 imry:1 times:1 motion:4 introduction:2 hence:5 pitaevskii:1 destruction:1 first:2 initial:5 variables:16 number:2 iht:1 transform:2 carry:1 impossible:1 open:1 angular:1 aharonov:1 illustrate:2 given:6 perturbation:2 unitarity:4 φe:3 sackler:1 system:14 construct:1 their:3 calculations:1 realization:1 scheme:1 final:1 gives:1 ih0:1 continuous:3 foliation:2 prediction:1 translation:2 representing:2 18b:1 observed:1 18a:1 cimento:2 zero:3 determined:2 were:2 tion:1 distinguished:1 exhibit:1 rimini:2 sees:2 nuovo:2 boston:1 spectrum:9 conjugate:2 misra:6 clearly:1 elsewhere:1 chem:1 angle:1 general:7 lim:3 dωk:6 ideas:3 mechanism:7 note:5 sciences:1 k1:10 potential:4 generalized:4 k4:8 coincide:1 a39:1 unperturbed:9 heisenberg:2 play:1 keldysh:1 unless:2 antoniou:3 trace:8 shall:3 trρ:1 unmeasured:2 phase:5 intrinsic:2 class:8 subspaces:6 clear:3 later:2 detectors:1 physica:5 typeset:1 traditional:1 feynman:1 mechanical:2 petrosky:2 physics:2 notion:2 fact:3 laws:1 precise:3 selection:1 show:6 definite:1 attempts:1 helv:2 trρ2:1 interpretation:1 aρ:2 based:1 parameters:2 aω:1 state:61 only:10 explicitly:3 candidates:1 admixture:1 integrable:1 constant:3 he:7 pointed:1 achieve:1 equilibrium:2 characterization:2 do:5 his:1 il0:2 means:3 dependent:3 zurek:2 de:4 expectation:8 truly:1 pions:1 beam:1 cannot:2 during:5 gen:1 evolution:33 bar:1 fields:1 arxiv:1 nauk:1 predicted:1 4πa:2 view:3 respond:1 kernel:4 set:6 computed:1 exists:3 undergoes:1 correlations:1 gottfried:1 detection:1 mentioned:2 see:12 result:2 recently:1 momenta:1 techniques:1 eigenfunctions:1 nondegenerate:1 macroscopic:1 convex:1 ωk:5 µr:2 written:2 closed:1 between:2 conditions:1 preserve:1 terms:4 nature:3 initially:2 a41:1 weak:1 however:8 vanishing:1 distinguish:2 jetp:1 concentrated:1 both:3 essentially:1 cor:1 lebesgue:1 limits:1 many:2 taking:1 conclusions:1 equal:9 ln:3 ilt:2 context:2 argue:1 whole:1 experimental:2 arbitrarily:1 relevant:1 point:5 simple:3 corresponds:7 translationally:1 alone:1 maintained:1 simply:1 nat:3 respect:2 writing:1 levitan:3 amrein:1 described:4 basis:5 due:3 been:3 screened:3 reduction:10 coarse:2 basic:1 microscopic:2 ph:1 prototype:1 dk:2 define:7 field:4 describe:1 corresponding:4 observable:6 quantities:2 concerning:3 subspace:8 cos:3 argument:1 gan:1 observe:1 external:1 worked:1 presented:1 those:1 case:7 extracted:1 look:1 exponential:2 akad:1 value:5 transformation:1 will:1 while:2 behavior:2 applies:2 exist:6 property:2 dkdk:5 walther:1 identical:2 unitary:1 vol:1 vi:1 thus:7 them:1 according:3 ii:2 characterize:3 obstacle:1 dual:1 yukawa:1 increased:1 connection:1 same:2 any:2 shifts:1 unity:1 quant:1 emphasize:1 d19:1 dimensionless:1 electro:3 ludwig:2 neutron:1 independent:11 used:5 raymond:1 trivially:1 upon:1 effect:1 hand:2 changing:1 recent:1 fourier:3 k22:3 k21:3 well:11 concrete:1 solve:1 components:2 ae:1 arising:1 usual:7 manifold:5 just:2 when:1 obtain:1 underlying:1 identify:1 atomic:4 λe:2 k2:11 scattering:2 yet:1 previous:1 adv:1 k3:8 preprint:1 generator:2 density:18 conclude:1 signals:2 belongs:1 lett:1 easy:1 theorem:1 b12:1 excited:1 momentum:2 take:1 real:1 aspects:1 eigenfunction:1 possible:2 additivity:1 hove:1 increases:1 press:2 using:3 formal:1 dimensional:1 necessary:1 particle:2 semi:3 follows:7 signal:1 translates:1 specific:1 wooters:1 unstable:9 either:1 integrals:1 martin:1 beverly:1 become:5 pointwise:1 reduced:8 accessible:3 reidel:1 because:1 old:1 often:1 classical:13 discrete:1 absolutely:2 some:4 b4:1 b5:1 b6:1 b7:1 b1:1 b2:1 moreover:1 b8:1 b9:1 scripta:1 dimensions:1 lead:1 measurements:4 integration:1 comments:1 eiξ:1 does:8 decomposition:1 provides:4 tends:1 prog:1 propagating:1 imply:1 demonstrated:1 yvon:1 rep:1 illustration:1 revtex:1 2m:1 tasaki:1 repts:1 hilbert:11 takes:3 15a:1 aca:3 actual:1 carried:1 freedom:3 discussed:3 dependence:1 o:3 essential:1 mixed:20 introduced:1 consequently:1 mathematical:2 rev:4 presence:2 pergamon:2 h0:5 integral:4 three:1 remarks:1 appropriate:1 ussr:1 references:2 determine:2 operator:33 wξ:3 next:1 van:1 ek:23 measured:1 strictly:1 there:3 available:1 u0:2 long:1 strict:1 ed:1 was:2 function:13 complete:1 form:10 pe:7 but:8 construction:1 atom:1 ramat:2 irreversible:3 truncation:1 rephaeli:1 made:2 whether:2 wish:2 inside:1 up:1 liouville:18 operationally:1 sum:1 demonstrate:1 problem:3 ωe:1 called:2 entropies:1 mechanics:14 required:1 associated:7 defined:19 coincides:1 measurement:7 denote:2 dξ:2 chap:1 au:1 formulation:1 dβ:3 physical:8 functions:1 no:4 liouvillian:8 commutes:1 generally:2 vanishes:4 schwinger:1 application:1 other:5 role:1 details:1 b10:1 b11:1 department:1 sufficient:2 picture:2 elements:8 intend:1 ilan:1 photon:1 preceding:1 reached:1 includes:1 a1:1 commutator:1 develops:1 a2:1 bounded:2 variable:3 exner:1 structure:5 fundamentally:2 implies:3 coupling:2 coulomb:3 interval:1 kinetics:1 d24:1 graining:2 appendix:8 time:18 observables:19 original:3
|
quant-ph9502011.txt |@word proposition:1 represent:2 concepts:1 consider:2 lack:1 results:1 leads:1 concept:2 stops:20 go:1 adhere:1 reasoning:1 whose:8 certainly:1 depend:1 ac03:1 equivalence:1 c5:1 whatsoever:1 under:1 include:2 division:1 imagines:1 mainstream:2 far:7 liability:1 every:5 govern:3 difference:1 condition:2 level:1 did:1 occurs:1 try:1 solved:3 differential:1 indices:4 noted:1 disclaimer:1 quantifiers:1 direct:1 imply:1 enclosed:1 rigorous:2 comprehend:1 even:1 index:8 what:16 apparatus:1 sum:1 expressed:2 version:1 above:2 new:1 ever:4 seeks:2 full:2 never:32 commercial:1 answers:2 understanding:1 behaviour:1 desired:1 them:2 berkeley:3 represented:7 strong:2 equations:2 obtained:1 search:3 rests:3 employees:1 allows:1 contradiction:5 products:1 advertising:1 published:1 action:1 provable:2 makes:2 useful:2 merely:5 logical:4 assertion:2 weaker:3 privately:1 should:3 establish:2 use:5 feb:1 proceed:2 would:18 give:1 next:1 therefore:6 survive:1 type:13 entails:2 more:4 introducing:1 formally:1 knows:1 becomes:2 sect:1 aware:1 virtue:3 particular:1 known:6 cases:2 document:2 must:10 high:2 account:1 ma:1 rights:1 science:3 work:3 values:4 henry:1 believed:1 sets:2 my:2 example:2 proof:9 claim:1 tenets:1 indicated:1 stated:4 process:27 december:1 sense:1 purposes:1 states:4 assumptions:1 numbers:10 allowed:3 conversely:1 occur:1 information:2 united:4 turn:1 rather:1 holds:1 machine:1 necessary:1 imbedded:2 pure:3 endorsement:2 answer:4 instead:2 begs:1 product:2 express:2 monatshefte:1 our:1 turing:3 after:1 derived:1 reflect:1 produce:1 designed:1 physik:1 cambridge:1 namely:1 natural:14 conscious:1 following:1 sq:1 provide:1 ones:1 responsibility:1 specifying:1 allow:3 suggest:1 kurt:1 granted:1 terms:2 acts:1 office:2 indeed:2 over:8 mainly:1 trade:1 symbols:7 brain:15 mathematicians:4 own:1 through:1 argued:1 existence:1 its:5 diagonalized:1 derive:1 how:4 solving:2 writing:1 forms:1 absence:1 disclosed:1 listing:4 frege:1 might:5 non:1 views:1 questions:2 runs:3 framework:2 thereof:3 they:4 oxford:2 now:1 nor:3 shadows:1 represents:2 finite:9 name:1 mathematician:3 university:6 truths:1 identified:2 applied:1 iff:3 each:6 found:1 characterized:2 mean:2 domain:1 square:1 mental:4 ed:1 energy:4 programmed:1 idea:1 him:1 constitute:1 computable:2 expect:1 quantum:2 laboratory:2 operation:2 avoided:1 adequately:1 out:2 living:1 shown:1 rp:3 fundamentally:1 restricted:1 since:3 research:1 may:1 get:3 correct:1 theory:3 lawrence:2 activity:7 possibility:1 reason:1 california:5 definition:1 language:1 could:14 computers:3 appearing:1 hence:6 onto:2 major:1 variables:1 number:17 owned:1 construct:1 another:1 necessarily:2 exists:5 service:1 indicate:1 introduction:1 system:3 least:1 their:4 assumption:9 thoughts:1 statement:1 convention:1 ranging:1 gives:1 collapse:1 relationship:1 brains:4 contains:1 serve:1 authors:1 attempt:1 operates:1 than:3 intrinsically:1 whereby:3 finitely:5 kind:1 penrose:14 see:1 computer:7 supposed:2 were:7 solely:1 result:2 pre:1 mind:7 argument:31 say:3 need:2 demonstration:1 lbl:1 refute:2 latter:2 agency:3 able:5 ideas:1 stapp:1 transcribed:2 take:1 indexed:1 so:4 coincide:1 accuracy:2 subscripts:1 sure:1 asserts:1 shall:1 who:1 reach:3 regular:1 sponsored:1 pair:8 intrinsic:1 jean:1 unknowable:1 cover:1 lacuna:1 construction:3 principle:3 mechanical:5 physics:4 section:1 fact:4 laws:1 show:2 supported:1 terminate:1 contemporary:1 relation:1 solutions:1 determined:1 find:1 ground:1 computability:1 knowledge:2 spite:2 implementation:1 writes:2 written:3 employer:1 being:1 only:6 explicitly:1 do:3 his:2 goes:2 notation:2 means:8 de:1 stop:28 cannot:4 finitistic:2 expresses:1 compute:1 neither:1 qp:4 processes:15 arxiv:1 yield:1 roger:2 contain:1 fixed:4 favoring:1 view:1 set:23 human:11 reference:1 hypothetical:1 reductio:4 connections:1 depends:3 individual:2 usefulness:1 fail:1 close:1 activities:1 analog:2 points:1 amalgamated:1 fails:2 mechanically:1 nuclear:1 state:1 smallest:1 various:2 between:1 subscript:3 encounters:1 available:1 recently:2 missing:2 importance:1 however:4 harvard:1 hypothesis:1 key:1 distinguish:1 come:1 relying:1 ranges:2 parentheses:1 equal:2 contract:1 connection:2 und:1 logic:1 distinction:1 otherwise:1 ck:11 presumably:1 conclude:2 simple:2 others:1 whatever:1 simply:1 lagrange:1 moreover:1 cq:11 cp:5 considers:1 startling:1 pp:1 described:3 basis:3 trademark:1 due:1 been:2 relatedness:1 odel:14 expected:1 pk:3 ph:1 universal:1 define:1 arises:1 corresponding:1 reasonings:1 both:1 sufficient:2 propositions:1 maps:2 coherent:1 deep:1 systematic:1 coherency:1 c3:1 c2:1 c1:1 c0:1 c7:1 former:1 those:1 c4:1 case:9 replaces:1 value:3 will:2 pace:1 while:1 replaced:1 stopping:10 property:1 procedure:1 supply:1 almost:1 thus:8 herein:2 surface:1 according:5 ii:1 examined:1 claimed:4 different:3 insofar:1 make:2 same:1 any:19 quant:1 arguments:4 established:1 several:1 difficult:1 fairly:1 used:4 infinity:1 mathematic:1 upon:4 effect:1 hand:1 director:1 domains:1 running:1 infinite:7 overt:1 opportunity:1 identity:2 simulates:1 off:1 reflection:1 well:1 thought:3 without:2 encounter:1 simulated:3 very:1 model:2 justify:1 opinions:1 consciousness:1 heavily:1 hypothesized:2 obtain:1 actions:1 shape:1 underlying:1 identify:3 atomic:1 aspect:1 immediately:1 yet:2 conclusions:1 regarded:1 point:2 exclusively:1 reasons:1 valid:2 theorem:2 input:1 extensive:2 apart:2 aspects:1 government:4 rules:13 possible:5 know:17 press:2 integer:1 unique:3 occurring:1 76sf00098:1 imposed:1 identifying:1 exploiting:1 specific:2 yields:2 either:1 arbitrary:1 output:5 reasonably:2 mathematical:8 pertaining:1 because:3 classical:2 sequence:1 some:15 back:1 recommendation:1 happens:1 provided:1 lead:1 confirm:1 integration:1 legal:1 does:7 refer:2 limitations:1 scientific:2 processing:2 fed:1 constructive:1 step:2 although:1 super:1 properties:1 manufacturer:1 about:1 carried:1 anything:1 entailed:1 dependence:10 recognized:1 practical:1 range:1 act:1 introduced:1 consequently:1 other:4 warranty:1 specifies:1 computational:12 statements:1 unbounded:1 into:4 within:4 down:1 included:1 beings:4 references:1 quickly:1 mere:1 argumentation:1 van:1 deal:1 assumed:2 strictly:1 there:21 question:5 approximate:1 specifically:1 restricts:1 way:6 conceivable:1 was:3 assumes:1 complete:3 form:4 but:7 idealized:1 properly:1 satisfactorily:1 line:18 trying:1 true:6 he:6 breakthrough:1 applying:1 characteristic:1 up:1 us:4 ur:1 discretized:1 below:1 demonstrate:1 problem:3 obtains:1 ab:1 proved:5 ad:4 defined:2 certain:3 abstract:1 specified:5 am:4 covers:1 general:2 aq:9 single:2 diverse:1 exist:1 governed:2 formulation:1 formalism:1 physical:1 absurdum:4 functions:2 beyond:2 completeness:1 no:14 operating:2 whereas:2 when:2 regents:3 details:2 outputs:3 department:1 really:1 offered:1 arithmetic:2 conclusion:8 elements:2 initio:1 symbol:4 problems:2 prepared:1 a1:1 important:1 variable:3 needed:2 structure:1 rq:3 implies:3 happening:1 using:1 assume:2 organism:1 required:1 rule:8 notion:2 implied:1 time:2 strings:1 once:1
|
quant-ph9502012.txt |@word neighbors:3 represent:2 concept:2 allowed:3 consider:3 springer:1 priori:1 rev:2 magnetic:1 global:2 focus:1 existing:3 psyche:1 eds:1 habits:1 computation:1 shafts:2 consists:6 sci:3 wholly:1 centimeter:1 causes:1 seemed:1 relationships:1 content:1 certainly:4 maximally:1 number:5 calculate:1 ac03:1 involve:1 interactions:2 tn:3 leibniz:2 program:1 device:2 present:1 under:2 branches:16 stochastic:1 ontological:6 include:1 facilitation:1 activities:5 force:1 infinite:1 advantage:2 outside:3 far:2 assuming:1 focussing:1 wigner:5 wave:5 liability:1 every:3 entries:1 participatory:1 bringing:1 condition:1 splits:1 entire:8 neurological:1 unlike:1 level:34 cosine:1 conceive:1 integrating:1 solution:1 occurs:4 large:15 coming:1 excessively:1 grafting:1 recall:1 quick:1 provided:2 disclaimer:1 limitations:1 revolution:1 neighborhood:1 occurrence:5 ten:1 construed:1 dealing:2 consistent:1 stochastically:1 direct:2 sign:1 past:1 go:2 imply:1 dualistic:5 perspective:2 publicly:1 pass:1 available:1 dynamics:8 odd:1 folk:4 linear:1 even:3 resurgence:1 what:11 appear:1 apparatus:1 cast:1 giving:2 specification:1 associate:2 expressed:2 access:1 paying:1 version:2 above:2 scientists:1 new:8 public:2 developments:1 body:8 evolving:3 full:1 led:2 efficacious:3 whose:1 vi:1 concepts:3 commercial:1 supposedly:1 here:6 understanding:4 conglomerate:1 following:1 objects:3 possibility:2 separation:2 berkeley:3 represented:14 ignore:1 sine:1 respect:1 appears:3 change:1 referring:1 box:1 great:1 ref:4 accepts:1 remarks:1 shift:2 employees:1 vectors:1 reason:3 experience:11 example:5 amount:1 simultaneous:1 products:1 advertising:1 suggestion:3 action:3 extends:1 makes:1 involves:2 york:1 composed:1 tour:1 churchill:1 divide:1 criticism:1 extra:4 qualities:1 merely:3 explained:1 treatment:1 marked:1 replace:1 psychological:6 privately:1 actions:2 should:9 causal:1 unit:1 enter:1 derivatives:2 use:1 feb:1 takes:1 would:36 probabilities:2 knit:1 give:3 predictions:2 properties:9 ψj:4 few:3 call:1 therefore:2 criteria:1 taken:2 inner:2 themselves:1 simpler:1 neurons:3 theoretical:7 today:3 more:6 sort:5 almost:1 becomes:2 apparent:2 mismatch:2 conducting:1 antennae:1 whatever:1 visual:1 appendix:3 controlling:1 basically:1 particular:4 known:4 foundations:3 hold:3 effort:1 analogous:1 must:9 me:1 high:10 account:7 ma:1 evolution:5 specifying:1 rights:1 science:4 equation:3 work:3 show:1 faced:1 theories:2 reproduce:1 degrees:1 deficiencies:1 values:18 princeton:1 henry:1 believed:1 my:4 could:11 something:2 control:4 heart:1 transition:2 bell:1 division:2 process:10 ontologically:3 winston:1 abandonment:1 purposes:1 accept:2 states:17 effectively:1 numbers:7 intricate:1 sense:6 interpreted:1 toward:1 tions:1 occur:12 bonded:1 verlag:1 information:20 needs:1 united:4 requirements:1 hoc:3 disruptive:1 rather:12 describes:1 accordance:1 holds:2 sudden:1 feature:4 species:1 chemical:3 how:10 nontrivial:1 behave:1 endorsement:2 instead:2 divides:1 belongs:1 product:2 de:2 description:58 includes:1 communicating:1 replacing:3 suppose:1 philosophy:1 collection:6 reflect:1 produce:1 lay:1 records:6 waves:1 cambridge:1 acquire:1 choice:2 data:2 parallel:3 engineering:2 changes:2 short:1 natural:4 dynamical:11 effective:1 conscious:4 facilitate:1 register:7 explicit:2 correspond:3 element:1 provide:3 complexity:2 tailor:1 responsibility:1 progressively:1 fundamental:6 media:1 representation:3 speculates:1 order:7 receives:1 opens:1 interpretation:2 office:2 considerations:2 indeed:1 over:6 govern:1 trade:1 symbols:1 brain:79 xi:7 disparities:1 statistical:6 argued:1 interpreter:1 excitations:1 its:20 roots:1 before:1 regions:3 accepted:1 conjunction:1 group:1 exclusion:1 fit:1 interesting:1 temporal:1 unexplained:1 durability:1 actually:1 forms:1 appended:1 absence:2 parts:3 microscopic:1 disclosed:1 constitutes:4 quant:1 encapsulates:1 main:3 might:10 pixel:2 overcome:1 interpretive:1 them:4 good:1 greater:2 combination:4 orthodox:2 material:2 school:1 introduce:3 bound:2 break:1 framework:8 thereof:3 they:11 half:1 substrate:1 now:4 day:1 nor:4 structural:4 represents:4 february:1 document:2 name:1 profound:1 always:1 university:5 accompanying:1 appropriate:2 sin:2 possibilities:3 sufficiently:1 firings:3 each:36 2l:6 inherent:1 entirely:1 difficult:1 characterized:2 mean:1 development:1 another:1 weight:1 evolve:2 experiment:1 hundred:1 energy:5 essentially:1 idea:10 constitute:3 fires:1 wires:1 worlds:2 favorable:1 measurement:1 quantum:92 laboratory:2 operation:1 beyond:6 adequately:3 special:4 out:8 principles:2 try:1 freedom:1 psychology:3 space:1 underlying:3 oscillation:1 jump:5 since:1 inadequacy:1 integrative:1 research:1 increase:1 may:2 contained:3 tests:1 reader:1 rm:5 engineer:1 issue:1 correct:1 foundation:2 perception:1 turning:1 theory:50 causally:1 lawrence:2 perfectly:2 activity:5 little:1 free:1 like:4 small:10 completely:10 salient:1 california:5 scientist:1 imagine:2 thrust:1 environment:1 associative:1 distinctive:1 beginning:1 universally:1 transistors:1 retained:1 language:1 via:1 starts:1 just:3 computers:10 positioning:1 keep:1 thing:4 person:1 place:2 massive:2 signature:1 hence:11 configurations:1 onto:2 assign:1 precepts:6 first:4 schema:7 already:8 designed:2 features:2 probability:7 striking:1 facilitating:1 thesis:4 scene:1 owned:1 lahti:1 workings:1 philosophical:1 done:2 adopted:2 directly:3 representations:2 reached:1 precisely:1 quality:9 singling:1 size:2 passes:1 given:6 necessarily:3 reference:5 service:1 similarly:3 introduction:4 extrinsic:8 system:35 construct:1 realistically:1 their:5 grasping:1 too:1 justified:1 underlie:2 postulate:1 john:1 structures:2 ranging:1 gives:1 pervasive:1 cease:1 collapse:5 relationship:3 behind:2 ch:1 brains:10 exactly:2 immediate:3 accords:1 part:5 parsimonious:3 simulate:1 authors:1 attempt:2 requisite:1 representing:3 than:13 specify:2 approximation:1 television:1 molecular:2 correlate:3 coherently:1 surrounding:2 sections:1 distinguishes:1 second:2 final:1 matter:33 future:7 contrary:1 supposed:2 were:3 elaborate:1 contrasted:1 treated:4 distinguished:1 descriptions:2 sees:1 entail:1 pistons:2 dynamically:3 modern:4 mind:40 locations:3 generalization:1 formula:2 say:6 close:1 need:9 seem:7 apparently:1 copenhagen:2 contents:1 relatively:1 realm:3 built:2 zero:2 patterns:3 thoroughly:1 speculative:1 agency:3 able:7 ideas:2 produces:2 belief:17 stapp:4 take:3 objective:4 so:6 analogs:1 mit:2 accuracy:1 heisenberg:13 inequalities:1 play:2 added:4 altered:1 electric:1 shall:3 any:39 underpinnings:1 who:1 vortices:1 spread:1 most:2 involving:2 sponsored:1 ensure:1 analyzable:1 reducible:1 mechanically:1 intrinsic:17 why:4 interacting:1 idealized:1 cause:1 constructed:1 advantageous:1 surprising:1 environmental:1 considered:2 neighboring:1 clear:2 cover:2 drive:2 points:8 electrons:1 principle:6 mechanical:18 everything:1 left:1 physics:30 notion:3 fact:17 laws:9 event:7 incorporate:1 particularly:1 intensity:1 restriction:1 german:1 definite:1 supported:1 devices:1 contemporary:6 discovered:2 bring:4 attempts:1 registers:12 wavelike:1 migration:1 subtle:1 longer:1 fine:1 find:1 ground:1 virtue:4 grafted:1 highest:2 based:1 knowledge:1 reconciling:4 explain:3 heavily:1 specified:8 enough:1 controls:1 employer:1 identifies:1 entities:27 only:15 going:1 generators:1 postulated:1 unsuited:1 adequate:3 local:27 density:1 awareness:3 demonstrated:1 books:1 do:8 move:2 goes:2 get:1 express:2 kind:7 preferred:1 define:2 cannot:3 nearly:1 combinations:1 exquisite:1 entity:13 him:1 assigned:2 processes:12 elevate:1 non:2 course:6 fields:6 arxiv:1 yield:1 whether:3 proposing:1 experiments:1 roger:2 organism:5 though:1 contain:2 through:3 highlevel:1 fixed:4 favoring:1 steam:1 view:4 unison:1 spell:1 set:9 aspect:9 observer:7 physically:2 generally:1 correlations:1 thereby:2 accord:3 packet:2 connections:1 differs:1 namely:4 computer:16 sec:1 usefulness:1 profoundly:1 existence:7 fail:1 simultaneously:1 acts:1 analog:1 capacity:4 runs:1 mentioned:1 nuclear:1 illusory:1 familiarity:1 materials:2 state:20 unable:2 various:8 tendency:1 between:8 conceptual:1 probably:1 neither:2 approach:5 quantities:1 endure:1 preserve:1 notice:1 attention:1 terms:10 ability:2 extend:2 nature:16 optimal:1 screen:2 sole:1 however:6 key:2 distinguish:4 outer:2 amer:1 come:1 pixels:1 appending:1 suggested:3 both:3 cos:2 perceptions:6 survival:3 resides:1 norbert:1 many:8 pertain:1 conclusions:1 equal:1 contract:1 discard:1 etc:4 admit:1 context:2 behaviour:3 argue:2 whole:12 regarded:3 experimental:1 otherwise:1 among:1 presumably:1 relevant:3 point:7 simple:15 character:9 others:5 vast:1 period:2 environments:1 alone:1 ab:1 simply:5 moreover:6 comprehend:1 offered:1 lies:1 reconcile:2 considering:1 sensible:1 require:1 described:11 symposium:1 basis:8 addition:2 trademark:1 due:1 been:3 evolutionary:3 migrate:1 reduction:3 much:2 combined:2 interest:1 basic:14 transformed:1 ph:1 extreme:1 systems:7 engine:1 obtained:1 life:2 arises:5 corresponding:3 deeper:1 efficacy:1 observable:1 am:2 concerning:1 formed:3 convert:1 depend:2 argument:2 observers:1 coherent:7 understand:4 external:5 func:1 demand:1 evidence:2 assigning:1 spirit:2 those:8 applied:1 conception:8 abandoned:1 being:5 empirical:6 value:10 choices:1 will:12 rationally:1 while:2 replaced:1 behavior:1 situation:2 property:1 region:2 composition:2 real:2 generate:1 larger:1 sorts:1 century:1 linked:1 characteristics:3 von:5 neuron:1 thus:9 herein:2 according:11 ii:1 itself:4 minds:1 dual:1 orthogonal:1 interacts:3 different:16 disparate:1 open:1 perhaps:1 things:8 make:4 views:1 interaction:1 connection:2 same:4 lbl:1 highlighted:1 shifts:2 unity:4 complex:4 epistemological:1 units:2 survey:1 several:4 events:13 higher:3 status:1 independent:13 used:2 centuries:2 see:1 singapore:1 assignment:1 conceived:6 upon:6 effect:4 hand:4 director:1 usually:1 levels:4 arose:1 never:1 aggregate:8 angle:1 opportunity:1 tradition:1 thoughts:20 recent:2 simulates:1 early:1 lower:4 supports:1 whereby:1 neural:3 edition:1 spacetime:4 locality:1 well:4 bohr:2 thought:11 objection:1 without:8 allow:2 components:11 simulated:1 very:5 entry:1 model:8 grossly:1 know:7 opinions:1 world:12 enormously:1 consciousness:13 less:2 increasingly:1 when:5 resolution:2 effects:2 inadequate:1 press:3 stored:2 identify:1 atomic:1 human:15 using:2 facts:3 alternative:6 macroscopic:1 yet:13 functionally:1 insight:1 adding:1 enters:2 integer:1 tight:1 haldane:3 characterization:1 seems:4 conceptions:1 appeared:1 disparity:1 book:1 collections:1 describable:4 easy:1 splitting:1 electrical:3 tell:1 apart:1 accomodate:5 excited:3 match:2 putnam:1 resolved:1 repetitions:1 aspects:16 branch:11 government:4 rules:1 showing:1 decomposed:1 posed:1 possible:10 corresponds:9 crux:1 department:1 boxes:1 philos:3 grid:6 logical:3 disrupted:1 confined:1 immediately:1 emergence:1 modifying:1 structurally:1 weights:3 color:1 occurring:2 desire:1 76sf00098:1 intertwined:1 helpful:2 particle:1 alternatively:1 qualitative:1 lett:1 philosophers:1 unnecessary:1 unified:1 specific:2 private:2 continue:2 steps:1 either:2 neuronal:1 arbitrary:1 translated:1 become:3 weiner:2 works:1 essential:3 grangier:2 logically:8 mathematical:3 pertaining:2 hallmark:1 because:6 functional:18 neumann:5 classical:97 sequence:2 plausible:1 some:34 back:2 identified:3 separated:2 understood:3 experienced:2 learn:1 recommendation:1 kinds:1 sufficient:1 exists:1 happens:3 separately:1 scale:13 describing:2 lead:2 realistic:1 electromagnetic:1 objected:1 separate:2 lean:1 legal:1 tend:1 does:12 aggregation:1 provides:3 tends:4 pattern:5 tech:1 minimal:1 refer:1 measuring:2 varying:1 realms:1 scientific:3 rub:1 dividing:1 jumps:2 processing:1 confer:3 likewise:1 pressure:3 restructuring:1 although:1 ontology:2 feeds:1 manufacturer:1 integers:2 about:4 actual:12 anything:1 universe:3 discussed:2 location:2 simulation:1 extension:1 range:2 interpret:2 nothing:2 terminology:1 alert:1 act:1 experiences:2 introduced:4 consequently:3 other:10 automatically:2 warranty:1 specifies:3 equally:1 own:2 into:21 within:17 integral:1 satisfactory:2 actualized:1 combine:1 accommodate:2 pair:1 beings:1 exploiting:1 references:1 tiny:1 strip:1 elementary:1 sized:1 conceptually:1 mental:4 type:1 deal:1 conceivably:1 classically:8 respond:1 strictly:1 there:27 question:5 approximate:1 long:1 start:1 influencing:1 physicists:2 way:18 ed:1 forward:1 subsequent:1 conceivable:3 was:10 assumes:1 naturally:2 function:2 analysers:1 arise:1 complete:3 form:2 phenomena:2 differences:2 ibid:1 but:25 somehow:1 subjective:1 neutral:2 low:1 newer:1 placement:3 line:3 trying:2 collapses:12 he:3 persisting:3 made:5 compute:2 consequences:4 evident:1 compositional:1 characteristic:1 cells:1 up:2 us:6 until:1 record:1 below:3 converted:1 limit:3 homunculus:1 problem:14 pm:7 beliefs:3 mechanics:49 unfolding:1 attacked:1 required:1 associated:12 ad:3 defined:2 certain:9 abstract:1 describe:5 influence:1 general:2 single:12 associates:1 exist:8 rule:1 our:30 importing:1 controlled:1 moves:1 physical:26 machine:2 again:2 radically:1 compared:2 completeness:1 no:31 amounts:1 determining:1 whereas:5 θm:5 storage:1 detail:4 reality:11 index:1 field:4 old:1 regents:3 role:4 normal:1 digital:1 formalize:1 tie:1 proposal:2 illusion:1 picture:3 elements:6 intend:1 superposition:2 excitation:2 gross:1 initio:1 ascribe:1 aggregates:1 prepared:2 evolves:2 meaning:1 important:3 suited:2 ranges:2 replacement:1 tendencies:4 needed:6 structure:6 fundamentally:5 ghost:2 assert:1 independently:1 correlated:1 individual:12 happening:3 schroedinger:2 established:1 proposed:2 frontier:1 together:5 original:1 superpositions:2 investigated:1 implied:1 correlates:3 reprinted:1 image:2 time:12 push:1 determination:1 quantity:1 requires:4 having:1 once:2
|
quant-ph9502013.txt |@word concept:1 sci:1 foug:2 results:1 illustrated:1 garching:2 controversial:1 consists:1 consider:1 devoted:1 whose:1 certainly:1 calculate:1 pˆf:1 arthurs:2 eˆ:2 tr:4 contained:1 ny:1 those:2 th:1 decomposition:2 analogous:1 supported:1 implicitly:1 choice:3 summarized:2 experimentally:1 difference:1 entire:1 presented:1 ref:2 applicable:1 deals:2 warszawa:1 optics:2 equation:1 zf:7 measurable:1 sign:1 second:5 value:4 coulombwall:1 further:1 theory:6 spectral:1 established:1 what:2 apparatus:3 cˆf:2 labeled:1 expressed:1 ˆb:15 experiment:9 ˆf:3 designing:1 values:4 net:1 row:1 contrast:1 counters:1 coefficient:1 edited:1 simultaneously:1 relates:1 respectively:1 gathered:1 equals:1 here:4 objects:1 aid:1 represented:1 quite:1 convert:1 exemplified:3 technical:1 suggests:1 periodic:4 walther:1 professor:1 inϕ:2 hospitality:1 fourier:2 makes:1 der:1 involves:1 uniquely:1 family:1 hermite:1 merely:1 leonhardt:1 phasors:6 ipq:2 viz:1 planck:2 use:2 feb:1 proceed:1 would:2 positive:2 contains:1 few:1 call:1 therefore:1 compactly:2 theoretical:1 today:2 more:1 hermitean:1 operators:10 berlin:3 popper:1 normalized:2 particular:2 known:2 cases:1 must:1 springer:3 debates:1 indicates:1 setup:2 work:2 oscillator:8 glauber:1 remain:2 obvious:2 following:1 averages:1 example:9 heart:1 references:1 hutchinson:1 bell:1 mirrors:1 expanding:1 high:1 effectively:2 numbers:1 yet:1 verlag:3 lamb:3 information:2 needs:1 rather:5 holds:5 georg:1 located:1 pair:1 significance:2 parameter:1 normalize:1 product:3 description:2 may:1 max:2 invitation:1 povms:1 bollinger:1 designed:1 records:2 waves:1 unchen:1 data:5 natural:3 physik:1 explicit:1 correspond:3 ones:1 so:5 fundamental:1 representation:1 order:2 typical:1 spreads:2 kbn:1 closely:1 produces:1 indeed:2 lahti:1 course:3 thermal:2 experiments:2 london:1 kopfermann:1 statistical:4 argued:1 pointer:2 its:8 tendency:1 thank:1 chosen:1 interesting:1 glogower:2 actually:1 permanent:1 degrees:1 defining:1 correspondence:1 eventually:1 good:2 noh:2 university:1 heinzen:1 number:1 obeyed:1 framework:1 walls:2 quantenoptik:1 they:1 krzysztof:1 now:3 eigenvalue:1 term:1 englert:3 name:1 fizyki:1 nfm:12 identified:5 realistic:3 each:3 found:3 universit:1 uniwersytet:1 2i:1 characterized:1 lasting:1 schemes:1 weight:1 map:1 hypergeometric:1 related:2 inverted:1 interferometer:1 used:5 measurement:15 quantum:34 laboratory:2 eq:1 aˆ2:1 quantenmechanik:1 large:1 space:1 since:2 rev:12 denotes:1 looking:1 iλq:2 forth:1 integrated:1 shows:1 counterpart:1 aˆn:3 philosophy:1 linear:1 associate:1 aˆf:12 differ:1 free:1 standard:3 york:1 members:1 detecting:2 milburn:1 advance:1 determining:2 could:1 filter:9 turn:2 length:1 murky:1 consequence:2 onto:1 first:3 origin:1 intuition:1 equates:1 features:1 probability:2 variables:1 primary:1 philosophical:1 done:1 relations:2 directly:1 impossible:1 illustrate:2 given:4 necessarily:1 temperature:1 phasor:3 ordering:1 unknown:3 adjoint:1 system:5 construct:3 their:1 ordered:1 scheme:2 immediate:2 za:1 optical:3 authors:1 than:1 relative:1 kind:1 determines:2 accordance:2 require:1 largely:2 see:3 submitted:1 annihilation:1 matter:1 determined:2 supposed:1 fˆ:4 normally:1 enables:1 powers:6 distinguished:1 result:1 berthold:1 mind:1 spectrum:1 raw:4 need:1 any:4 unprocessed:1 convenient:1 latter:1 note:2 instance:1 ideal:1 take:2 analogy:1 finding:1 new:1 heisenberg:4 even:1 begin:1 shall:5 most:3 said:1 germany:2 definitions:2 phase:21 intrinsic:11 average:3 analog:3 typeset:1 looked:1 accounted:1 tech:1 principle:1 exp:11 mechanical:3 hn:2 physics:5 fact:1 quantity:2 particularly:1 probe:4 least:1 purely:1 relation:8 earth:1 schenzle:1 agrees:1 teoretycznej:1 situations:1 guidance:1 operational:24 only:2 explicitly:1 factor:2 employed:1 constant:1 local:1 equilibrium:2 dn:1 do:1 his:1 establishes:1 di:1 dependent:2 familiar:1 zurek:2 express:1 expectation:6 da:7 beam:1 cannot:1 storey:1 words:1 supplies:1 report:1 during:1 him:1 dp:2 dq:2 approach:7 arxiv:1 factorization:1 twice:1 microscope:1 paper:1 ˆn:1 valid:1 view:3 monochromatic:1 requirement:1 set:5 reference:6 bergou:1 detection:4 intensity:2 devices:3 paul:3 best:2 eres:2 detect:1 ways:1 eigenstates:1 state:5 identification:1 between:4 conceptual:1 operationally:2 numerous:1 available:1 warszawski:1 terms:3 however:3 jr:1 r30:1 analyzed:2 both:2 limits:1 uncertainty:4 equal:3 called:1 connection:1 argue:1 photons:1 experimental:4 grounds:1 splitters:1 relevant:1 fields:1 colons:1 point:2 iϕ:1 address:1 homodyne:3 simply:1 polynomial:1 proved:1 factors:1 schleich:1 pr:19 unusual:1 sine:1 described:2 aˆ:10 due:1 been:4 defined:2 cosine:4 treat:1 interest:2 likewise:1 itano:1 ph:1 ann:2 pl:1 generating:8 enable:1 corresponding:5 observable:8 quantities:4 wheeler:1 photon:2 fortschr:1 coherent:1 understand:1 spirit:1 present:1 case:4 replaces:1 laser:1 pacs:1 evaluated:1 employ:1 while:1 replaced:1 situation:2 property:2 procedure:1 iq:3 von:2 thus:4 according:1 itself:1 busch:1 different:5 jargon:1 grant:1 perhaps:2 granted:1 same:1 princeton:2 propensity:12 quant:1 units:2 dimensionless:1 infer:1 independent:1 literature:1 upon:1 effect:2 hand:1 moment:1 experimenter:2 purpose:3 hans:1 normalization:1 recent:2 lower:1 off:1 mention:1 nevertheless:1 poland:1 well:2 analysis:4 harper:1 mathematische:1 without:1 components:1 kelly:2 position:6 model:2 dimension:1 left:1 distances:1 just:3 freyberger:1 moments:1 guided:1 rest:1 λa:3 underlying:1 identify:4 potentiality:1 world:1 polish:1 momenta:1 october:1 macroscopic:3 λn:1 mittelstaedt:1 sektion:1 density:11 regarded:1 measure:1 character:2 emphasis:1 signals:1 spread:2 lett:6 eigenstate:1 momentum:6 real:2 aspects:1 read:1 sums:1 possible:2 corresponds:1 possibly:2 birth:1 press:1 using:3 unique:2 displaced:1 necessary:1 like:1 particle:3 δp:1 δq:1 specific:1 arbitrary:1 served:1 δb:1 ˆbn:1 terminology:2 δa:3 mathematical:1 because:2 neumann:2 classical:17 creation:1 phenomena:1 acad:1 examples:2 respect:1 grundlagen:1 extended:1 provided:1 lead:1 electromagnetic:1 measurements:6 recorded:3 integration:1 overlap:1 does:3 connecting:1 provides:1 unavoidably:1 refer:3 measuring:5 noise:4 radially:1 confluent:1 illustration:2 revtex:1 although:1 refers:2 properties:6 bz:1 comparison:1 about:3 actual:2 extension:1 algebraic:1 freedom:1 basis:4 discussed:1 meaning:2 collett:1 range:1 nothing:1 instytut:1 introduced:4 specifies:2 equally:2 plethora:1 wineland:1 communication:1 into:1 down:1 device:7 weighted:1 accounts:2 controversies:1 operator:15 strasse:1 uncertainties:1 statistics:2 institut:2 additional:1 riegler:2 measured:3 there:3 question:2 long:1 start:1 inasmuch:2 quanta:1 mandel:2 way:5 was:1 naturally:2 function:16 considerably:1 ef:1 form:3 basic:2 denoting:1 but:5 construction:2 link:1 ho:1 odkiewicz:5 partially:1 made:1 wish:1 us:1 ur:1 owing:1 limit:3 dv:1 distribution:2 clear:3 mechanics:4 interval:2 associated:5 zeno:1 povm:3 certain:1 abstract:1 received:1 am:1 covers:1 general:6 ap:1 single:1 pˆ:9 dλ:1 our:3 exist:1 formalism:2 physical:4 functions:1 susskind:2 no:2 amounts:1 whereas:1 when:2 reality:1 field:5 other:3 role:1 normal:1 acceptable:1 nice:1 models:1 june:1 includes:1 generated:1 a2:2 suited:1 variable:5 implies:1 trigonometry:3 typically:1 required:1 rule:1 observables:6 decoherence:1 dϕ:4 once:1
|
quant-ph9502014.txt |@word primed:1 four:1 parameterization:2 reparameterization:2 copernicus:1 depend:2 manifolds:1 under:5 hibbs:1 wave:2 condition:1 hamiltonian:1 leave:1 math:2 linearizing:4 zero:1 further:1 choices:1 theory:2 nonlinear:17 current:2 establishes:1 new:5 clausthal:4 evolving:1 led:1 degree:1 here:3 free:2 path:1 equations:11 annales:1 galilei:1 remark:2 generalizing:1 institute:2 leaves:4 resulting:1 action:2 rediscover:1 foundations:1 quotient:1 via:2 classification:1 feb:1 usa:1 positive:1 next:1 call:1 therefore:1 associated:1 brunswick:1 type:1 theoretical:2 more:2 company:1 odinger:14 projective:2 cases:1 derivation:1 equation:9 work:1 theories:1 values:6 give:1 december:1 effectively:1 sense:1 νj:1 aff:6 get:1 maps:1 symposium:2 parameter:4 map:1 sommerfeld:1 description:2 algebra:1 replacing:1 after:1 orbits:1 fd:7 representations:2 derives:1 short:1 parameterized:1 diffeomorphism:1 so:2 representation:1 order:1 terms:2 acts:1 interpretation:2 indeed:1 course:1 paper:1 thesis:1 satisfies:2 before:1 group:14 symmetry:1 ln:2 affine:2 actually:1 choose:1 maximal:1 eventually:1 them:1 propose:1 introduce:1 framework:1 they:2 now:2 polish:1 invariants:6 university:4 l2:1 each:1 2m:9 side:1 characterized:3 homogeneous:1 ei:2 reduce:1 been:1 quantum:9 our:3 eq:3 special:1 sabatier:1 space:4 furthermore:1 since:1 wholly:1 contained:1 hill:1 rj:4 linear:6 8m:3 fisica:1 possibility:1 york:1 members:1 asi:1 r4:1 r5:2 r1:1 r2:2 r3:2 could:1 noted:3 turn:1 hence:1 castle:1 first:1 einer:1 probability:4 number:1 given:3 law:1 publication:1 introduction:1 indeterminate:1 unspecified:1 their:1 calculations:1 final:1 adopts:1 foliation:3 diffusion:3 struktur:1 submitted:1 ehrenfest:7 gives:1 symmetries:1 rewrite:1 linearizable:1 generalization:1 eigenschaften:1 any:1 viewed:1 ray:1 lie:1 depending:1 ideas:1 note:2 emphasis:1 8m2:2 shall:1 quote:1 3x:1 connected:1 class:1 tpa:1 calculated:1 feynman:2 proceedings:2 points:1 principle:3 mechanical:3 physics:4 selection:1 show:1 german:1 gauge:14 solutions:3 d2:1 just:1 parameters:9 should:1 only:2 factor:1 local:2 means:2 de:1 subfamilies:1 2md:1 progress:1 gen:1 evolution:1 densities:1 fields:1 arxiv:1 investigate:1 view:1 coefficient:2 set:2 testing:1 j2:1 depends:1 arg:3 inequivalent:1 forthcoming:1 doebner:7 functionals:1 enough:1 µj:1 invariant:8 conditions:1 recently:1 however:1 goldin:7 ir1:1 taking:1 quantization:1 fulfilled:1 connection:2 und:1 symplectic:1 whole:1 jersey:1 unitarily:1 cj:2 point:1 corresponds:2 dimensional:2 respect:3 transformations:12 laplacian:2 foliated:1 ph:1 ann:1 systems:1 nattermann:4 corresponding:1 quantities:1 c3:2 c2:8 c1:5 c5:2 c4:2 case:1 look:1 arnold:1 remaining:1 technical:2 rutgers:1 property:1 detailed:1 vol:1 ir:3 thus:1 non:1 ii:1 im:2 currents:2 righthand:1 same:3 complex:2 quant:1 dimensionless:1 independent:2 weinberg:1 singapore:1 infinite:2 invariance:2 linearize:1 schr:15 well:1 sets:1 position:2 model:2 dimension:1 usual:1 proposed:1 obtain:2 formulated:1 identify:1 using:1 λj:1 functionally:1 previous:1 nicolas:1 4m2:3 preprint:1 family:12 density:5 belongs:1 transformed:2 lett:1 theorem:1 transformation:3 real:2 iγ:2 admitting:1 five:1 press:1 integer:1 subfamily:6 modifications:1 like:1 integrals:1 mcgraw:1 essential:1 mathematical:2 sketch:1 because:2 madrid:1 phenomena:1 deduce:1 nonzero:1 leaf:2 dimensions:2 2c5:1 measurements:3 refer:1 scientific:1 equivalent:2 expansion:1 hilbert:2 kinematical:1 world:1 nonvanishing:2 whence:1 obeys:1 act:1 germany:1 statements:1 ciemat:1 into:2 appropriate:2 references:1 inverting:1 schrodinger:1 there:2 complete:1 form:1 some:4 but:1 made:1 consist:1 up:1 us:1 xxvi:1 mechanics:4 fulfills:1 constant:1 fokkerplanck:1 defined:2 certain:1 abstract:1 describe:1 general:6 examine:1 departments:1 formulation:1 physical:2 again:2 functions:2 when:1 ny:1 book:1 properties:1 mathematics:1 torun:2 linearization:2 structure:4 orbit:1 together:2 4m:6 time:3
|
quant-ph9502015.txt |@word concept:2 consider:5 rev:19 desirable:2 results:1 four:2 scalar:6 grateful:1 research:2 schweber:1 particles:5 ıs:2 depend:1 ıa:1 finally:3 alvarez:7 helps:1 under:1 norm:7 fax:2 straightforward:2 very:2 implicitly:1 wave:6 trouble:1 condition:3 leads:2 school:2 hamiltonian:10 turns:1 proposals:4 solution:1 cooke:2 restoring:1 eigenvalues:4 equation:13 smaller:1 force:1 yaffe:1 direct:2 literature:1 past:1 second:4 dynamics:2 linear:2 bilinear:1 aim:1 what:1 plays:2 stands:3 kleingordon:1 analogously:1 expressed:1 consistently:1 goes:1 droz:1 new:2 inertial:1 contrast:1 satisfy:2 27a:1 notions:1 ibid:1 respectively:1 french:2 tachyons:4 free:5 along:1 strong:1 equations:3 implicit:1 galilei:1 obtained:1 instituto:1 remarks:1 rests:1 involved:1 allows:3 commonly:1 controversy:1 simultaneous:2 procedure:1 chang:1 fourier:1 criticism:1 projection:2 bunge:2 rumpf:2 treatment:2 dobson:1 names:1 sgn:3 use:2 feb:1 projector:3 would:2 mendoza:1 covariant:2 positive:12 negative:2 sitter:4 call:1 m0:2 m2:2 taken:1 ψc:12 theoretical:1 possible:1 more:3 sort:2 becomes:1 operators:5 odinger:2 fµν:2 mec:1 appendix:6 particular:2 known:5 must:2 a5a:1 gadella:1 account:2 a5b:1 extension:1 integrating:1 avoiding:1 originally:2 work:2 theories:1 fock:4 del:1 exceptions:1 root:2 example:1 proof:1 compare:1 relativistic:7 exactas:1 neglected:1 belonging:1 states:14 uckelberg:7 lal:1 want:1 sense:1 rescaling:1 santilli:1 discussion:1 acts:1 feature:1 dependent:1 buenos:4 hostler:1 acta:3 ordinary:1 parameter:15 oscillatory:1 simplicity:1 product:3 may:1 after:1 derived:2 lengthy:1 reflect:1 representations:1 law:1 quasiclassical:4 johnson:5 correspond:2 element:3 pandit:1 spectral:1 so:1 allow:1 representation:3 order:8 restriction:3 helv:3 interpretation:8 developed:1 insight:1 mainly:1 interpreted:1 course:1 paper:1 london:1 mentioned:4 satisfies:3 its:2 cited:1 derive:1 group:5 thank:1 acknowledge:1 interesting:1 fix:1 coordinates:1 actually:1 previously:1 φc:7 systems:2 mail:2 argentina:2 main:1 defining:1 eventually:1 non:1 teitelboim:1 horwitz:5 universality:1 framework:4 they:2 st:7 now:8 discuss:1 establishes:1 eigenvalue:2 february:1 dirac:10 level:2 identified:1 φm:3 astronom:1 each:1 2m:1 identifies:2 classifies:1 2i:2 mean:6 spinor:2 square:2 another:1 independent:2 there:1 energy:1 idea:1 related:4 contracting:1 antiparticle:3 used:3 grav:1 quantum:4 our:2 eq:13 event:1 out:1 shown:1 matrix:1 space:7 restricted:2 nuovo:4 since:8 squared:2 projected:1 denotes:1 rd:5 rel:1 get:1 ref:15 math:5 earlier:1 theory:9 localization:1 ısica:2 departamento:1 standard:10 approaches:1 besides:1 checked:1 sowjetunion:1 irreducible:1 additional:1 definition:2 retained:1 recovering:1 could:1 m20:3 keep:1 motion:5 massive:1 universidad:2 consequence:1 moving:2 onto:3 eqs:1 first:5 origin:1 already:2 hurtado:1 relate:1 variables:3 powerful:1 number:3 minimum:2 spinning:2 directly:1 iafe:1 given:15 antiparticles:3 discussed:1 leading:1 adjoint:3 system:7 needed:1 too:1 normalization:1 scheme:1 final:1 recovered:1 adopts:1 shell:14 sonego:2 ih2:2 continuous:2 part:2 x2:1 schr:2 x0:6 x1:1 than:2 holland:1 cimento:4 zero:2 appealing:1 determined:2 speaking:1 were:1 naturally:1 treated:1 anica:1 offshell:1 footnote:1 ann:3 argument:1 generalization:1 conjugate:1 seen:3 recover:1 demonstration:1 any:9 form:5 lim:3 self:2 formulaci:1 note:4 centered:1 generalized:6 analogy:1 canonical:1 simultaneity:1 kawaguchi:1 heisenberg:2 even:2 begin:1 unless:1 ds2:2 shall:1 aires:4 letter:2 preliminary:1 device:1 suc:1 intrinsic:1 class:1 xµ:30 considered:11 bracken:1 playing:1 looked:1 feynman:17 principle:2 exp:2 notion:5 fact:5 stephens:1 show:7 vigier:2 labels:1 purely:2 spaces:1 relation:3 solutions:1 x3:1 d4:3 should:1 only:7 factor:1 moses:1 hamiltonians:1 his:1 above:2 means:3 df:3 de:11 db:2 expectation:1 words:2 collins:1 ds:15 dq:6 evolution:15 approach:1 arxiv:1 factorization:3 garcia:8 common:1 including:1 vincent:1 fixed:2 valid:3 view:1 ser:1 fellowships:1 frame:2 nambu:2 packet:1 see:25 arc:3 result:2 arg:2 discussions:1 terms:2 alternative:1 subject:2 satisfying:3 eigenfunctions:1 review:1 definite:3 lµν:1 label:1 state:6 difficulties:1 identification:2 invariant:2 subscript:1 conditions:3 preserve:1 notice:4 recently:1 extend:1 transpose:1 however:7 jr:1 indefiniteness:1 here:1 antica:1 assumptions:1 both:1 essentially:1 last:1 many:1 taking:6 uncertainty:2 according:1 quantization:2 hψ:1 context:1 expression:3 ll:2 galilean:1 among:2 nonrelativistic:3 reasons:1 roman:1 cf:1 dimensional:3 cx:1 associated:3 indefinite:12 cu:1 considering:3 mention:1 due:1 been:3 appears:1 ph:1 pm:2 arises:1 corresponding:8 subspace:5 remark:2 gen:2 else:1 observe:1 derivative:1 presented:1 spin:9 case:19 p0:3 unlike:2 pacs:1 value:9 will:7 technical:1 while:1 behavior:1 property:5 characterizing:1 detailed:1 unitary:2 a4:3 espacio:1 endowed:1 metric:3 thus:1 equal:3 reads:2 orbital:4 different:8 null:1 perform:1 juan:1 connection:2 same:6 lbl:1 complex:1 quant:1 pauli:1 units:1 proved:1 events:2 development:1 evolve:1 tiempo:1 extended:3 reinterpretation:2 hand:2 parametrized:2 uses:1 unpublished:4 spinorial:2 identity:1 eigenvectors:2 off:5 pµ:41 well:7 telegdi:1 analysis:1 barut:4 without:4 position:2 con:1 dimension:1 usual:5 λs:1 manifold:2 proposed:3 being:1 accurate:1 lorentz:2 obtain:7 rest:2 identify:1 using:4 momenta:1 previous:1 heuristic:2 villars:1 point:1 character:1 parametrization:21 priori:1 lett:3 easy:1 asoc:2 guarantees:1 transformation:1 take:4 real:5 iλ:1 spinless:1 reuse:2 easily:1 henneaux:1 term:1 admitting:1 dewdney:1 five:3 ciencias:1 press:1 immediately:2 projects:2 mod:4 like:2 particle:7 follows:2 loses:1 specific:1 steps:1 zitterbewegung:1 become:1 works:3 reduced:5 therein:3 because:2 parametrizations:4 aparicio:5 some:3 back:1 choosing:1 moreover:2 proper:18 happens:1 provided:1 does:2 decomposition:1 provides:1 prog:2 proc:1 minimal:2 power:1 rep:1 retains:1 agreement:1 although:1 found:7 imaginary:2 super:4 about:2 pα:2 world:2 constraint:1 introduces:1 a3:1 o:5 compatible:1 sake:1 a2:1 nothing:1 introduced:1 thacker:2 soc:1 h2:8 into:2 within:1 integral:1 suppl:1 lies:1 hermitian:1 references:3 operator:11 classical:18 strictly:1 initial:3 long:1 noting:1 facultad:1 way:2 series:1 was:8 propagator:1 therefore:5 function:3 elsewhere:2 newtonian:1 piron:2 removes:1 but:4 gaussian:3 illuminating:1 line:4 naturales:1 made:2 uu:2 la:1 up:1 us:8 below:1 un:1 limit:9 problem:4 define:1 similar:2 mechanics:6 ab:2 constant:4 computing:1 defined:2 likewise:1 universal:2 contribute:1 am:1 general:1 ar:2 dλ:1 formulation:2 formalism:11 check:1 functions:2 no:2 when:4 vanishes:2 schwinger:4 field:1 other:5 role:3 theor:2 dxµ:3 picture:2 briefly:1 thaller:1 resembles:1 includes:2 a1:7 commutator:1 meaning:2 important:3 a5:1 uba:2 a7:1 a6:1 variable:2 rqm:3 ago:1 coupling:2 fsf:5 assume:1 values:7 dτ:1 packets:2 mass:33 time:25 backward:2 having:1
|
quant-ph9502016.txt |@word emile:1 managed:1 consider:5 illustrates:1 caused:2 magnetic:1 varying:1 results:5 existing:1 leads:4 eds:1 commute:1 microwave:1 go:1 follow:1 expressions:4 involved:1 causes:4 factorizing:1 compact:1 depend:1 calculate:3 concerned:1 equivalence:1 acting:2 simplify:1 finally:1 device:1 present:1 under:2 dλ2:2 γg:2 dramatically:1 γe:2 degeneration:1 p2:2 amplitudes:1 advantage:3 far:1 induce:1 wave:21 every:1 decide:1 fall:3 mixing:1 affect:1 difference:2 exact:8 fakult:1 condition:5 look:1 level:18 bn:8 turns:2 t2:3 solution:6 large:19 solved:1 convenience:1 vector:2 math:3 small:16 eigenvalues:1 optics:1 der:1 phillips:1 upper:7 wronskian:2 force:2 organized:1 ten:1 measurable:1 literature:1 sign:7 approximation:6 consists:1 konstanz:4 dissipation:1 enclosed:1 equal:2 manner:1 further:3 dynamics:6 eλa:3 linear:6 even:1 employ:1 what:3 ˆt:1 power:1 rate:1 itˆ:12 d2:3 section:9 agrees:1 bl:1 above:4 new:4 falling:6 increasing:1 method:3 devoted:1 led:1 deduces:1 respectively:4 doing:1 loose:1 here:7 atoms:14 behaviour:6 growing:1 ramsey:1 free:4 separation:1 aid:2 alone:1 corrections:10 standard:2 equations:4 appears:3 change:2 ordinary:3 obtained:4 almost:3 perturbs:1 rigorously:1 technical:1 shift:16 study:3 studied:2 wherever:1 1f1:5 commonly:1 amount:2 simultaneous:2 resulting:3 action:1 resonance:8 narrow:3 makes:2 fulfill:1 examining:1 via:2 useful:4 br:1 ix:6 france:2 explained:3 wij:12 wii:2 replace:1 logarithmic:2 ii:2 sgn:1 apply:6 total:3 cloud:1 remaining:2 use:9 refers:1 feb:1 asymptotic:1 would:6 commun:1 remains:5 positive:1 until:1 contains:8 γi:1 induction:1 next:1 few:1 explicitly:1 call:1 therefore:5 expanding:1 taken:3 unphysical:2 theoretical:2 milliseconds:1 more:8 separated:1 introducing:1 incorporates:1 initial:7 operators:7 envelope:1 odinger:2 validity:1 tested:1 derivation:3 appendix:5 particular:3 known:4 urgen:1 hold:1 must:4 high:1 keeping:1 valued:2 ma:1 inertial:1 work:1 reproduce:1 remain:1 obvious:3 three:1 following:6 making:1 modifies:1 drops:1 spontaneous:7 example:1 proof:1 compare:1 omit:1 bouyer:1 indicated:1 stated:1 calculation:3 introduces:1 sense:1 neglected:5 states:6 indicates:1 application:1 numbers:3 allowed:1 interpreted:1 drive:1 bassi:1 algebraical:3 ic:2 ωeg:2 absolute:5 influenced:1 end:1 straightforward:2 fortunately:1 hoo:1 discussion:4 acts:1 feature:1 write:1 very:9 nontrivial:1 w22:17 actual:1 pure:1 w21:13 instead:1 centimeters:1 parameter:4 sin:16 simplicity:1 pleasure:1 description:3 singular:1 may:13 oscillators:1 after:7 derived:3 different:2 applications:1 produce:1 features:2 physik:1 ready:1 grow:2 diagonal:2 short:1 dynamical:1 third:3 rn:3 whenever:1 light:2 explicit:1 correspond:1 element:1 accelerated:6 so:11 allow:1 enter:1 ingredients:1 first:14 adams:1 order:6 prefactor:2 holds:7 interpretation:4 ith:1 oteo:1 indeed:1 over:2 dy:8 vary:1 choose:1 years:1 combinations:1 paper:6 including:1 dw:2 mentioned:1 y0:21 kinetic:1 y2:6 its:7 before:1 s2:3 derive:6 rapidly:1 thank:1 decay:3 ln:1 matrices:1 solving:1 varies:1 τa:36 better:1 compelling:1 systems:2 rabi:22 mail:2 main:4 setting:2 versus:2 non:3 good:1 greater:1 combination:1 yn:8 bernoulli:1 impossible:1 processes:1 introduce:4 number:8 mention:2 steane:1 detunings:2 effects:1 they:8 focus:1 singularity:1 now:7 yu:1 transparent:1 yv:1 develops:1 easily:1 term:13 finite:1 2p:1 lies:1 hamiltonian:12 identified:1 alter:1 sufficiently:2 trap:1 reasonable:3 each:4 2m:3 universit:1 side:1 characterized:1 homogeneous:8 development:2 differential:5 ei:3 directly:1 r2n:2 ee:10 series:1 energy:5 hypergeometric:1 ea:2 w12:17 related:5 t3:1 interferometer:1 frequency:18 disappears:1 combining:1 tˆ:1 laboratory:1 happen:1 transitions:11 eq:60 out:13 try:1 shown:2 dominates:1 matrix:13 factors:6 restricted:1 furthermore:1 since:17 crucial:1 denotes:4 looking:1 replacing:3 contained:3 investigation:1 at2:6 formula:4 get:6 induced:1 ref:8 occurs:4 independence:1 shows:2 populating:1 8k:1 doppler:20 turning:2 theory:1 written:5 abramowitz:1 contain:1 given:3 possibility:1 quite:2 clarify:1 reason:3 complicated:1 corrects:1 ask:1 hand:1 e0:2 definition:1 interaction:1 r1:3 r2:6 starts:1 could:1 transition:10 moment:1 ψg:5 times:6 motion:7 turn:4 εl:1 u21:3 u22:1 consequence:5 neglect:1 juergen:1 origin:2 intuition:1 already:6 xn:6 enlarges:1 probability:4 striking:1 fading:1 moler:1 reintroduced:1 nε2:1 reflected:2 reaches:1 restrict:2 done:2 construct:1 another:2 carry:1 ihc:1 precisely:1 miss:1 york:1 equation:7 perturbation:5 marzlin:4 πe:1 introduction:2 eqs:3 system:7 relations:3 πr:1 their:7 cooling:1 appl:3 rates:1 too:3 calculations:5 u11:2 brevity:1 πx:2 scheme:2 final:1 speaking:1 shifted:5 sengstock:1 mostly:1 square:2 completed:1 continuous:1 serve:1 direct:1 putting:1 larger:1 part:8 somewhat:1 manipulation:1 off:3 x0:1 cosh:1 representing:1 than:4 coefficients:1 remember:1 it2:1 kind:1 determines:1 accordance:1 kaiser:1 sections:1 require:2 second:7 limiting:2 preparation:1 determined:2 recovered:1 amplitude:2 were:1 identical:1 enables:1 solely:1 it3:1 perturbative:1 lowest:1 rainer:1 generality:2 rewrite:2 reproduces:1 cohen:4 mind:1 argument:3 peculiar:1 multivalued:1 close:1 seen:2 handled:1 clearly:2 karl:1 relatively:1 acceleration:14 zero:5 magnus:10 convenient:1 latter:1 responsible:2 able:1 gravity:16 note:8 k2:1 k1:1 internal:13 absorbed:1 forces:2 finding:1 many:1 switching:1 unperturbed:1 raman:4 andez:1 exactly:7 altered:3 ducloy:1 mlynek:1 who:1 fails:1 logarithmically:1 algebraic:1 exploited:1 germany:1 formulae:1 phase:16 inserted:1 class:1 exponent:1 4u:1 cause:1 give:1 especially:2 consequences:2 considered:1 σi:1 calculated:2 implications:2 kn:3 kl:2 optical:1 principle:1 exp:24 velocity:6 usual:1 normally:1 calculates:1 fact:10 quantity:1 precise:1 particularly:1 intensity:3 show:3 appearing:1 rotating:4 purely:2 registers:1 relation:6 solutions:3 earth:5 trivial:1 find:3 ground:6 q1:1 slow:2 based:1 situations:1 iγi:1 start:1 should:5 dalibard:3 only:26 going:1 postfach:1 factor:14 parabolic:1 population:4 iee:1 ieg:1 do:1 handle:1 goes:1 riehle:1 means:5 dependent:13 beams:1 de:2 scoles:1 beam:8 wallis:3 cannot:3 nearly:1 closely:2 despite:1 dv:2 during:5 dt:1 du:2 net:2 prime:1 evolution:21 course:1 conditions:2 arxiv:1 shape:1 factorization:1 experiments:1 prevents:1 cycles:5 discussing:1 valid:3 view:2 salomon:1 set:6 reference:6 edited:1 physically:3 frame:4 arrives:3 relative:3 differentiation:1 see:15 radius:1 result:19 arg:4 discussions:1 simultaneously:2 2πn:1 subject:1 appear:1 phases:1 gravitation:1 commutation:2 consistency:1 away:1 dipole:2 iω2:1 state:18 various:2 closed:2 between:7 mathematical:3 iπω:1 approach:5 iγe:1 ωl:9 iπα:1 terms:4 reproduced:2 missing:1 initially:4 neglection:1 weak:1 vanishing:5 analyzed:1 suppressed:1 problem:2 aim:1 both:4 essentially:4 feeling:1 last:4 b2n:1 freely:4 conclusions:1 hence:8 incomplete:1 fulfilled:1 und:1 context:4 interesting:2 uni:2 argue:1 expression:6 finds:1 experimental:1 adjusted:1 relevant:1 sinh:1 cm:1 point:2 simple:5 seems:1 period:1 factorize:1 importance:2 taylor:2 simply:3 cancel:3 respect:5 writing:1 late:1 most:1 described:2 geometries:1 addition:1 induces:1 due:2 been:8 alters:1 detuning:18 describes:6 slowly:1 treat:2 interest:4 recognize:1 expected:1 degrees:1 ph:1 u12:3 treatment:1 life:1 corresponding:3 photon:3 cos:9 finished:1 x2n:2 external:2 derivative:2 improved:1 worked:4 θv:1 former:1 those:1 θu:1 case:14 p1:2 laser:46 eit:1 exponential:5 pacs:1 frozen:1 appearance:1 value:2 transformation:5 will:23 suppose:1 familiar:1 error:2 situation:4 eik:1 procedure:1 periods:1 resolved:1 cylinder:1 unitary:6 coupled:1 phenomenological:1 allows:1 vk:1 thus:2 surprisingly:1 according:1 couples:1 ik:3 examined:1 contradiction:1 df:1 rid:2 vanish:3 containing:4 thereby:2 anymore:1 perform:5 powers:1 make:3 lett:3 same:7 any:8 shorter:1 shifts:1 εn:2 complex:3 quant:1 wavepacket:2 pauli:1 big:1 several:2 grows:2 difficult:2 breakdown:3 independent:5 used:9 singapore:1 cubic:1 interruption:1 numerical:1 effect:12 rσ1:2 driven:1 average:1 running:10 levels:1 moving:6 potentials:2 infinite:1 anticipated:1 opportunity:1 identity:2 cycle:3 relies:1 lower:6 task:1 schr:2 center:9 nevertheless:1 changes:1 modeled:1 well:5 analysis:2 without:2 solve:2 comes:1 gain:2 simulated:1 exponentials:1 position:2 model:10 arising:2 left:1 interpret:3 world:1 just:3 less:1 being:2 storage:1 stegun:1 obtain:2 rest:3 vanishes:1 λb:3 λa:2 atomic:11 aspect:1 immediately:1 campbell:2 uller:2 λn:2 accelerates:1 previous:3 adding:1 enters:1 density:1 absorption:3 regarded:1 conclude:2 character:1 weiss:1 discuss:2 iω:2 k0:1 transformed:2 corresponds:1 easy:5 quick:1 formal:1 solvable:2 excited:7 momentum:19 real:2 sterr:1 evaluation:1 around:1 depends:5 represents:1 read:2 replaced:1 possible:6 iζ:24 increases:1 know:2 using:9 apart:1 loss:1 necessary:3 like:2 particle:1 follows:3 performing:1 exploiting:1 audretsch:4 indication:1 either:1 contradict:1 become:1 hyperfine:1 essential:1 replacement:1 accessible:1 sketch:1 because:17 methods:1 exposed:2 some:2 back:3 ertmer:1 understood:1 deduce:1 towards:1 meters:1 2z:1 moreover:1 oscillations:12 root:2 bord:4 neglecting:2 happens:1 provided:1 scale:1 dense:1 dimensions:1 lead:1 broad:1 witte:1 per:2 everything:1 does:4 harmonic:1 unit:2 moderate:1 eant:1 demonstrated:1 refer:1 inserting:5 process:1 scientific:1 detuned:1 rep:1 seconds:1 damps:1 equivalent:2 confluent:1 oscillating:4 perpendicular:1 expansion:18 tannoudji:4 step:4 although:1 found:2 zγ:1 imaginary:3 includes:1 2n:14 earlier:1 stage:2 chapter:2 comparison:1 about:1 central:2 jessen:1 y2n:2 hausdorff:2 freedom:1 kasevich:1 discussed:2 dependence:12 o:13 practical:2 a2:1 squared:1 act:1 introduced:3 slightly:1 fern:1 therein:2 outlook:1 rev:7 chu:1 inclusion:1 spreeuw:1 noting:1 into:4 within:1 splitting:1 negative:1 occurring:1 included:5 right:2 references:3 22z:1 determine:1 operator:38 strategy:1 theoretically:1 wavepackets:2 van:1 additional:5 coherent:1 comparing:1 transfer:11 strictly:1 there:8 question:1 approximate:1 long:8 why:1 width:1 accordingly:1 much:3 handbook:1 way:7 2ωl:1 was:11 eg:9 interferometry:4 function:8 ef:2 complete:5 form:10 guess:1 metastable:1 regard:1 but:15 displacement:1 hk:5 neutral:1 properly:1 recoil:5 w11:17 atom:50 convergence:1 hc:12 true:1 proposal:1 rolston:1 observation:1 absent:1 made:4 applying:1 surprising:2 evident:1 instructive:1 whether:1 characteristic:2 gravitational:16 attached:1 up:3 us:2 ur:1 assume:1 below:1 limit:10 anew:1 spectroscopy:2 sum:2 distribution:2 ψe:5 similar:4 clear:3 detailed:1 bearing:1 oho:1 constant:6 defined:3 certain:2 abstract:1 describe:4 influence:14 general:2 proper:1 dλ:12 our:13 moves:1 commuting:1 check:2 physical:11 functions:8 peter:2 no:7 amounts:2 giacobino:1 whereas:2 when:3 detail:1 field:15 definitions:1 other:2 details:1 branch:2 becomes:7 deviation:1 picture:3 elements:7 τa2:15 calculating:1 separate:2 thereafter:1 variation:1 emission:10 commutator:1 meaning:1 important:3 bounded:1 suited:1 variable:4 structure:3 acknowledgment:1 implies:2 coupling:1 perturbatively:1 values:3 baker:2 space:2 packets:1 dσ:2 together:2 mass:11 4k:2 time:58 n2:1 dover:1 original:1
|
quant-ph9502017.txt |@word represent:3 concept:1 consider:1 remarkable:2 similarity:1 depends:4 excellent:4 focus:1 leads:6 eds:1 fig2:1 fig1:3 consists:2 issues:3 devoted:3 depend:1 violate:5 integral:1 irrelevant:1 deterministic:2 nonlocal:23 quasi:4 under:3 stochastic:1 must:1 applied:2 expressing:1 deeper:1 very:2 void:3 polarization:6 wave:13 orientations:9 summarized:2 experimentally:1 matrices:3 condition:3 disturb:1 beam:4 presented:2 cosine:1 integrating:1 large:1 a129:1 phase:3 eigenvalues:2 warszawa:1 optics:2 noted:1 concluded:1 work:2 sin2:3 za:1 unpolarized:1 surrounding:1 second:9 perspective:1 subtle:1 further:1 linear:2 even:4 established:1 what:3 clauser:1 contradicts:1 apparatus:17 section:1 expressed:5 uniform:2 ˆb:1 version:3 new:4 ever:2 consisting:1 σaz:1 outgoing:2 led:1 respectively:3 fields:2 answers:2 understanding:1 mermin:1 cos2:5 address:2 directions:12 path:2 along:6 quite:1 change:4 calculate:1 obtained:1 search:1 incoming:3 rigorously:1 institute:1 involved:1 leaves:1 vectors:2 reason:1 eberly:3 prior:1 simultaneous:2 professor:2 published:1 opinion:1 suitable:2 studies:2 involves:1 york:1 criticism:1 via:1 spatially:2 projection:2 marginal:3 polarizers:3 outcomes:11 first:6 analyzing:1 stern:23 total:2 unit:3 opponents:1 use:1 feb:1 would:1 prove:1 representing:1 positive:12 negative:2 predictability:1 predict:4 going:1 call:1 criteria:2 type:1 theoretical:2 today:1 more:3 separated:3 introducing:1 brings:1 operators:4 odinger:1 confidence:4 everywhere:1 normalized:2 particular:2 known:4 foundations:2 cases:1 detects:1 iii:1 carried:2 helped:1 include:1 debates:1 divorced:1 permits:1 mod:1 setup:1 averaged:1 theories:7 debated:1 assumptions:1 values:5 concepts:2 following:21 making:2 spontaneous:4 example:7 performed:2 figure:4 give:1 process:6 distributions:1 effort:2 sphere:1 indicates:1 minimum:1 numbers:4 sense:2 distinguishable:2 occur:3 axis:1 information:1 available:4 provide:6 antiparallel:9 means:3 range:1 write:3 how:2 criterion:2 answer:1 instead:3 field:36 ensemble:1 description:9 may:4 weaknesses:1 averages:1 pqm:4 violates:2 discomfort:1 jumping:1 value:6 waves:2 representations:1 law:7 fixed:1 parallel:4 realized:1 short:1 natural:1 dynamical:1 joint:5 whenever:2 light:10 correspond:3 element:1 complexity:1 so:3 fundamental:5 correlation:15 order:8 triggering:1 prefactor:2 holds:2 interpretation:11 help:1 produces:1 developed:1 over:4 move:1 equally:1 years:2 produced:1 course:1 paper:6 through:1 statistical:5 argued:1 existence:1 vita:1 its:5 perfect:3 regions:1 derive:1 directional:2 scully:3 forms:1 detected:8 permanent:1 fig:12 pcl:2 redhead:1 hidden:28 overcome:1 correspondence:2 non:1 good:2 views:1 weakness:1 cover:3 introduce:1 framework:3 oke:1 they:2 krzysztof:2 oxford:3 now:2 discuss:1 eigenvalue:2 february:1 dirac:1 fizyki:1 fully:1 university:4 realistic:1 inequality:25 reasonable:2 each:4 found:1 entirely:1 uniwersytet:1 characterized:2 reproducing:1 sequences:6 different:8 just:5 series:3 idea:3 breakthrough:1 operator:1 literature:1 measurement:4 quantum:85 our:4 transitions:2 eq:7 event:3 yet:5 out:2 leave:1 shown:2 matrix:3 space:3 electronic:1 rep:1 since:1 rev:4 projected:1 rz:1 research:1 particles:21 lord:1 i0:2 denoted:6 formula:3 induced:1 issue:1 correct:1 shows:2 after:2 theory:19 albuquerque:1 free:1 standard:1 completely:2 a112:1 bayes:1 put:2 org:4 carets:1 milburn:1 definition:1 dλb:6 σmin:1 dλa:7 could:3 days:1 bears:1 disturbed:1 place:1 isotropic:1 unknown:1 consequence:1 uses:1 exhibited:1 first:2 indebted:1 there:5 probability:18 feel:1 variables:22 disproved:1 number:1 reaches:1 restrict:1 clear:1 philosophical:1 set:1 done:1 unspecified:1 knight:1 calculational:1 imperial:1 open:1 illustrate:1 given:18 rewritten:1 introduction:2 leading:1 interact:1 system:17 relations:2 their:4 assumption:2 thoughts:1 statement:2 show:4 perfectly:1 behaved:1 frame:1 gives:1 interests:1 lot:1 tool:1 proving:1 direct:2 believe:1 convinced:1 png:8 relative:4 polarized:2 determines:4 wigner:3 sections:1 intensity:2 states:1 classes:1 polarizer:7 outcome:2 projections:1 false:1 rewrite:2 reproduces:1 well:2 ann:1 modern:1 argument:2 attenuation:2 already:1 substantial:1 close:1 need:1 seen:1 constrained:2 apparently:1 any:4 indeed:1 strength:1 genuine:2 built:1 zero:2 analyzers:3 speculative:1 ideas:2 definite:1 oriented:8 ideal:1 take:6 analogy:1 forming:1 objective:21 formulas:3 play:1 electric:1 opposite:2 singlet:9 most:2 involving:4 instytut:1 letter:1 pair:2 pais:1 measured:6 class:1 probable:1 observation:2 consequences:1 characterizes:1 considered:1 average:4 adopt:1 detectors:5 typeset:1 mechanical:15 typical:1 physics:6 shimony:1 fact:11 quantity:3 simultaneously:1 nonpositive:7 violation:4 random:12 discovered:1 relation:2 gerlach:23 earth:1 debate:1 ground:1 teoretycznej:1 dice:1 parameters:8 situations:1 written:1 should:1 failed:1 only:7 experiment:2 my:1 factor:2 local:30 dn:1 do:4 his:4 get:1 dependent:3 de:1 differ:1 expectation:5 speculated:1 famous:2 words:1 despite:1 fe:1 processes:2 podolsky:3 fields:1 arxiv:5 remove:1 dissociating:1 experiments:5 common:1 though:1 london:1 discussing:1 wrote:1 view:3 apparatuses:2 preserve:1 multiplying:1 questions:1 exists:1 unpublished:1 correlations:27 ends:1 detection:2 see:9 individual:4 college:1 result:6 disturbing:2 nonlocality:7 best:2 closer:3 detect:1 inequalities:2 pictures:1 review:2 definite:1 superb:1 symmetric:1 state:14 determined:1 various:3 disprove:1 between:9 understood:1 prentice:1 caves:1 approach:2 knowing:1 adv:1 warszawski:1 terms:3 investigated:1 nature:6 fold:2 emitted:2 analyzer:5 incident:2 key:1 analyzed:1 article:2 come:1 problem:1 both:2 cos:15 limits:1 according:3 against:1 connection:2 iv:1 incompleteness:1 passing:1 expression:2 experimental:4 mechanics:31 bell:24 simple:1 character:2 corresponds:2 insist:1 dimensional:1 represented:3 simply:2 interrelations:1 respect:1 speak:2 conference:1 better:1 pp:1 described:5 tremendous:1 ewski:1 due:2 been:8 secret:1 describes:2 expected:1 marginals:2 ph:5 extreme:1 hardly:1 universal:1 systems:3 direction:9 corresponding:7 indeterminacy:1 coherence:1 photon:1 zeilinger:1 angles:3 spin:62 realities:17 case:8 noncommuting:1 look:2 unlike:1 pacs:1 appearance:1 directionality:1 spontaneously:2 will:6 cast:1 while:1 replaced:1 shall:10 pˆ:2 property:3 study:1 orientation:6 mexico:3 almost:1 zeitschrift:1 tests:2 encouragement:1 equal:4 ii:1 itself:1 obey:1 ie:2 disappear:1 acknowledgments:1 az:1 author:1 perhaps:1 identities:2 make:2 formulations:2 radiation:5 satisfying:2 same:9 clearly:2 stimulated:1 quant:5 arguments:1 pauli:4 influenced:1 figures:1 constructed:1 events:1 independent:5 used:3 http:4 posed:1 defy:1 permit:1 upon:1 nj:1 hand:4 moving:1 purpose:2 angle:3 normalization:2 recent:1 elec:1 schr:1 center:2 makes:3 poland:2 locality:8 epr:27 anybody:1 analysis:1 bohm:5 without:3 components:2 na:41 position:2 left:1 spherical:1 ny:1 enormously:1 proposed:1 among:1 being:4 accurate:1 obtain:5 reviewed:1 λb:70 λa:65 formulated:1 predicts:4 alternative:1 eigenstates:1 based:7 letting:1 note:1 dissociation:2 conclusions:2 similarities:2 point:1 had:1 hall:1 questioned:1 versa:1 theorem:1 prominent:1 interprets:1 excited:1 momentum:2 real:3 ield:5 aspects:2 spectacular:1 format:4 bialynicki:1 off:1 disagreement:1 possible:5 plenum:1 early:3 possibly:2 know:1 press:2 using:4 vague:1 advanced:2 like:3 milonni:1 englewood:1 appearing:1 particle:8 success:1 follows:2 reduces:1 either:2 always:1 conclusion:1 essential:1 spins:6 because:8 old:1 deal:1 sequence:3 tells:1 conditional:7 some:2 born:8 duration:1 lead:2 2e:1 stronger:1 electromagnetic:1 measurements:4 integration:2 classical:3 does:8 exposition:3 select:1 dissociates:2 prog:1 prof:1 limitations:1 truth:1 ps:4 elucidate:1 equivalent:6 arbitrary:3 agreement:1 clarendon:1 revtex:1 occurred:2 santa:1 dna:8 properties:7 bz:1 constrains:1 about:2 malus:9 usa:2 anything:1 certainty:2 dnb:7 discussed:1 chance:3 o:6 probabilities:3 carries:1 realism:7 act:1 introduced:6 considerations:1 raised:1 warsaw:1 into:5 predictions:1 three:9 down:1 lies:1 right:1 references:1 determine:1 einstein:10 elementary:3 easy:1 theoretically:1 descriptions:5 birula:1 additional:2 undiscovered:1 assumed:1 initial:1 question:4 equation:1 why:1 accordingly:2 much:2 way:4 was:3 function:36 considerably:1 mixture:1 complete:1 form:17 governs:1 phenomena:1 regard:1 hv:1 but:5 failure:1 repeated:1 contradictory:1 ho:1 delta:1 odkiewicz:7 he:2 made:2 versions:1 probabilistic:7 up:1 us:7 record:1 limit:1 continuously:1 demonstrate:1 distribution:40 similar:2 called:2 strongly:1 associated:2 conserves:1 certain:1 abstract:1 describe:1 am:1 satisfied:1 single:3 exist:1 dλ:2 formulation:2 formalism:2 commuting:1 check:1 physical:9 functions:5 compared:1 completeness:1 puzzling:2 no:5 allow:2 nb:29 rosen:3 reality:13 field:13 other:5 papers:1 department:2 really:1 unobservable:1 revision:1 conclude:1 elements:1 kinds:1 emission:4 deriving:1 meaning:1 important:2 bounded:1 variable:8 formal:1 astronomy:1 structure:1 ghost:55 independently:2 correlated:6 remote:2 longer:1 vice:1 assume:6 came:1 odds:1 required:1 speculations:2 scientific:2 inhibited:1 lying:1 time:3 far:1 observables:5 meystre:1 starting:1 lett:2 once:2
|
quant-ph9502018.txt |@word consider:1 rev:11 results:2 gx:1 leads:1 certainly:1 depend:3 b262:1 rayleigh:1 finally:1 th:2 anharmonic:5 divergent:2 scienti:1 nite:1 very:1 rise:1 condition:3 treating:1 level:1 ref:1 large:1 small:1 eigenvalues:1 tognetti:2 speci:1 arnimallee:1 direct:1 approximation:3 second:4 value:1 odd:1 even:2 giving:1 sum:3 3n:1 new:1 method:1 degree:4 staudinger:1 here:1 desired:1 asymmetry:1 stancu:1 path:1 extrema:1 observing:1 obtained:2 great:2 shift:1 trial:1 makes:1 summation:1 b227:1 select:1 use:1 feb:1 prove:2 e0:1 therefore:1 bender:2 rearranging:1 becomes:2 ghandour:1 c44:1 c45:1 quartic:3 work:1 oscillator:5 values:1 proof:2 calculation:2 expanding:1 numbers:1 extremality:2 nontrivial:1 a173:1 optimal:1 ordinary:1 parameter:3 quantenmechanik:1 replacing:1 after:1 derived:2 physik:2 forschungsgemeinschaft:1 deutsche:1 barnes:1 order:8 restriction:1 help:3 developed:1 its:1 derive:2 d36:1 interesting:1 d35:1 d32:1 d30:1 derivative:3 factorial:1 scaling:7 identically:1 now:1 easily:2 february:1 indeed:1 2r:2 2g:2 2b:1 each:2 2l:2 d42:1 d47:1 series:7 energy:4 related:1 quantum:2 our:1 eq:3 since:5 crucial:1 rational:1 increase:1 fellowship:1 performs:1 formula:1 evaluation:2 theory:4 standard:1 b123:1 term:7 remainder:1 universally:1 b33:1 interaction:2 exponentially:4 first:1 variables:1 powerful:1 number:1 cients:3 long:1 reached:1 xp:1 given:1 perturbation:11 introduction:1 theoretische:1 least:1 1b:1 identity:1 variational:10 gives:1 a34:1 x2:2 x1:1 x4:1 scheme:1 require:1 see:2 powers:4 result:2 rewrite:1 turned:1 mater:1 any:1 strength:1 note:1 empirically:1 potential:8 take:1 thoma:1 strengths:1 accuracy:4 heisenberg:1 shall:1 observation:1 average:1 typeset:1 feynman:1 points:1 physics:1 quantity:1 mainz:2 show:1 ritschel:1 discovered:1 rst:2 d7:1 giachetti:2 duncan:1 only:1 factor:3 extremum:1 di:1 dependent:1 de:18 ones:2 fastest:1 dw:7 expansions:4 attest:1 computed:1 exists:1 edition:1 depends:1 ebw:8 radius:1 truncating:1 vint:2 best:1 symmetric:1 smallest:1 approach:2 discovery:1 recently:1 extremized:1 however:1 wu:2 le:1 magn:1 preprint:2 last:1 vanishing:1 coe:3 otherwise:1 simpli:1 vaia:1 simple:1 ca:3 harmonic:3 2nd:1 universitat:2 polynomial:4 respect:1 strong:1 described:1 publishing:1 due:1 been:2 johannes:1 much:1 ph:1 abstract:1 determination:1 systematic:1 general:2 fur:2 exponential:1 evaluated:1 will:1 while:1 property:4 polymer:1 converts:1 recursion:1 freie:1 quant:1 split:1 und:1 dimensionless:1 independent:1 investigated:1 singapore:1 trivially:1 upon:1 levels:1 purpose:1 kleinert:8 recent:2 2gr:1 position:1 xed:1 obtain:3 vanishes:3 thanks:1 world:1 co:1 speed:1 weg:1 lett:9 extremization:1 possible:2 increases:3 using:1 necessary:1 stevenson:4 follows:3 reduces:1 yields:3 integrals:1 arbitrary:2 reduced:2 truncated:1 understood:1 growth:1 choosing:1 statistik:1 does:3 demonstrated:1 inserting:1 janke:1 power:2 expansion:8 d43:1 revtex:1 meyer:1 o:1 essential:2 greatly:3 sissakian:1 mannheim:1 raised:1 into:4 references:1 schrodinger:1 statistics:1 institut:2 additional:1 c51:1 removing:1 there:1 approximate:1 fast:4 ed:1 was:2 function:1 jones:1 forming:1 tarrach:2 but:1 reed:1 convergence:4 line:1 whether:1 up:2 limit:1 demonstrate:1 similar:1 mechanics:2 required:1 constant:2 int:1 universal:2 meaningless:1 textbook:1 convergent:3 proves:1 proceeds:1 b176:1 nd:1 detail:1 rewriting:1 details:1 papers:1 rx2:1 denote:1 polynomials:1 gutenberg:1 variable:3 b313:1 ago:1 independently:1 coupling:5 d22:1 berlin:4 together:1 time:1 requires:1 having:1
|
quant-ph9502019.txt |@word limited:1 consider:1 caused:1 results:4 zinn:1 gr:1 certainly:1 depend:1 calculate:2 b262:1 show:1 ts:2 program:1 th:1 anharmonic:4 divergent:1 g4:1 scienti:1 rational:1 very:2 exact:1 ref:3 solution:1 plotting:1 large:1 small:3 tognetti:2 upper:2 speci:1 consistent:1 arnimallee:1 approximation:4 zero:2 value:6 further:1 even:1 section:1 3j:3 3n:1 goes:1 new:3 3g:1 method:1 degree:1 staudinger:1 respectively:1 here:1 stancu:1 path:1 strong:9 logarithmic:1 obtained:2 allows:1 trial:1 periodic:1 resulting:1 nmax:1 b227:1 use:1 feb:1 asymptotic:2 negative:1 e0:1 therefore:1 bender:3 taken:1 more:2 envelope:2 berlin:2 c44:1 c45:1 quartic:1 decay:1 equation:1 work:2 oscillator:4 labeled:1 values:3 example:1 calculation:2 cited:1 high:1 numbers:2 g2:1 decaying:1 rather:1 gcn:1 how:1 a173:1 optimal:2 ordinary:1 oscillatory:2 quantenmechanik:1 algebra:1 replacing:1 after:1 produce:1 physik:2 data:3 constants:1 forschungsgemeinschaft:1 natural:1 22nd:1 ny1:1 lines:2 deutsche:1 extremal:1 barnes:1 order:8 superscript:1 developed:2 russian:1 b300:1 its:1 derive:1 lb:5 deriva:1 energies:5 d35:1 d32:1 d30:1 complex:1 fig:4 lp:1 derivative:1 good:1 factorial:1 easily:2 february:1 2r:1 2g:1 reasonable:1 d43:1 d42:1 2n:1 d47:1 el:4 en:2 series:10 energy:3 used:2 frequency:2 quantum:3 our:5 extract:1 shown:2 since:1 rev:11 denotes:1 increase:1 fellowship:1 adapt:1 nite:2 evaluation:1 sliding:1 math:4 shows:1 theory:7 divergence:1 b33:1 nth:1 b123:1 dubna:1 remainder:1 generate:1 care:1 interaction:1 plane:1 exponentially:2 first:1 symbolic:1 system:1 cients:12 relations:1 maple:1 given:2 perturbation:12 leading:1 theoretische:1 least:1 kleinert:8 variational:6 gives:1 a34:1 estimates:1 exactly:1 part:1 x2:4 than:3 x4:2 determines:1 third:1 approximations:2 see:3 limiting:1 1n:1 powers:3 tives:1 ann:1 mater:1 close:1 any:2 acceleration:1 note:4 instance:1 potential:2 thoma:1 accuracy:3 heisenberg:1 formulas:1 most:2 inserted:1 calculated:2 feynman:1 exp:1 mechanical:2 physics:1 quantity:1 slope:1 mainz:2 rayleigh:2 ritschel:1 rst:3 d7:1 agrees:1 ground:3 giachetti:2 proposed:1 duncan:1 state:3 should:1 only:3 transcendental:1 do:1 dependent:1 cannot:1 fastest:1 report:1 expansions:3 optimally:1 hioe:1 unpublished:1 up:5 edition:1 depends:1 ebw:6 radius:1 result:2 terms:3 vint:2 best:1 written:1 approach:4 available:1 recently:2 reproduced:1 wn:10 however:2 wu:3 cut:1 magn:1 preprint:1 improve:1 many:1 eyeball:3 equal:1 d36:1 coe:15 co:1 vaia:1 conclude:1 simple:2 harmonic:2 2nd:1 semiclassical:1 simply:1 universitat:2 respect:1 publishing:1 due:1 been:2 johannes:1 cient:3 expected:1 ph:1 systems:1 wants:1 digits:4 corresponding:1 quantities:1 precision:2 systematic:1 convergent:2 fur:2 exponential:1 solid:1 straight:1 evaluated:1 will:1 behavior:2 tunneling:2 couplings:4 procedure:1 polymer:1 refs:2 ii:2 converts:1 suggests:1 perform:1 recursion:1 proceeds:1 freie:1 parts:1 quant:1 split:1 und:1 dimensionless:2 higher:1 independent:1 literature:1 closest:1 singapore:1 hand:1 vainshtein:1 expand:1 mentioning:1 lower:2 well:1 left:1 xed:1 just:1 being:1 accurate:5 thanks:1 using:1 speed:1 previous:1 enters:1 weg:1 strongcoupling:1 lett:11 easy:1 montroll:1 input:1 around:1 term:4 know:1 integer:1 precise:1 follows:2 stevenson:4 yields:4 integrals:1 truncated:2 some:1 growth:1 table:5 oscillations:1 statistik:1 provided:1 scale:1 does:1 power:2 expansion:11 bw:1 imaginary:2 refers:1 meyer:1 about:2 justin:1 world:1 dependence:2 o:2 langer:1 sissakian:1 converging:1 mannheim:1 into:3 down:1 novosibirsk:1 theoretically:1 schrodinger:2 statistics:1 institut:2 additional:1 c51:1 yamazaki:1 approximate:1 fast:2 function:1 considerably:1 form:1 tarrach:2 but:2 reed:1 related:1 convergence:3 line:2 bounds:3 limit:1 problem:1 ub:5 mechanics:1 constant:2 int:1 denote:1 check:1 regime:2 nj:1 compared:1 b176:1 agreeing:1 dashed:2 nd:3 rewriting:1 application:1 setting:1 papers:2 rx2:1 a17:1 calculating:1 uniformly:1 gutenberg:1 b313:1 structure:1 jones:1 coupling:11 d22:1 curve:1 ghandour:1 tted:1 far:1 4g:2 requires:1 having:1
|
quant-ph9502020.txt |@word discards:1 managed:1 limited:2 keep:1 focus:1 existing:4 four:3 muller:1 fig2:1 overlap:7 computation:2 fig1:3 optical:1 whose:2 depend:1 calculate:2 disposal:2 technique:3 send:11 chapt:1 present:8 under:1 discovering:1 worth:1 sent:10 ingredient:1 case:9 string:3 advantage:8 orthogonal:19 very:9 none:1 choice:5 graphic:1 decide:1 experimentally:2 emphasized:1 difference:4 electronics:2 condition:2 common:1 splitter:3 randomness:1 squares:2 pbs:1 level:2 transmission:43 notes:1 having:5 mirror:1 eve:60 plotting:1 large:1 small:4 possibilities:1 added:2 smaller:2 d3:5 pulse:20 second:8 implemented:4 even:9 what:2 errors:13 essence:1 appear:1 rate:30 randomize:1 section:22 shares:1 decoding:2 sequential:1 above:7 resilient:2 shared:6 bsym:2 public:4 contrast:3 paragraph:1 satisfy:2 pose:1 opt:2 exchange:3 intercepts:1 component:3 here:2 intercept:6 dover:1 free:1 making:1 represented:1 ratio:1 safer:3 strong:7 imperfections:1 wait:1 obtained:6 sending:1 great:1 dashed:2 incoming:1 sender:2 institute:1 shift:4 twofold:1 reason:3 adopt:1 amount:4 published:1 usually:1 bob:53 makes:2 plotted:1 named:1 deterministic:4 useful:1 secure:2 explained:1 replace:1 analyzing:1 pp:1 apply:1 counts:3 total:3 linearly:1 plot:3 use:21 feb:1 figure:5 would:14 prove:2 remains:1 positive:2 chooses:3 next:1 classically:1 explicitly:1 call:2 therefore:18 criteria:1 type:1 theoretical:2 more:17 separated:1 israel:2 relevant:2 becomes:1 limitation:1 normalized:2 particular:3 known:4 cases:3 iii:7 states:75 account:2 valued:1 science:1 work:4 modified:1 remain:1 minimum:1 values:2 concepts:1 following:5 strategies:2 example:2 compare:5 weaker:3 curves:3 give:2 bennett:7 neglected:1 purposes:1 implementations:1 high:5 sphere:3 overheard:1 attain:1 want:2 times:1 guarantee:1 information:58 rather:1 get:20 american:1 orthogonality:1 write:2 how:3 strategy:14 pair:4 opposite:1 answer:1 instead:3 preferable:3 sin:9 brassard:5 description:2 may:11 db:2 after:3 containing:1 applications:2 wrong:5 produce:1 verified:1 horizontal:1 data:1 parallel:2 short:1 attempt:5 third:1 whenever:1 light:4 correspond:5 provide:3 2d:2 cannot:10 algorithms:1 fundamental:1 correlation:2 representation:1 order:4 restriction:1 developed:2 over:4 inconclusive:9 iae:9 course:5 thermal:3 experiments:1 through:6 eavesdropping:14 mentioned:2 japan:1 satisfies:1 still:5 ieee:2 its:3 before:1 perfect:1 superior:1 group:1 thank:1 personal:1 cryptology:2 actually:2 destroyed:1 according:1 systems:18 quant:5 hidden:1 main:6 overcome:1 ly:1 them:7 good:2 combination:2 polarizations:2 safe:2 nonorthogonal:1 introduce:4 reciprocally:1 transmissions:4 they:11 half:4 now:8 discuss:1 wiley:1 restrict:1 indeed:3 2q:3 always:6 university:1 presented:1 grows:1 orthonormal:1 did:1 transmitted:1 reasonable:1 each:7 entirely:2 attenuation:1 side:2 characterized:1 referred:3 schemes:9 significantly:2 experiment:1 series:1 barnett:2 reduce:4 principles:1 related:1 deterministically:4 used:18 expect:1 sifted:2 quantum:19 our:7 tenth:1 haifa:1 out:5 try:3 shown:5 matrix:2 space:4 robert:1 since:4 rev:6 research:1 participants:1 safety:21 performs:1 lecture:1 guesses:1 eavesdrop:2 correct:6 independence:1 shows:2 disclose:1 fiber:3 log2:2 theory:4 contain:3 ntt:1 possibility:2 difficulty:2 completely:3 advantages:1 york:3 enhance:2 put:1 org:4 estimate:1 ash:1 generate:2 r5:1 pairs:4 created:1 could:6 computers:2 honest:2 creates:5 turn:2 length:2 threat:1 signature:1 corrections:1 scheme:17 onto:3 first:8 there:9 probability:8 encoding:5 variables:2 number:4 huttner:4 channels:3 instances:3 utilized:1 adopted:1 another:3 changing:1 message:2 precisely:1 given:12 likely:1 introduction:2 twenty:1 system:58 approximately:2 their:11 attack:2 assumption:1 rates:1 too:4 siam:1 perfectly:4 bits:7 damaging:2 low:2 little:1 correlations:1 fraction:7 geneva:2 sin2:2 tapster:3 part:1 differentiate:3 shifter:1 than:9 png:8 relative:1 polarized:2 unfortunately:2 showed:1 split:2 require:1 namely:2 rarity:3 matter:2 future:2 townsend:2 were:1 india:1 providing:1 distinguished:1 motivation:1 comput:1 well:1 modern:1 measure:4 bs1:2 bs2:1 randomly:1 discussions:1 say:4 unlikely:1 conjugate:2 need:1 any:17 computationally:1 courier:1 zero:6 uncorrelated:1 polarization:12 extracted:2 potential:2 read:1 take:3 transmit:1 so:4 detector:2 strengths:1 channel:16 ivanovic:1 circles:1 towards:1 shall:9 atsugi:1 measures:1 most:5 satisfying:1 phase:16 probabilistic:3 why:1 technion:1 salvail:1 considered:2 clear:3 later:2 detectors:4 km:2 typeset:1 proceedings:1 points:1 principle:8 built:1 physics:2 fact:12 laws:1 optimal:1 thomas:1 somewhat:1 intensity:2 show:5 text:1 meetings:1 random:6 obtains:1 attempts:3 represent:2 reception:1 d2:5 find:1 d1:2 based:7 implementation:13 unpractical:1 proportion:1 behind:1 should:6 technologically:1 only:19 bases:8 factor:1 ieb:5 europhysics:1 do:4 his:8 cryptography:6 means:6 dependent:1 mainly:2 simplest:1 overall:1 beam:4 ones:4 legitimate:3 new:15 lossless:2 resend:6 arxiv:5 method:3 she:36 wish:1 switzerland:1 pulses:44 discussing:1 set:1 reference:9 sensitivity:1 testing:1 up:2 detection:6 depends:2 full:3 result:12 fail:1 close:1 optimum:1 arm:1 best:1 techniques:2 hilbert:4 fails:1 detect:1 capacity:1 review:1 symmetric:2 state:7 won:1 various:8 between:24 progress:2 reading:1 approach:1 available:10 gives:1 never:1 recently:2 creating:2 vertical:2 missing:1 weak:26 however:15 interfere:1 acute:1 key:10 analyzed:2 rapidly:1 optional:2 distribution:2 faced:1 both:11 cos:5 kluwer:1 many:3 equal:5 against:2 agree:1 enabling:1 sensitive:4 disastrous:1 figures:1 receiver:2 expense:1 experimental:2 ch:1 conclude:1 had:2 excess:1 corresponds:5 directions:2 simply:2 wider:1 moreover:6 along:1 expensive:1 conference:1 ps:4 ensures:4 puts:2 basis:28 addition:1 create:5 due:3 been:1 shortening:1 povm:3 secret:4 much:7 combined:1 basic:2 ph:5 fig:13 wants:2 suggested:2 generating:1 corresponding:4 received:1 fire:1 sufficient:1 photon:20 coherent:11 lift:1 doesn:1 receive:1 hers:1 protocols:1 applied:1 dash:2 developing:1 value:3 will:41 technical:1 while:7 replaced:1 error:21 property:1 remembering:1 unsatisfactory:1 losses:6 vol:1 vi:2 thus:3 non:12 discrepancy:1 iv:4 ii:11 illustrates:1 technology:3 trusted:1 binary:2 different:10 participant:1 perform:1 suggest:2 make:3 format:4 same:7 poincar:3 shifts:1 imoto:1 pad:1 emphasize:6 schematic:1 advances:2 modification:3 infer:1 difficult:4 independent:1 practice:1 http:4 see:8 functions:2 hand:1 average:4 uses:10 angle:1 totally:2 recent:1 relies:4 lower:2 task:2 keeping:1 epr:2 anybody:1 analysis:4 without:5 comes:1 easily:1 quantitative:1 laboratories:1 ekert:6 usual:3 distances:2 abilities:1 protocol:14 just:2 less:3 transmitting:1 when:29 distribute:1 rotated:1 obtain:5 lossy:8 aspect:1 october:1 yet:2 previous:6 note:1 kanagawa:1 signal:5 candidate:1 density:2 photons:17 guaranteed:1 except:1 transparent:1 deal:1 causing:2 combine:1 lett:5 easy:5 technological:3 input:2 distinguish:2 mod:2 remaining:1 noting:1 generalized:1 real:1 insensitive:1 increased:1 represents:1 iα:5 mor:1 results:12 possible:7 dark:2 department:1 increases:1 know:6 listening:1 vacuum:3 confined:1 using:8 bit:5 like:1 loss:1 necessary:1 schematized:1 splitting:1 reduces:3 alice:42 discarded:4 either:4 fully:1 become:1 works:1 reduced:2 mathematical:1 because:1 methods:1 classical:4 sends:4 creation:2 some:2 springer:1 sure:1 b0:2 b1:2 choosing:1 respect:4 extended:1 guess:1 ourselves:1 tutorial:1 happens:1 facing:2 projection:2 phoenix:3 sufficiently:1 leak:1 decision:1 unavoidable:1 per:5 does:8 select:2 provides:2 unavoidably:4 prob:4 refer:1 limitations:1 noise:1 scientific:1 power:1 slight:2 journal:1 processing:3 combines:1 broken:1 protagonist:1 revtex:1 bangalore:1 interferometric:1 properties:1 gained:2 comparison:2 about:5 eavesdropper:12 certainty:1 discussed:2 dependence:1 practical:7 ensure:2 stand:2 discard:3 introduced:1 slightly:1 block:1 equally:1 letters:3 communication:3 into:3 obtaining:1 three:2 nothing:2 appropriate:1 references:1 ηq:1 operator:1 conceptually:1 nowadays:1 realisation:1 rely:5 computer:1 additional:1 her:9 few:2 initial:1 reduction:1 long:2 decode:1 start:1 appears:1 trigger:1 symbiosis:2 way:4 analyze:1 was:11 ensured:1 function:6 complete:1 enough:2 smolin:1 dangers:1 but:11 idea:1 game:1 gain:2 encoded:2 line:9 proposal:1 he:6 count:4 made:2 interferometer:1 whether:2 characteristic:1 maximum:5 devices:1 dordrecht:1 projecting:3 problem:6 similar:2 called:2 gisin:2 mechanics:1 sometimes:1 associated:1 computing:1 defined:3 cover:1 abstract:1 measurement:2 influence:1 proven:1 denote:1 peres:4 separating:1 single:10 exist:1 rule:1 triangles:2 again:1 mutual:7 us:8 dotted:4 no:13 extract:3 whereas:1 malicious:1 generally:1 acknowledgments:1 other:10 test:3 really:2 conclusion:1 elements:1 kinds:1 users:6 calculating:1 separate:1 problems:1 disclosed:1 prepared:1 important:1 palma:2 conclusive:1 cryptographic:7 correlated:5 faster:2 assume:8 required:2 together:1 original:2 equivalently:4 mimic:1 ternary:1 time:3 international:1 leaked:5 silica:1 strings:4 once:1
|
quant-ph9502021.txt |@word represent:1 partial:1 consider:5 limited:1 induces:1 activated:2 results:3 existing:3 four:2 comments:1 computation:1 fig1:1 consists:2 faster:1 localized:4 duplicated:2 amplification:1 tr:6 ts:6 send:2 finally:3 does:3 device:2 protocols:5 under:1 dramatically:1 sent:11 ingredient:2 string:1 confidential:1 orthogonal:28 very:5 every:1 experimentally:1 difference:1 exact:1 arrange:1 splitter:5 school:1 presented:1 transmission:17 t2:42 eve:26 occurs:1 leave:1 solved:1 adjust:1 small:3 equation:1 upper:4 tel:2 exposed:2 direct:1 second:4 fiber:2 traveling:3 leakage:1 theory:2 even:4 errors:7 appear:2 rate:3 access:2 waiting:1 version:2 shared:1 public:1 told:1 simultaneously:2 exchange:1 respectively:1 never:1 following:1 them:1 possibility:2 lev:1 directions:1 along:2 respect:1 obtained:1 sending:13 receive:2 leaves:1 larger:1 allows:3 reason:1 amount:2 loop:1 bob:34 narrow:1 changes:1 delays:1 via:2 spatially:1 secure:6 extra:2 private:1 replace:1 apply:1 counts:2 use:8 feb:1 superpositions:1 prove:1 chooses:2 comparing:1 therefore:7 distortions:1 encode:1 goldenberg:1 until:2 preserved:1 separated:1 introducing:3 israel:1 started:3 stable:1 emission:1 tested:1 particular:3 known:3 foundations:1 cases:1 detects:1 must:10 evolves:5 science:1 setup:6 work:1 modified:2 learn:1 believed:1 arrive:3 example:1 proof:4 compare:1 figures:1 figure:2 mirrors:1 relativistic:2 bennett:6 india:1 states:31 assumptions:1 caused:1 performed:2 want:2 tal:1 david:1 distinguishable:1 information:12 redundancy:1 end:2 advantage:2 carriers:1 s1:6 s0:6 feature:1 orthogonality:2 delay:5 symposium:1 brassard:4 simplicity:1 intended:1 may:2 insecure:1 after:3 coming:2 requirements:1 data:5 efficiently:1 attempt:5 whenever:1 light:2 complexity:1 so:2 block:3 fundamental:1 correlation:1 order:5 enter:2 indeed:1 over:3 years:1 timing:3 through:2 eavesdropping:6 still:1 ieee:3 its:5 before:3 derive:1 thank:1 chosen:1 decreases:1 aviv:2 wasting:1 detected:9 degrees:1 choose:3 annual:1 quant:2 might:3 emphasize:1 maximal:1 non:13 good:1 polarizations:1 practice:1 impossible:1 introduce:2 course:1 they:9 half:3 arriving:1 now:3 developments:1 university:1 classified:1 altering:1 transmitted:5 each:4 found:2 side:1 schemes:1 directly:1 experiment:1 scheme:7 idea:1 related:2 inverted:1 interferometer:3 sandu:1 used:11 measure:4 quantum:19 our:10 operation:1 t1:36 extract:3 message:10 shannon:1 out:1 emerges:2 ultimately:1 restricted:2 since:14 crucial:1 particles:4 emerged:1 get:3 receiving:3 issue:1 correct:3 shows:1 earlier:1 linear:1 assured:1 free:5 assures:2 completely:1 org:1 detecting:1 advance:1 pairs:1 starts:2 could:1 computers:1 times:7 turn:1 length:1 disturbed:1 exponentially:2 hence:1 uses:1 first:6 already:2 probability:3 encoding:2 faculty:1 coding:4 huttner:2 channels:10 done:3 another:2 reached:1 ring:3 passes:1 necessarily:1 checked:1 privacy:1 unitarity:1 unknown:1 eqs:5 sackler:1 system:2 their:3 intermediate:1 too:3 realization:1 perfectly:1 bits:14 final:2 speaking:1 discussion:3 imperfect:1 optical:2 shifter:1 authors:1 copy:1 than:3 png:2 relative:2 polarized:1 encrypting:1 zero:2 preparation:1 were:3 tion:1 solely:1 cloning:1 false:1 correction:1 bs1:4 bs2:5 idler:1 distorted:1 exchanging:1 recover:1 any:13 conversion:1 traditionally:1 depending:1 ideas:1 polarization:6 sciences:1 ideal:1 take:1 transmit:2 negligible:1 detector:3 techniques:1 smolin:1 channel:19 accuracy:2 towards:3 unless:2 trace:1 shall:4 price:2 measures:2 systems:1 most:1 letter:2 phase:6 mach:3 dummy:4 salvail:1 later:2 detectors:2 proceedings:2 part:3 principle:1 physics:1 laws:1 shor:1 show:1 encrypted:1 agreed:1 random:9 registers:1 disturbs:1 tempted:1 longer:1 find:2 d0:5 d1:5 believe:1 based:8 popescu:1 title:1 implementation:1 explain:1 behind:1 should:4 transmitting:1 only:6 bases:2 partially:1 achieve:1 do:2 his:1 cryptography:7 means:2 methods:1 beam:5 cannot:8 new:2 combinations:1 during:1 resend:1 evolution:7 sources:2 arxiv:2 method:5 she:9 fixed:1 discussing:1 interference:1 requirement:2 set:2 achieved:2 generally:1 correlations:1 lior:1 detection:2 depends:1 computer:1 result:3 enhanced:1 close:1 arm:1 seems:1 fails:1 detect:1 rings:2 sites:3 state:11 difficulties:1 bruno:1 correctly:2 between:7 probably:1 conditions:1 available:1 ends:1 emitted:3 however:5 interfere:2 efficiency:2 key:8 problem:2 improve:1 suggested:1 received:1 last:2 limits:1 many:2 uncertainty:1 equal:1 called:2 etc:1 usable:1 receives:1 passing:1 extracting:1 otherwise:2 relevant:1 afterwards:1 conclude:1 reasons:1 had:1 cryptosystem:1 anti:1 cryptology:1 moreover:2 conference:1 destroyed:1 raise:1 basis:8 addition:2 encryption:1 due:3 strategy:1 extraction:1 faithfully:2 basic:2 expected:1 ph:2 fig:2 direction:1 flight:2 photon:5 precision:1 demand:1 present:9 case:3 novel:1 look:1 publicly:1 informing:1 value:4 will:6 while:2 reliability:1 error:7 35th:1 procedure:2 losses:2 thus:7 site:11 respected:1 different:5 perform:1 large:2 same:8 tells:1 pad:1 wavepacket:11 modification:1 party:1 gets:1 difficult:1 arrives:2 http:1 raymond:1 see:1 zehnder:3 effect:1 hand:3 moving:5 purpose:1 frequently:1 caption:1 task:1 no:5 vaidman:1 without:8 components:1 recombine:2 left:1 distances:1 protocol:8 just:4 being:5 storage:5 rotated:1 obtain:1 valuable:1 front:1 speed:1 yet:1 captured:1 previous:2 note:1 enters:1 photons:8 guaranteed:1 signals:2 source:3 lett:2 theorem:1 tolerable:1 identical:2 tests:2 rev:3 format:1 read:2 mor:2 measurement:1 possible:6 dark:2 discreet:1 know:2 secrecy:4 press:1 using:13 bit:7 necessary:1 lost:3 particle:29 follows:1 signal:3 alice:32 either:2 beverly:1 security:7 essential:2 exceed:2 right:1 wavepackets:14 classical:4 sequence:1 sends:3 some:12 added:2 mirror:2 superposition:2 bottom:3 measurements:2 legal:3 sr2:7 sr1:6 assuming:1 measuring:1 noise:4 obey:1 ps:1 late:2 processing:1 broken:1 bangalore:1 publishing:1 comparison:1 about:2 stations:2 eavesdropper:7 tuned:1 introduces:2 practical:3 mutually:2 range:1 stand:2 discard:1 automatically:1 computational:1 beamsplitter:1 previously:1 communication:7 into:5 arms:1 down:1 nothing:1 appropriate:1 references:1 intervention:2 rely:1 estimating:2 assumed:1 strictly:1 there:4 secret:2 long:4 noticed:1 width:1 detectable:3 way:8 was:4 assumes:1 naturally:1 function:2 complete:1 form:2 enough:4 registered:2 delayed:7 but:10 cloned:4 gain:1 estimation:1 encoded:1 trying:1 proposal:2 he:3 builds:1 places:1 versions:1 prevents:1 transmits:1 us:2 crystal:1 those:1 distribution:4 more:1 similar:1 agree:2 cryptosystems:5 distance:1 mechanics:2 sometimes:1 leaked:1 zeno:1 abstract:1 combining:1 linearity:1 proven:4 general:2 peres:1 single:5 replica:2 laboratory:1 corresponding:2 incorrect:2 high:1 mutual:2 avoided:1 ingredients:1 eq:3 ekert:2 when:7 other:8 better:1 test:1 users:9 divincenzo:1 problems:1 shown:1 variation:1 palma:1 included:1 astronomy:1 cryptographic:3 correlated:3 auxiliary:1 together:4 original:1 portion:2 time:38 international:1 requires:2 strings:2
|
quant-ph9502022.txt |@word footing:2 allowed:1 consider:6 magnetic:2 rovelli:1 dynamic:1 focus:1 illustrated:1 scalar:5 commute:1 c2:7 consists:1 uϕ:2 imbedding:1 gr:1 devoted:1 woodhouse:1 dimensionality:3 depend:5 calculate:1 tx:5 technique:1 editors:2 james:1 preprint:1 presents:1 company:1 charge:1 unpleasant:3 device:2 tk:2 th:2 under:8 hill:1 p2:2 fax:1 amplitudes:1 hibbs:1 orthogonal:1 very:5 dokl:1 wave:1 electron:8 valued:1 lecture:1 difference:3 rn:16 condition:2 entire:1 quantized:3 hamiltonian:13 t4:4 t2:5 grandfather:1 leave:1 item:2 vector:7 phase:1 math:5 guiding:1 section:6 manifestly:1 proof:1 possibility:1 zn:3 occurrence:1 zj:4 direct:2 sign:3 past:3 second:11 summer:1 arnold:1 rigorous:1 casual:14 victor:1 even:4 what:1 projectors:1 appear:2 arveson:1 deeply:2 sum:2 brief:1 kisil:14 infinitesimal:1 suspect:1 lifshitz:4 new:11 principal:1 method:2 guillemin:1 notions:1 degree:2 hq:5 never:1 component:2 here:6 diagonal:2 believed:1 interno:2 free:16 separation:1 alone:1 path:4 sine:1 equations:5 z1:3 obtained:2 search:1 granting:1 root:1 studied:1 allows:1 contradiction:1 mx:1 suggests:2 natures:1 usually:8 symmetrical:1 fourier:1 rafael:1 involves:2 named:1 useful:2 projection:32 classification:1 forbid:1 annihilations:1 explained:1 ipn:1 gurevich:1 logical:1 outcomes:1 expect:1 addressed:1 unitary:2 logically:1 lanczos:1 willey:1 meson:1 unit:1 identically:1 use:5 feb:1 takes:1 would:5 analytic:1 sake:1 positive:3 lying:1 negative:6 next:1 linear:1 going:1 memory:1 themselves:1 type:6 theoretical:2 more:5 flat:1 sons:1 symposia:2 composite:1 remark:10 operators:7 odinger:12 herein:3 berlin:2 correspondingly:2 observations:1 sharply:1 particular:1 foundations:1 cases:2 fermionic:1 topic:1 springer:4 isomorphism:3 vladimir:14 ilya:2 equation:34 work:1 oscillator:1 theories:1 simplify:1 fock:5 del:3 novikov:1 following:10 meet:1 trans:1 my:3 example:13 dxj:2 point:6 claim:1 dedicated:1 yeshiva:1 figure:4 give:4 relativistic:79 sense:4 pro2:1 states:14 contradicts:2 pq2:1 lorentz:13 numbers:1 arise:2 exclude:1 enrique:1 made:1 verlag:4 information:2 counting:1 end:1 rather:2 means:2 georg:1 write:1 how:3 thermodynamics:1 pure:3 answer:1 explains:1 priori:1 simplicity:2 express:1 description:5 algebra:17 may:20 after:2 mapping:1 dx0:2 ronald:1 applications:2 produce:2 multiplication:8 representations:8 summarize:1 compatibility:1 types:6 namely:2 stress:1 short:3 natural:9 dynamical:3 four:3 prerequisites:1 light:11 sp:5 lines:1 corollary:3 rpq:2 cosmology:1 marlow:1 cannot:1 encyclopedia:1 allow:1 pleasure:1 xia:1 restriction:2 wigner:1 words:2 indeed:2 over:1 dy:6 stability:1 momentums:1 wiener:1 paper:5 mentioned:1 existence:7 y2:3 its:9 before:1 style:1 discontinuous:1 group:6 till:1 interesting:1 relativity:5 coordinates:3 ds:4 creations:1 degrees:5 systems:2 pergamon:2 mail:1 hidden:1 main:4 definitely:1 deformation:1 outside:1 non:14 someone:1 fourth:2 yn:1 rpr:1 propose:1 introduce:10 number:4 framework:1 hamilton:6 effects:1 they:2 hands:1 oxford:3 employed:1 bogoliubov:1 now:6 yu:1 discuss:1 kirillov:1 february:1 dirac:14 2s:1 parameter:5 university:3 presented:1 realistic:3 x21:2 l2:25 editor:1 reasonable:1 each:1 found:2 notes:1 constraints:1 spinor:5 square:3 r2n:11 energy:7 idea:2 operator:27 ξj:3 decays:1 obtains:3 measure:5 quantum:34 our:20 special:4 out:1 principles:1 try:1 shown:1 matrix:1 rr:2 space:33 spectrum:4 superluminal:3 lagrangian:6 douglas:1 particles:21 acting:1 conclusions:2 multiply:1 dxdy:4 reader:1 formula:1 wick:1 red:1 shows:2 foundation:1 theory:25 interactions:1 contain:1 given:2 departamento:3 standard:12 approaches:1 york:8 disposition:1 generate:1 r4:9 definition:1 enormous:1 r0:14 derivation:1 phrases:1 transition:2 ds2:2 keep:1 motion:3 turn:1 gordon:7 transfer:1 onto:4 first:9 w1:1 xi:2 xn:1 features:1 probability:1 isometrical:2 variables:1 primary:1 dominating:1 least:2 another:4 braces:1 city:2 little:1 toy:3 publication:1 introduction:6 unknown:1 adjoint:2 system:8 construct:3 their:6 assumption:1 1e:1 fermions:1 calculations:3 kuzmin:1 inconvenient:1 scheme:3 speaking:1 gives:5 isomorphic:1 explanation:1 observable:3 immediate:1 part:6 jordan:1 too:2 dt2:1 x2:1 x1:1 unrealistic:1 than:3 specify:1 toronto:2 approximation:1 develop:1 third:1 edition:4 course:2 fundamental:1 zero:4 annihilation:1 future:15 contrary:1 coburn:4 result:1 pre:1 nikolai:2 motivation:1 false:1 p23:1 electrodynamics:1 correction:2 ram:1 matem:3 berestetskii:1 correspond:3 already:2 say:1 arisen:1 need:4 seen:1 any:2 contents:1 generalizes:1 angle:1 depending:4 jection:1 isolated:1 polarization:1 sciences:1 ideal:1 f2:10 generalized:1 analogy:1 techniques:1 bernd:1 heisenberg:2 lectures:2 continuous:1 qualities:1 melnik:1 rhq:1 object:2 arellano:1 birkh:1 most:1 connected:2 representation:17 reducible:2 why:1 exico:1 tξ:4 χr:20 consequences:2 considered:4 calculated:1 sometimes:1 flow:1 feynman:3 proceedings:2 points:5 velocity:2 shirkov:1 physics:4 notion:6 incomplete:1 joining:1 impression:1 particularly:2 phenomenon:1 show:1 lewis:3 bergman:1 notations:1 purely:2 spaces:2 relation:1 solutions:5 keywords:1 interpretation:3 find:1 poggio:1 causality:1 ensembles:1 parameters:1 title:1 implementation:1 explain:2 enough:1 should:15 lemma:2 only:22 explicitly:2 generators:1 subsection:5 integrable:1 boulder:1 do:9 insight:1 admissible:1 klein:7 meanwhile:1 familiar:1 de:4 da:1 2mc:3 ones:3 joins:1 probably:1 dv:4 reconstruct:1 procedures:1 boundary:2 secondary:1 commuting:1 nicholas:1 consisting:1 podolsky:2 textbooks:1 fields:13 arxiv:1 mathematicians:1 factorization:1 summary:1 twice:1 qc:1 experiments:1 minkowski:5 view:1 intervening:1 set:2 achieved:4 respect:1 y1:1 see:9 p21:1 projections:22 sea:1 p22:1 discussions:1 subject:2 hilbert:1 cornelius:1 extragalactic:1 ways:1 justifies:1 artificial:1 symmetric:1 case:5 state:3 determined:1 identification:2 john:1 between:9 invariant:8 geometric:5 previous:3 approach:10 x20:1 x23:2 x22:2 preserve:1 dµn:10 terms:1 sections:1 cinvestav:4 wn:1 alexander:1 weak:1 however:1 p2j:2 comm:2 bose:1 dx22:5 dx23:5 dx20:2 improve:1 suggested:1 both:2 improved:3 x2j:1 many:5 infinitely:1 equal:4 quantization:59 deduction:2 etc:3 admit:1 streams:1 tangent:5 passing:1 mean:1 expression:1 permitted:2 relevant:1 cn:24 nonrelativistic:1 simple:3 overview:1 harmonic:1 dimensional:10 anti:5 conjugation:1 izvestija:2 consideration:12 wider:1 moreover:2 cp:1 considers:1 appeared:3 pr:42 duj:1 pq:38 described:2 transformations:2 basis:2 trajectory:6 three:3 rhode:1 describes:1 combined:1 basic:1 pj:1 connes:1 ph:1 algebras:4 hardly:1 topics:1 odessa:1 arises:1 corresponding:11 deeper:1 restrictions:1 theorem:3 photon:2 covariance:1 wish:1 neumann:1 maps:4 understand:1 external:1 berezin:9 last:1 denote:5 spin:36 present:2 c4:3 sound:1 noncommuting:1 akad:1 appearance:1 chap:6 value:7 will:17 euclidean:4 behavior:2 applies:1 situation:1 procedure:7 iy:2 ix:2 vectors:2 mexico:3 ip:4 metric:4 thus:15 them:5 iv:1 ii:4 characterize:1 itself:2 im:4 cone:22 curved:1 vx:4 qj2:2 bargmann:10 variational:1 different:4 because:3 propagation:7 large:1 make:4 belong:2 ırez:1 connection:1 same:1 rieffel:1 complex:3 quant:1 seminar:1 constructed:1 subalgebra:1 events:5 higher:2 independent:1 used:2 infinity:1 ni:1 disagreement:1 island:1 felix:2 mutual:1 hand:1 parametrized:3 action:1 moment:2 moving:2 auser:1 internal:1 invariance:3 opportunity:2 recent:1 schr:12 nevertheless:1 whole:1 locality:1 well:1 roughly:1 concrete:1 without:5 solve:1 components:2 lim:6 coordinate:2 quantitative:1 model:8 oscillation:1 usual:7 isometry:1 unified:1 manifold:1 oziewicz:1 half:2 obtain:3 homogeneity:1 difficulties:1 select:1 spitkovsky:2 thanks:1 questions:2 touch:2 paul:1 ams:2 based:2 segal:10 bibliography:1 family:2 field:9 photons:1 alternate:1 seems:1 realize:1 parts:1 other:5 easy:1 aticas:3 usage:1 transformation:1 momentum:2 real:1 depends:2 rules:2 results:1 possible:3 iη:1 corresponds:1 know:1 background:1 press:6 world:1 bit:1 postal:1 skeptical:1 like:7 particle:32 follows:1 qualitative:1 polya:1 automorphisms:1 remind:4 arthur:1 4mc:6 steps:1 integrals:2 arbitrary:1 mcgraw:1 spins:3 mathematical:8 calculus:1 right:1 often:1 classical:6 luminal:2 quantizations:6 some:4 dx21:5 polynomial:1 growth:1 statistic:2 proper:4 trujillo:1 matching:1 total:1 axiomatic:2 demonstrates:1 avoid:1 measurements:1 isometrically:3 providence:1 does:4 decomposition:2 eliminate:2 provides:2 refer:1 zitterbewegung:2 glimm:1 agreement:3 illustration:1 nauk:1 clarendon:1 step:3 prohibited:1 variation:1 imaginary:1 properties:2 von:1 meyer:1 constrains:1 about:1 origins:2 constraint:2 freedom:7 violence:1 introduces:2 meaning:1 o:16 assertion:2 covariant:1 greatly:1 done:1 introduced:1 book:2 berger:1 colorado:1 unbounded:1 image:1 integral:5 functional:2 remarks:1 weyl:1 references:3 realizations:1 einstein:4 elementary:6 bosonic:1 matrixes:2 spinors:4 fill:1 additional:3 assumed:1 strictly:1 there:9 question:3 pages:4 appl:2 bosons:1 physicists:1 way:4 forward:1 was:8 toeplitz:12 function:25 academic:2 creation:1 elsewhere:1 form:5 hs:7 m2:2 but:10 gaussian:2 volume:8 mc:3 construction:8 link:1 russian:1 implies:1 kravchenko:1 level:1 count:1 pi:4 jaffe:1 evident:1 inhomogeneous:2 characteristic:10 inside:1 variations:1 us:11 probabilists:1 note:2 books:1 fermi:1 uj:1 ussr:2 problem:3 andr:1 laplace:1 delete:1 mechanics:13 interval:1 associated:1 isomorphically:1 af:1 defined:11 request:1 abstract:1 describe:3 general:4 single:3 dx:12 exist:2 formulation:2 dη:1 formalism:1 apartado:1 simplest:2 defines:5 again:1 functions:7 paradox:2 no:2 rosen:2 application:3 setting:1 details:1 mathematics:5 you:1 pitaevski:1 unobservable:1 conclusion:1 expositions:1 thaller:1 generates:1 models:3 subspace:1 bundle:1 irving:3 william:1 generated:8 important:1 astronomy:1 structure:14 dimensions:1 algebraic:2 remote:1 factorized:1 assume:1 values:2 dτ:1 prequantization:2 holes:1 pseudo:2 appendix:1 mass:3 fact:1 time:16 observables:8 applied:1 backward:1 inc:1 original:1 once:1
|
quant-ph9502023.txt |@word chebyshev:3 yeh:1 lebedev:2 consider:2 produces:1 moments:1 lewis:1 over:1 supported:1 nτ:4 kanai:5 russian:1 pulses:1 statistical:1 husimi:1 sci:1 expressions:1 determined:1 repts:1 its:1 phenomenon:3 caldirola:6 system:1 parameters:2 infinitely:1 chosen:1 matrices:1 less:1 tr:1 add:1 complex:1 squeezing:11 lett:5 under:1 mail:1 main:2 remaining:1 kick:2 continuity:1 begins:1 fax:1 aspects:1 εk:3 kτ:7 dependent:2 kind:1 wave:2 mention:1 electron:1 ones:1 every:1 2γt:2 appearing:1 thus:3 exact:1 discuss:1 advanced:1 correlated:1 following:3 evolution:1 increasing:1 dirac:1 absent:1 particle:1 prospekt:1 follows:1 arxiv:1 invariants:1 solution:3 damped:3 solved:1 vibrations:1 math:2 dodonov:2 science:2 undamped:2 through:3 il:1 optics:1 satisfy:1 force:2 transform:1 classical:2 sequence:3 ed:1 energy:1 sin2:1 ωt:1 depends:1 frequency:9 b0:5 cim:2 quantum:8 small:1 eq:2 subject:1 will:2 shown:1 describing:1 matrix:2 support:1 nuovo:2 measurements:1 rev:1 expressed:5 find:1 increase:1 state:3 leninsky:1 formula:1 previous:1 conditions:3 s11:1 participation:1 coefficient:9 foundation:1 lugiato:1 kicked:1 terms:2 theory:1 cosh:1 s12:1 bn:5 were:1 weak:3 proc:1 here:1 bk:2 behaviour:1 kicking:1 sinh:1 manko:1 strong:3 properties:1 thank:1 obtained:1 cos:11 institute:3 olga:1 study:1 changed:1 discussed:1 dependence:2 o:2 russia:1 motion:2 σx:4 ak:4 action:1 fian:1 myers:1 consequently:1 explicit:2 coincides:1 organizers:1 author:1 malkin:1 press:1 into:2 formulae:2 plenum:1 three:1 references:1 nova:1 periodical:2 2un:1 substitutions:1 research:1 unit:1 conference:1 given:2 amer:2 feb:1 hasse:1 introduction:1 2ωt:1 initial:5 due:4 relations:1 periodically:1 glauber:1 appears:1 describes:1 msk:1 damping:13 electrodynamics:1 nato:1 ph:1 was:5 frame:4 systems:1 function:5 progr:2 controlled:1 nonstationary:1 kronig:2 penney:2 moscow:1 odinger:1 coherent:1 part:1 external:2 delta:5 kicks:6 cases:2 role:2 iii:1 coefficients:2 must:1 case:9 ii:1 account:1 exponential:1 integrating:1 variances:1 equation:7 oscillator:13 second:1 us:1 kumar:1 aim:1 mt:2 below:1 un:36 obvious:1 amplitude:1 starts:1 squeezed:2 problem:3 example:1 regimes:3 wishes:1 constant:1 brown:1 defined:2 characteristics:1 refs:2 influence:2 argument:1 states:1 numbers:1 seen:1 elements:1 physical:3 agarwal:1 different:4 form:3 zero:1 grant:1 tombesi:1 acknowledgments:1 when:1 necessary:1 potential:1 quant:1 take:1 forces:1 physica:1 theor:2 eµ1:1 sin:17 eµ2:1 simplicity:1 play:1 investigated:1 excitation:5 may:3 buch:1 after:2 polynomials:3 a0:5 moment:2 connected:1 potentials:1 dekker:1 plays:1 man:6 short:1 schr:1 considered:3 expression:3 dτ:2 interval:2 ko:6 walls:1 su:1 s22:1 s21:1 mass:1 exp:4 time:11 coordinate:1 model:4 2mω:1 parametric:4 talk:1
|
quant-ph9502024.txt |@word concept:2 partial:1 magnetic:1 results:1 roy:1 quadrature:2 consists:2 4e2:1 whose:1 tr:3 answered:1 quasi:1 th:1 under:1 quasienergy:4 applied:3 geometrical:9 dispersions:1 hamiltonian:5 solution:1 discrete:1 vector:3 eigenvalues:3 markov:1 oscillator:4 cosh:1 haake:1 even:1 ˆq:1 nonlinear:3 expressed:3 nonstationarity:2 new:2 satisfy:1 kicked:2 ibid:1 behaviour:2 ansatz:1 sinh:3 represented:1 institute:2 study:1 hermite:2 plenum:2 apply:1 planck:3 use:2 feb:1 charge:1 a50:1 taken:3 resonator:2 nauka:1 becomes:2 operators:2 varying:2 iin:2 deformed:2 science:2 equation:2 det:2 values:1 following:3 give:1 states:5 means:1 zaccaria:2 answer:1 l873:1 may:10 oscillators:2 after:1 different:1 physik:1 man:16 dynamical:1 effective:1 light:1 sp:2 so:4 wigner:2 deform:2 produces:1 pointed:1 interpreted:1 mαβ:1 london:1 satisfies:1 its:1 group:7 malkin:4 boson:1 systems:18 main:1 deformation:4 them:1 ya:1 introduce:1 walls:2 effects:1 they:2 multidimensional:1 invariants:1 mode:2 found:2 2n:7 constraints:1 periodical:3 ed:2 energy:2 gaussian:3 related:2 frequency:2 quantum:15 relates:1 eq:2 special:2 out:2 shown:1 matrix:3 rep:1 since:2 rev:2 chaos:1 research:1 leninsky:1 formula:2 ref:6 math:1 standard:1 reason:1 e3:1 definition:1 created:2 times:2 motion:20 symmetry:3 relate:1 variables:1 number:3 another:1 given:2 system:10 relations:2 too:1 floquet:5 a32:1 a30:1 moscow:2 continuous:1 kind:1 showed:1 annihilation:1 determined:1 amplitude:4 russia:1 spectra:1 symmetries:2 correction:1 spectrum:8 any:2 chirikov:1 generalized:3 forces:1 coincide:1 analogs:1 ˆp:1 components:3 most:1 regular:1 connected:1 nothing:1 class:2 nonlinearity:7 soviet:1 average:1 partition:1 coincides:1 exp:6 kt:6 effect:8 physics:2 notion:1 lebedev:2 phenomenon:1 relation:1 d2:1 q1:1 criterium:2 parameters:2 hamiltonians:2 zeldovich:1 notation:1 di:1 dependent:1 ko:16 ones:1 dt:1 evolution:3 arxiv:1 dodonov:4 qi:1 qj:1 qn:1 quasienergies:1 see:2 result:2 biedenharn:1 macfarlane:1 analog:1 phases:3 commutation:1 review:2 marmo:2 symmetric:1 state:12 invariant:2 approach:1 publishers:1 terms:4 august:1 nature:1 initially:1 analyzed:1 multivariable:1 jetp:1 taking:1 uncertainty:1 equal:1 called:1 hω:5 berry:4 casimir:7 mean:1 expression:1 among:1 point:1 corresponds:1 dimensional:2 polynomial:1 considering:1 iω:1 described:3 due:7 been:6 int:1 combined:1 interest:1 pj:2 ph:1 pi:1 pn:3 ann:1 corresponding:1 quantities:1 photon:13 coherent:2 external:1 case:3 p0:2 p1:1 laser:1 variances:1 evaluated:1 will:2 squeezed:3 nonstationary:12 property:1 a22:2 unitary:3 chaotic:2 vi:1 refs:2 thus:2 obeying:1 qj2:1 2ut:1 containing:1 generic:2 same:5 quant:1 dimensionless:1 constructed:2 symplectic:2 functions:1 moment:2 moving:3 identity:1 i2n:3 ritus:1 usual:1 being:1 obtain:1 λa:2 yes:1 rotation:1 density:1 quadratures:1 belongs:1 lett:3 trifonov:2 real:4 harmonic:1 vacuum:2 press:2 mod:1 loss:2 b108:1 particle:3 follows:1 either:2 integrals:5 classical:1 creation:1 some:1 demonstrates:1 does:1 provides:1 proc:3 pr:1 obey:1 2m:2 imaginary:2 repts:1 periodically:2 n5:1 discussed:1 dependence:1 o:1 mixed:4 introduced:5 soc:1 into:1 integral:13 phase:14 hermitian:2 references:1 sov:1 operator:21 statistics:1 initial:2 question:1 nova:1 dispersion:1 hef:2 quadratic:2 was:4 function:9 form:6 conjugacy:2 but:2 repeated:1 construction:2 delta:1 russian:1 algebras:1 characteristic:2 us:1 below:1 distribution:13 calculated:1 mechanics:1 proved:2 defined:2 certain:1 abstract:1 influence:1 general:2 aq:6 conserved:1 exist:3 gruber:1 defines:1 qα:1 nj:1 qβ:1 cim:2 nn:2 streit:1 field:1 calculating:1 problems:1 polynomials:1 a0:3 a8:1 multimode:1 correlated:3 assume:1 hnn:2 time:5 n1:2 n2:2 nuovo:2
|
quant-ph9502025.txt |@word partial:1 eds:1 quadrature:1 subjected:1 squeezing:2 analogous:1 presentation:1 amplitudes:2 wave:1 rm:2 husimi:12 nieto:1 matrices:1 presented:1 irreducible:4 solution:1 leninsky:1 truax:1 markov:1 optics:1 upper:1 mi:1 cosh:2 zero:1 value:1 odd:9 canonical:1 even:10 xψ:1 nonlinear:1 appear:1 expressed:4 fiore:1 international:1 coefficient:1 ibid:1 here:1 behaviour:1 groups:2 remark:1 antisymmetric:1 institute:2 shift:1 vectors:2 hermite:6 plenum:1 feb:1 a50:2 ψn:2 m2:1 type:1 introducing:1 operators:2 odinger:17 berlin:1 normalized:2 kgl:1 must:1 high:1 deformed:3 science:1 equation:6 mn:1 det:1 cat:7 male:1 nikonov:1 states:28 r12:6 crystallized:1 di:1 pure:1 parameter:1 l873:1 blocks:1 algebra:2 may:9 oscillators:2 representations:1 man:20 transposed:2 dynamical:4 light:4 green:1 correlation:2 representation:5 talk:1 interpreted:2 y1:3 existence:1 satisfies:2 y2:3 its:3 group:10 malkin:5 ln:1 interesting:1 forms:3 systems:3 versus:1 they:2 multidimensional:1 realize:2 nos:1 easily:2 inversion:1 invariants:1 possibilities:1 vibrations:1 mode:2 each:1 found:3 2n:5 weyl:2 female:1 series:1 energy:3 gaussian:4 used:3 constitute:1 inhomogeneous:1 frequency:3 quantum:4 shown:3 matrix:5 since:1 rev:8 research:1 vector:1 dsf:1 formula:1 math:2 linear:5 frank:2 romano:1 base:1 r1:3 r2:4 created:1 transition:2 motion:11 oscillator:30 crystallographic:1 symmetry:3 variables:3 number:3 done:1 another:1 rederive:1 given:1 publication:1 glauber:1 relations:4 their:1 quadratic:1 too:1 frame:1 a32:1 a30:1 polyatomic:1 moscow:3 akad:1 serve:1 x2:2 yurke:1 second:1 submitted:1 amplitude:3 ber:1 russia:1 a49:1 symmetries:1 generalization:4 progr:1 forced:3 note:1 take:2 analogs:1 heisenberg:2 blue:1 molecule:1 nonlinearity:3 considered:3 soviet:1 calculated:1 ko:20 physica:1 proceedings:1 exp:8 physics:2 lebedev:2 phenomenon:1 dependences:1 relation:5 solutions:4 d2:1 find:1 ground:1 explicitly:1 condon:2 factor:2 a79:1 means:1 dependent:3 dx:1 evolution:1 arxiv:1 dodonov:7 satisfy:1 set:1 sensitivity:1 packet:1 intensity:1 result:1 biedenharn:1 macfarlane:1 analog:1 satisfying:2 commutation:4 review:1 marmo:2 λn:1 symmetric:2 state:11 between:2 invariant:1 approach:1 αn:1 publishers:1 terms:4 2αx:3 multivariable:1 lopez:1 improve:1 suggested:1 uncertainty:4 σx:3 symplectic:5 casimir:1 σp:2 photons:1 sinh:6 2nm:1 point:1 2nf:1 cx:1 pr:1 described:1 basis:3 due:3 been:11 describes:1 pe:1 ph:1 ansari:2 corresponding:3 photon:1 ortogonal:1 case:2 laser:1 exponential:1 variances:1 evaluated:1 evaluating:1 squeezed:6 nonstationary:2 stoler:1 iy:1 a22:2 a27:1 thus:2 zaccaria:3 different:1 qaq:1 generic:2 complex:1 quant:1 finite:1 higher:1 extended:1 lie:1 sudarshan:1 effect:3 levels:2 uses:1 kim:1 normalization:1 costa:1 schr:17 nn:1 well:2 components:1 position:5 model:1 parametric:19 λr:2 λx:1 reviewed:1 λa:1 alternative:1 eigenstates:3 preprint:1 cm:1 han:1 interprete:1 discuss:1 lett:7 trifonov:2 eigenstate:1 momentum:5 generalized:2 eigenfunction:1 eigenvalue:1 iε:1 vacuum:1 press:1 using:1 mod:1 workshop:1 specific:1 integrals:6 classical:1 phenomena:1 orthonormal:1 electromagnetic:1 overlap:2 proc:2 conference:1 minimization:1 shifting:1 properties:3 og:1 discussed:5 dependence:1 o:2 mixed:1 introduced:2 integral:7 references:2 determine:1 operator:4 there:1 nova:1 cats:1 ed:1 m1:1 was:2 function:5 form:7 some:1 construction:3 hn:2 hm:1 russian:1 infn:1 made:2 gravitational:1 wiss:1 limit:1 distribution:1 constant:1 nauka:1 int:1 abstract:1 describe:2 hmn:1 aq:8 exist:1 check:1 constructed:2 ni:1 nm:1 antenna:1 na:1 nf:1 field:1 other:1 nq:1 theor:1 excitation:1 nonclassical:3 polynomials:6 a2:1 a8:1 multimode:9 correlated:6 packets:2 coherent:15 nasa:1 time:4 n1:1 n2:1 n5:1
|
quant-ph9502026.txt |@word partial:3 eds:1 quadrature:4 consists:2 expressions:1 worked:1 λik:1 inverse:1 depend:2 calculate:1 tr:3 crater:1 γk:9 squeezing:2 γn:1 th:1 analogous:1 applied:2 miele:1 r12:8 wave:1 dsf:1 dispersions:1 rm:2 husimi:2 matrices:5 hamiltonian:2 solution:1 leninsky:1 small:1 markov:1 optics:1 zn:3 det:7 cosh:7 zero:3 value:1 zz:1 odd:27 canonical:1 even:28 will:2 nonlinear:1 sub:1 expressed:10 3n:1 above:5 values:5 coefficient:1 respectively:3 here:1 behaviour:2 ansatz:2 sinh:7 represented:1 equations:2 z1:3 z2:3 obtained:4 institute:2 larger:1 bry:1 hermite:14 yuen:1 plenum:1 unitary:1 ipu:1 use:3 feb:1 a50:2 approach:1 call:1 m2:1 taken:1 type:1 nauka:1 becomes:1 operators:5 odinger:17 berlin:1 normalized:1 particular:1 cases:1 iin:2 producing:1 kgl:1 must:1 account:1 science:1 equation:7 mn:1 oscillator:8 cat:10 fock:1 obvious:1 following:5 male:2 example:2 nikonov:1 give:3 predict:1 states:51 numbers:2 a79:1 di:1 pure:2 mi:1 product:3 blocks:6 may:9 constants:1 man:17 transposed:2 branches:1 dynamical:1 sech:1 explicit:1 element:1 so:1 correlation:1 representation:2 βk:8 order:1 talk:2 wigner:15 help:1 βk2:1 interpreted:1 mαβ:1 through:1 statistical:2 mentioned:1 japan:1 satisfies:1 y2:7 its:4 before:1 derive:1 group:1 malkin:6 interesting:1 csch:1 forms:3 dp:2 defining:1 2zz:1 arguments:1 introduce:1 they:2 multidimensional:1 discuss:1 2u:1 φk:4 invariants:2 2x:1 2d:1 mode:11 2b:1 each:4 2m:3 2n:26 constraints:1 determine:1 ed:1 energy:2 gaussian:5 related:1 quantum:4 eq:4 special:1 out:1 matrix:31 types:1 nuovo:2 since:2 rev:7 research:1 rd:1 vector:15 2λm:1 formula:2 2k:11 math:3 shows:1 fiber:1 linear:5 interactions:1 frank:2 diagonal:3 standard:1 dx:4 definition:1 r1:8 r2:9 created:4 determining:1 transition:1 motion:8 levels:1 δik:4 βn:6 first:2 xk:1 initial:2 probability:5 variables:5 number:7 another:3 given:11 publication:1 similarly:1 introduction:1 system:4 relations:5 their:1 1c:1 identity:1 statement:1 gives:3 a32:1 a30:1 polyatomic:1 moscow:3 akad:1 x2:3 yurke:1 2az:1 begins:1 see:1 annihilation:2 amplitude:2 light:6 ber:1 russia:1 symmetries:1 argument:2 generalization:1 manner:2 conjugate:3 any:2 forced:1 depending:1 generalized:2 finding:4 green:1 modulus:1 ˆp:1 i2n:4 ˆq:1 molecule:1 systems:5 most:1 nothing:1 soviet:1 calculated:5 ko:17 physica:1 exp:23 mechanical:1 effect:2 physics:3 fact:1 quantity:2 lebedev:2 phenomenon:1 show:1 dependences:2 notations:2 russian:1 relation:6 solutions:2 nonfactorizable:1 d2:5 ground:1 q1:1 parameters:1 condon:2 factor:2 hamiltonians:4 notation:1 means:1 dependent:3 pions:2 beam:1 cannot:1 words:1 new:1 du:1 coth:4 evolution:2 fields:2 arxiv:1 dodonov:8 qi:1 qk:4 qj:1 qn:1 kernel:3 exists:1 correlations:1 packet:1 y1:8 namely:2 result:2 σqq:2 analog:1 satisfying:1 commutation:1 phonons:2 review:1 symmetric:10 state:28 between:1 αi:11 drawn:1 αk:5 conditions:1 αn:6 publishers:1 terms:11 wa:2 initially:1 2αx:3 analyzed:1 multivariable:5 both:1 prescription:1 σn:7 x2k:1 taking:1 conclusions:1 equal:2 etc:1 σx:2 casimir:2 mean:2 experimental:1 2nn:2 cm:2 point:1 poissonian:2 2nf:1 factorize:1 cx:3 polynomial:3 pr:1 duk:1 described:2 second:1 basis:3 due:4 been:7 ai:5 workshop:1 combined:1 pj:2 ph:1 pi:1 pn:3 abstract:1 define:1 ansari:1 generating:1 corresponding:5 easy:1 photon:16 coherent:40 hmi:1 2n2:3 2n1:2 evidence:1 present:1 case:7 p0:4 p1:1 laser:1 tanh:4 variances:2 evaluated:1 aim:1 replaced:1 squeezed:10 nonstationary:4 property:1 stoler:1 uncertainty:4 n2n:2 a27:1 ip:3 refs:2 thus:1 qj2:1 2ut:1 different:3 d13:1 generic:5 d19:1 same:2 φb:2 complex:7 quant:1 split:1 dimensionless:1 constructed:2 independent:2 used:2 peaks:1 sudarshan:1 nj:1 qβ:1 uses:1 kim:1 normalization:1 σp:2 schr:17 modes:3 well:1 components:9 coordinate:2 position:3 model:1 parametric:7 charged:1 λr:2 just:1 being:1 λx:1 eigenstates:1 λm:2 preprint:1 2nm:1 han:1 density:9 photons:8 quadratures:1 lett:4 versa:1 ipk:1 trifonov:3 eigenstate:1 momentum:3 take:1 real:1 eigenvalue:2 evaluate:1 decomposed:1 iε:1 vacuum:2 press:2 using:1 dimensional:3 like:3 particle:3 follows:1 yields:1 integrals:5 become:1 replacement:2 methods:1 classical:1 creation:2 some:3 examples:1 nondiagonal:1 2xk:1 overlap:2 proc:3 conference:1 obey:1 minimization:1 σik:3 problems:1 found:3 super:1 properties:2 discussed:2 o:1 a2:1 mixed:5 introduced:5 block:2 soc:1 presence:1 into:4 integral:8 appropriate:2 references:1 female:2 operator:6 schrodinger:1 statistics:3 there:2 transform:4 nova:1 dispersion:7 quadratic:5 m1:1 was:1 function:46 form:8 but:2 displacement:1 hk:2 hn:4 hm:1 σpp:2 σpq:3 infn:1 xi:1 b83:1 cim:2 international:1 hni:1 wiss:1 αm:1 uk:6 demonstrate:1 distribution:11 similar:1 average:1 mechanics:1 ab:3 defined:1 certain:1 ak:5 describe:4 general:2 single:2 exist:1 az:1 distributions:1 physical:2 qα:1 ni:5 functions:9 nk:1 nm:1 nn:10 no:2 nf:1 field:3 other:7 ns:3 conclusion:1 elements:3 a13:1 models:1 nonclassical:5 polynomials:11 important:2 vectors:3 fedele:1 structure:1 multimode:34 correlated:10 implies:1 vice:1 assume:1 hmn:2 hnn:2 4n:2 nasa:1 time:7 xk2:1 n1:14 n2:12 n5:1
|
quant-ph9502027.txt |@word reorganized:1 consider:1 remarkable:2 modi:1 green:2 excellent:3 results:27 leads:2 computation:1 go:2 expressions:2 zinn:3 whose:2 calculate:1 re:1 show:1 tr:2 elliptic:1 under:1 anharmonic:7 include:1 divergent:2 applied:5 performs:1 g1:1 very:5 frequencies:1 keeping:1 splitting:6 ective:5 chapters:1 associated:1 exact:6 condition:2 solves:1 level:3 turns:2 notes:1 ers:1 t2:2 applicable:1 t0:4 integrated:1 large:7 solved:1 demonstrated:2 small:9 eigenvalues:19 tognetti:1 variationally:3 correct:3 expanded:1 neighborhood:1 arnimallee:1 approximation:6 elegant:1 zero:6 zx:1 evaluated:3 7th:2 qualitatively:1 implemented:1 odd:3 linear:2 even:8 trick:2 barrier:12 rate:4 trivial:1 section:4 shares:1 current:1 optimization:1 above:1 new:1 increasing:1 ner:1 method:14 contrast:1 j2d:1 transparency:1 respectively:1 error:1 agreement:2 desired:3 asymmetry:3 bj:2 guida:1 path:10 along:1 extrema:4 equations:3 appears:2 obtained:9 remark:1 generalizing:1 nth:2 technical:1 shift:1 inspired:1 trial:2 amount:2 usually:1 buckley:1 proof:3 studies:1 plotted:2 reg:2 via:4 useful:1 divide:2 scales:1 plenum:1 highly:1 scaled:1 1st:1 apply:1 planck:1 linearly:1 readily:2 conventional:5 feb:1 asymptotic:2 prove:1 remains:1 contains:5 permitted:1 few:1 2e1:1 bender:4 themselves:1 e2:1 theoretical:1 more:5 fractions:1 becomes:3 apparent:1 envelope:1 x30:1 vpe:30 berlin:3 appendix:10 particular:1 known:1 must:3 logarithm:1 states:7 account:1 quartic:4 permits:1 recall:2 equation:7 oscillator:19 theories:1 reproduce:2 values:8 ning:2 smear:1 following:6 im:10 averages:1 subnuclear:1 numbers:5 figure:6 give:3 calculation:11 expanding:1 xcl:1 uctuations:2 high:7 indicates:1 minimum:5 performed:1 validated:1 hydrogen:1 information:1 rescaling:2 end:3 rather:1 discussion:1 six:1 feature:1 far:2 criterion:2 justin:3 optimal:5 coleman:1 parameter:2 belongs:1 inputs:1 description:1 algebra:4 may:6 earlier:1 derived:1 corrections:2 plane:4 quantenmechanik:1 physik:1 improving:1 renormalizability:1 wave:8 grow:1 constants:1 short:1 purely:1 third:1 lines:3 su:3 their:1 ones:1 negligible:1 decreasing:1 integrand:1 words:1 order:46 typical:1 breaking:1 interpretation:1 help:2 xlim:1 produces:1 developed:2 over:2 move:1 interpreted:1 stability:1 paper:2 looks:1 resummed:1 left:1 facilitates:1 still:2 its:4 before:1 rapidly:1 decay:4 energies:1 continued:2 solving:1 decreases:1 better:1 gtr:1 complex:16 choose:2 into:5 eventually:1 non:3 good:5 greater:1 integral:10 evolution:1 bound:1 scaling:1 they:4 instead:2 rotation:5 now:5 discuss:1 matched:3 chromodynamics:1 eigenvalue:5 february:1 reasonably:1 hamiltonian:5 hanggi:1 2g:1 each:1 instability:1 t1:2 voth:1 ann:2 en:1 ej:3 series:10 energy:14 used:3 solution:8 frequency:2 obtains:2 year:1 quantum:16 our:9 approximated:2 beyond:5 eq:6 out:4 try:1 ultimately:1 matrix:1 3rd:1 rs:10 restricted:3 furthermore:1 since:7 rev:8 semi:1 attracted:1 nite:1 ref:1 sliding:10 math:2 shows:9 turning:7 theory:12 reformulated:1 written:1 seventh:9 inapplicable:1 free:1 standard:1 resums:1 completely:1 necessarily:1 dx:2 estimate:1 rises:1 remainder:1 e0:1 rewritten:1 hence:1 interaction:1 english:1 transition:4 success:1 turn:2 exponentially:9 barriers:9 quadratically:1 onto:1 neglect:1 first:1 origin:1 initial:2 symmetry:2 n13:1 powerful:2 number:3 system:2 cients:8 konishi:1 n11:2 done:1 long:1 another:1 zichichi:1 clarity:1 n14:1 given:8 perturbation:17 temperature:2 pushed:1 introduction:1 eqs:3 bay:1 theoretische:1 heights:4 needed:2 intermediate:2 rates:7 too:1 calculations:2 zeros:2 variational:15 gives:2 asymmetric:1 favorably:1 tool:1 exactly:1 zeroth:2 immediate:1 part:12 because:1 airy:1 x2:14 x3:7 x0:20 believe:1 than:6 x4:1 distance:1 veff:5 plateaux:2 accordance:1 double:1 approximations:3 second:7 matter:1 appealing:1 determined:1 contrary:1 were:1 powers:2 perturbative:1 lowest:4 motivation:1 carlitz:1 summable:1 argument:2 already:1 mater:1 pisarski:1 further:1 need:1 ccr:4 orders:5 astonishingly:1 genuine:1 lim:1 k3:2 k2:2 k1:2 potential:25 k7:2 useless:1 k5:2 k4:2 so:1 coincide:1 inverted:1 eff:1 accuracy:1 lectures:1 unless:1 shall:3 who:1 techniques:2 most:1 optimized:2 but:4 analytically:1 extremely:1 advantageous:1 surprising:1 average:1 partition:4 traditional:1 feynman:2 points:3 principle:2 exp:7 mechanical:4 usual:1 physics:3 ned:1 fact:3 perspective:1 particularly:1 rayleigh:7 delta:1 friction:1 converge:2 rst:17 relation:5 solutions:3 talkner:1 d2:3 translation:1 ground:4 giachetti:1 based:3 parameters:1 duncan:2 true:1 explain:1 enough:1 should:2 only:6 version:1 factor:1 circle:1 local:2 extremum:1 do:3 di:2 dependent:2 de:4 pave:1 cannot:1 fastest:2 closely:1 collins:1 erent:1 dt:3 mx1:2 divided:1 approximants:1 processes:1 approach:4 expansions:2 yield:3 nes:1 processed:1 contain:1 view:1 n12:1 knowing:1 n10:2 set:2 pade:1 statistical:1 exists:1 sensitivity:2 cao:1 observed:1 see:10 computer:4 bare:1 result:14 11th:1 contour:1 acquires:1 closer:1 ways:1 away:1 missing:1 tend:1 state:5 chosen:2 correctly:1 probably:1 boundary:1 conditions:3 across:1 unappealing:1 available:1 terms:3 reproduced:2 extend:1 nature:1 jt:1 attention:1 weak:1 however:1 nd:2 reproduces:1 magn:1 analyzed:1 improve:1 both:3 last:2 treated:2 region:3 equal:1 etc:2 became:1 coe:8 instanton:3 context:1 altherr:1 expand:1 contribution:1 otherwise:1 arbitrarily:2 ch:3 point:9 simple:4 asymptotically:2 cf:2 height:2 semiclassical:5 nitely:3 exploit:1 simply:2 weiss:1 universitat:1 polynomial:1 table:6 nicole:1 strong:1 described:1 ciently:1 addition:1 due:3 been:8 z1:2 5n:1 cient:4 much:1 interest:1 ph:1 correction:4 fig:4 determinant:1 lived:1 corresponding:3 easy:1 t3:2 systematic:2 improved:9 convergent:2 fokker:1 present:5 case:3 fur:1 exponential:2 solid:1 means:5 resummation:5 value:4 will:7 near:1 p2:2 replaced:2 coalescing:1 behavior:5 many:1 situation:2 tunneling:14 couplings:1 procedure:6 real:4 engl:1 ve:1 conv:1 almost:1 refs:1 wkb:35 thus:2 encountered:1 converts:1 vanish:3 disappear:1 increased:2 perform:1 recursion:2 radiation:1 lett:7 same:1 freie:1 parts:6 quant:1 split:1 widely:1 units:1 und:1 proved:1 physical:1 higher:3 development:1 independent:1 extended:3 closest:1 cubic:17 numerical:4 upon:1 hand:2 action:1 strength:1 purpose:1 k6:2 kleinert:10 lower:3 task:1 makes:1 well:8 obviously:2 without:1 sets:1 coordinate:5 position:2 model:1 grounds:1 possesses:1 weakest:1 just:1 being:3 when:4 accurate:1 obtain:4 cease:1 applications:1 singularity:2 preprint:1 hint:4 regarded:1 cl:1 hae:1 eld:5 improvement:1 reasons:1 wu:4 valid:2 treatment:2 cations:1 hirschfelder:1 input:2 consideration:1 excited:4 match:3 generalized:2 identical:1 around:7 easily:1 term:2 harmonic:3 similarly:2 press:1 using:3 2nd:1 dimensional:2 imposed:1 like:3 particle:4 systematically:3 follows:1 reduces:1 performing:1 loses:1 discarded:1 yields:6 integrals:4 arbitrary:1 popular:1 become:2 stevenson:1 accessible:2 drop:2 methods:2 classical:10 dt0:3 successfully:1 searching:2 supplementary:1 calculated:5 choosing:2 respect:2 proper:2 harmonically:1 statistik:1 describing:1 dimensions:1 operation:1 bottom:1 integration:4 minimal:2 inserting:1 process:1 power:1 bm:4 use:3 expansion:24 step:1 8n:2 found:8 renders:1 imaginary:12 properties:2 meyer:1 comparison:3 about:1 carried:1 extension:2 saddle:3 freedom:1 numerator:2 dependence:2 o:11 sake:1 greatly:1 slightly:1 mannheim:1 presence:1 h0:6 within:2 numerically:1 backscattering:1 encircling:1 down:2 lies:1 hermitian:1 right:1 references:1 determine:2 pollak:1 next:1 schrodinger:14 rely:1 statistics:2 institut:1 coalesce:1 inserted:1 there:2 approximate:3 fast:3 dispersion:2 borel:2 low:6 way:6 ed:1 was:2 suzuki:1 function:11 medium:1 form:1 metastable:3 drummond:2 soper:1 construction:1 related:2 atom:1 convergence:9 line:1 removed:1 dissipative:2 subtracted:1 applying:1 instructive:1 erice:1 smooth:1 up:5 us:3 limit:7 similar:1 called:1 regimes:1 mechanics:2 constant:9 ln:1 int:1 certain:3 abstract:1 describe:1 textbook:1 general:2 transl:1 presented:1 arises:1 5th:1 formalism:2 distributions:1 proceeds:1 regime:12 abyss:1 functions:9 compared:1 dotted:1 no:4 dashed:2 whereas:1 generally:1 vanishes:1 nal:1 application:1 other:2 compares:1 correlation:2 deviate:1 conclusion:1 calculating:2 preceding:1 chem:3 variation:1 a1:1 generated:1 uctuation:1 variable:1 risken:1 singapore:2 sides:1 legitimate:1 jones:2 coupling:8 polymer:2 n4:5 n5:5 n8:3 n9:2 simplicity:1 n2:10 n3:8 requires:1 original:1 n6:2 n7:4
|
quant-ph9502028.txt |@word thomas:1 leads:3 eds:1 consists:1 scs:6 calculate:1 deterministic:1 quasi:11 connecting:1 p2:1 supported:1 amplitudes:4 hibbs:1 straightforward:1 very:1 wave:2 hdt:1 four:2 incoherent:1 hamiltonian:1 transmission:8 deals:1 indices:1 warszawa:1 optics:1 za:1 unpolarized:1 go:1 second:1 concludes:1 dynamics:2 linear:3 plays:1 apparatus:8 sum:1 expressed:1 uniform:1 new:6 acknowledgments:1 diagonal:2 cos2:8 address:1 represented:1 path:17 strong:1 equations:4 change:2 obtained:4 incoming:2 dividing:1 involved:1 study:1 eberly:1 poisson:2 action:1 suitable:1 studies:2 involves:2 plenum:1 courtens:1 stern:8 unit:2 feb:1 usa:1 commun:1 probabilities:2 positive:2 contains:1 negative:4 bialynicki:1 more:1 operators:1 normalized:1 given:4 iii:1 work:1 oscillator:1 infinitesimal:2 values:1 following:10 example:4 performed:1 states:9 sphere:12 numbers:1 information:1 rather:1 discussion:1 holds:1 write:1 pure:1 sin:6 product:1 ladder:1 derived:2 law:26 dynamical:1 joint:4 light:6 grant:1 provide:1 correlation:2 representation:4 order:2 typical:1 horne:1 kbn:1 over:3 paper:1 through:7 unite:1 statistical:7 its:1 before:2 subinterval:1 φb:1 exhibits:1 squaring:1 detected:3 permanent:1 systems:4 pcl:2 hidden:6 non:1 than:1 entire:1 investigated:1 krzysztof:1 rotation:1 dp1:1 discuss:1 february:1 dirac:1 trary:1 fizyki:1 2s:9 characterizes:2 university:2 identified:1 applied:2 each:1 found:1 uniwersytet:1 characterized:1 weight:1 idea:1 attenuation:3 obtains:3 sion:1 quantum:34 dωp:3 out:1 shown:1 matrix:2 space:4 rev:3 particles:4 formula:6 math:1 shows:1 theory:4 albuquerque:1 york:3 dω1:1 dω2:1 skagerstam:1 dλb:1 dλa:1 transition:3 motion:3 first:1 simplifies:1 features:1 probability:12 variables:5 primary:1 simplified:1 another:1 reached:1 take:1 differ:1 glauber:1 introduction:1 leading:1 system:8 analog:1 indicate:1 sˆ:3 detection:1 polarized:2 depends:1 polarizer:4 amplitude:11 motivation:1 rewrite:1 ann:1 generalization:4 seen:1 paths:1 angle:6 mermin:1 lim:1 polarization:3 erator:1 generalized:1 analogy:1 subintervals:1 canonical:3 formulas:1 added:1 object:1 singlet:1 involving:4 instytut:1 phase:2 clear:1 detectors:1 feynman:4 bracket:2 exp:6 mechanical:4 physics:1 fact:1 laws:1 emerging:1 show:1 random:1 purely:1 relation:2 gerlach:8 q1:2 q2:1 teoretycznej:1 dp2:1 parameters:1 distributed:2 written:2 should:1 factor:1 local:1 mixture:1 familiar:1 beam:5 dv:1 dp:2 dq:1 evolution:1 exhibiting:1 podolsky:2 arxiv:1 method:1 investigate:1 set:1 correlations:4 warszawski:1 up:3 relative:3 intensity:1 result:4 discussions:1 best:1 inequalities:1 shimony:1 definite:1 state:11 various:2 between:4 caves:1 numerous:1 ends:1 reproduced:1 incident:1 configuration:2 cos:14 many:1 according:2 pdq:2 quantization:1 connection:1 expression:9 comes:1 bell:1 harmonic:1 directions:4 scully:2 respect:1 described:3 dqdp:3 been:1 describes:1 basic:1 ph:1 direction:4 describe:1 corresponding:5 θb:2 θa:2 θe:1 zeilinger:1 coherent:4 angles:3 berezin:1 spin:39 realities:2 case:3 p1:2 pacs:1 solid:3 evaluated:1 cast:2 behavior:1 orientation:3 mexico:3 vi:1 ii:1 curved:1 author:1 klauder:1 same:1 φa:1 unity:1 quant:1 φi:2 higher:2 used:1 see:3 singapore:1 trajectories:3 average:2 uses:1 purpose:1 center:2 nevertheless:1 poland:1 well:2 academic:1 position:1 know:1 spherical:3 just:2 λb:5 λa:5 thanks:1 predicts:1 dφd:1 polish:1 oriented:1 dqp:1 density:4 photons:1 character:2 lett:1 easy:1 spin1:1 momentum:1 iφ:1 opp:1 quasidistribution:1 evaluate:1 possible:2 corresponds:1 objective:1 entangled:3 confined:1 using:5 unique:2 advanced:2 formal:1 particle:2 dq2:1 reduces:1 integrals:4 arbitrary:11 become:2 malus:40 reduced:1 spins:3 because:2 classical:25 some:1 gilmore:1 examples:1 provided:2 integration:3 comments:1 contributing:1 decomposition:1 provides:2 equivalent:2 eiφ:1 properties:3 bz:1 about:1 carried:1 world:1 discussed:3 o:2 mixed:2 recognizes:1 bloch:9 lieb:1 into:2 integral:11 functional:2 down:3 einstein:2 operator:1 birula:1 there:1 accordingly:1 way:3 was:1 function:22 complete:1 form:12 but:1 failure:1 ho:1 odkiewicz:4 partially:1 maximum:1 ωi:3 limit:10 ωn:1 ωa:4 distribution:18 ωb:3 similar:2 calculated:1 mechanics:6 associated:2 measure:1 am:1 general:2 θi:1 formulation:1 distributions:2 functions:3 no:1 eq:2 rosen:2 valid:1 role:1 department:1 coherence:1 superposition:1 dq1:1 suited:1 variable:2 astronomy:1 structure:3 correlated:1 quasiprobability:1 dω:6 dφ:1 4s:1 scientific:1 time:1 labelled:1
|
quant-ph9502029.txt |@word limited:1 remarkable:1 zhang:1 caused:1 focus:1 illustrated:1 eds:7 ciudad:1 entropy:24 houches:2 consists:1 follow:2 zinn:1 localized:2 inverse:1 depend:2 alamos:2 γp:1 corrections:2 essentialy:1 environment:22 quasi:3 critical:6 squeezing:2 helps:1 under:3 te:1 zeh:1 carried:1 interacting:1 conjecture:1 preserved:1 orthogonal:1 very:5 continues:2 account:2 wave:2 lyapunov:8 corollary:1 every:1 sensitivity:1 fall:1 little:2 logarithmically:2 encounter:1 paz:5 leads:3 dominate:1 mc:1 hamiltonian:10 cause:1 notes:1 solution:2 hillery:1 large:2 vector:1 section:1 small:3 prevent:1 strongly:1 smaller:2 force:3 oscillation:1 folds:1 consistent:1 prediction:1 mantica:1 prevents:1 past:1 fold:1 rate:14 timescales:1 teq:4 dynamics:19 estimated:1 linear:3 even:9 what:1 nonlinear:1 apparatus:2 sum:1 brief:1 uniform:2 reminiscent:1 above:6 new:5 ever:1 method:1 contrast:10 coefficient:1 compresses:1 processing:1 led:1 ibid:2 never:1 asymmetry:1 les:2 pancake:6 relaxation:5 represented:2 along:7 quite:1 directions:8 implicit:1 logarithmic:1 arena:1 parameters:1 remarks:1 leaves:1 stretching:5 meiss:1 completely:1 resulting:3 poisson:10 action:2 noticeably:1 narrow:2 makes:2 astute:1 deterministic:1 followed:1 figure:1 transit:1 plenum:2 inequality:2 decrease:1 nonequilibrium:1 zeits:1 resolutions:1 total:1 planck:4 λdb:1 derivatives:1 feb:1 superpositions:10 would:4 positive:4 predictions:1 next:1 discrepancies:1 classically:2 sample:1 therefore:4 memory:1 taken:2 survive:1 stage:3 type:1 theoretical:1 today:3 more:7 separated:1 becomes:6 apparent:1 validity:1 reversibly:1 domination:1 reversible:3 virtue:1 proceed:3 excellent:2 known:3 cases:1 potential:10 must:1 logarithm:2 hardware:1 keeping:1 quantized:1 deformed:1 equation:13 oscillator:2 london:1 remain:2 vs:1 values:1 rewritten:1 freedom:1 following:1 example:3 references:3 indicated:1 mirrors:1 process:6 exactas:1 neglected:1 ann:1 states:20 effectively:1 assumptions:1 chin:2 something:1 sought:1 difference:1 times:1 verlag:3 information:3 monitoring:2 rather:4 verify:1 discussion:2 holds:1 haake:1 carries:1 write:1 how:2 buenos:1 significance:1 instead:1 bit:1 reestablish:1 sin:1 isotropic:1 map:1 untill:1 may:2 db:1 oscillators:1 after:9 collection:1 consequence:4 justin:1 ove:1 cambridge:1 summarize:1 grow:2 a91:1 short:3 natural:1 dynamical:9 effective:5 light:1 approximation:5 explicit:1 correspond:1 provide:1 so:9 ultimate:1 fundamental:1 enter:1 representation:2 order:5 require:1 typical:2 wavelengths:1 spreads:1 wigner:12 deform:1 ur:1 essence:1 over:9 encouraged:1 major:1 feature:1 course:3 thermal:4 paper:2 including:1 statistical:2 existence:2 satisfies:1 still:3 pointer:6 its:16 before:2 regions:1 derive:1 rapidly:1 monitor:1 decay:3 susceptible:2 interesting:1 τd:2 solving:1 decreases:1 2λt:1 estimating:1 absence:1 production:13 degrees:3 systems:29 argentina:1 main:1 τr:3 h0:2 correspondence:6 eventually:1 non:4 good:1 practice:1 fig:1 often:1 underdamped:1 effects:1 they:4 half:1 inception:1 multidimensional:1 now:1 discuss:2 unpredictability:3 susceptibility:1 term:8 finite:1 fixed:1 characterizes:2 university:2 traced:1 2d:1 unpredictable:1 token:1 magnitude:1 knight:1 found:1 2n:7 quarter:1 summarily:1 side:2 d45:1 domain:1 everyone:1 hubert:1 evolve:1 series:1 gaussian:1 constitute:1 contracting:3 reader:2 used:3 interplay:1 measurement:4 quantum:59 laboratory:1 happen:2 patch:8 eq:2 neighbourhood:1 out:3 shown:3 matrix:6 space:23 gradient:3 furthermore:1 since:1 rev:6 chaos:15 denotes:1 increase:8 conclusions:1 conjectured:2 formula:3 get:1 induced:3 issue:2 occurs:1 independence:1 decoherent:1 proviso:1 theory:5 voros:1 ısica:1 diagonal:3 departamento:1 diagnostic:2 difficulty:1 approaches:1 base:1 complicated:1 york:5 asi:1 additional:2 definition:2 interaction:7 could:1 transition:3 decohering:4 keep:1 counterpart:1 turn:1 place:3 exponentially:7 δij:1 signature:1 hence:6 support:1 first:1 intuition:1 there:2 probability:2 striking:1 reaches:2 approximate:1 approximately:3 pablo:1 slower:1 precisely:1 open:6 size:2 given:9 temperature:3 width:3 introduction:1 durable:1 behaves:1 system:34 least:2 defining:1 1a:1 their:4 zaslavsky:1 master:3 too:2 compromise:2 stora:1 leggett:1 interference:1 exponents:4 recovered:1 chirikov:2 fraction:1 wavelength:1 tool:1 continuous:1 eliminates:1 x9:1 numerical:1 somewhat:1 eliminated:1 believe:1 representing:2 than:12 preferential:1 begins:1 wide:1 holland:2 princeton:2 anticipate:1 zero:2 final:1 matter:1 determined:1 assume:1 were:1 providing:1 buzek:1 exhibit:4 d40:1 separations:1 correction:1 argument:1 invalidated:1 already:1 manner:1 further:1 need:1 tχ:4 demonstration:1 orders:1 irreversibility:2 d47:1 proximity:1 strength:3 self:3 able:1 lii:1 onset:1 majority:1 high:1 subjects:1 take:4 forces:2 negligible:2 coincide:2 subject:1 analogs:4 progressively:1 heisenberg:3 lectures:3 begin:1 broglie:2 allow:1 mercader:1 shall:3 object:1 falls:1 most:1 regular:7 aires:1 significant:3 phase:21 kay:1 hu:1 had:1 singled:1 volume:7 especially:1 consequences:1 fills:1 clear:1 devastating:1 analog:1 physica:2 face:1 bracket:17 principle:5 exp:2 χn:1 scully:2 typically:3 assistance:2 fact:2 laws:1 hyper:4 show:4 anyway:1 rotating:2 purely:1 attempts:2 relation:2 help:1 indicator:1 based:1 nevertheless:1 spite:4 maintaining:1 habib:2 situations:1 written:3 should:3 analytic:1 only:13 implemented:1 gradual:1 attained:1 integrable:7 local:4 interested:1 equilibrium:7 diffusion:8 his:1 dominant:1 means:1 dependent:2 familiar:1 zurek:12 de:4 stop:1 expectation:1 preferred:13 truly:1 joint:1 cannot:2 longest:1 lahti:1 evolution:14 resolve:1 gauged:1 conditions:1 arxiv:1 motion:1 gutzwiller:1 summary:2 though:2 ascertain:1 through:2 orce:1 valid:2 approaching:1 precluding:1 set:4 computed:1 observer:1 achieved:2 national:1 accord:1 opposite:1 see:2 full:2 result:9 discussions:1 simultaneously:1 halliwell:1 springer:3 nonlocality:1 best:2 wonder:1 caldeira:1 evaluation:1 exponent:3 excitations:1 review:1 complementary:1 below:3 tend:7 symmetric:1 state:8 various:2 frontiers:1 closed:1 between:10 αi:3 progress:1 approach:3 available:2 comparable:2 terms:6 ehrenfest:1 nature:7 initially:1 weak:1 however:1 moyal:7 casati:1 uniformized:1 extent:6 distinguish:1 universitaria:1 come:2 distribution:10 observable:6 essentially:2 last:2 limits:1 always:2 σc:5 many:2 uncertainty:1 previously:1 etc:1 berry:1 context:5 distinction:1 whole:1 pabell:1 diagnose:1 relevant:2 timescale:18 point:1 simple:2 guaranteed:1 asymptotically:2 vast:1 harmonic:3 environments:1 sampling:1 dimensional:1 alone:1 ii:1 121a:1 simply:3 stretched:3 polynomial:2 associated:2 superselection:4 moore:1 decohere:1 pp:3 second:1 basis:5 addition:1 trajectory:1 three:1 been:2 quickly:3 faithfully:1 much:7 damping:1 interest:4 basic:1 ph:1 dynamically:1 2i:2 obtained:1 direction:8 arises:1 corresponding:8 samples:1 commutes:1 am:1 coherence:6 σi:6 observers:1 maps:1 coherent:6 understand:1 external:2 folding:6 standard:1 case:7 uncertain:1 xxxvi:1 exponential:8 ǫj:1 ǫi:2 expanded:1 single:1 value:2 will:69 while:1 behavior:7 squeezed:2 di:1 study:2 characterizing:2 larger:4 coupled:4 chaotic:20 von:4 thus:11 obeying:1 characterize:1 reads:1 neurons:1 properties:1 busch:1 acquires:2 everyday:1 different:3 wiley:1 atmanspacher:1 april:1 perhaps:2 graham:4 juan:1 radiation:1 lett:2 same:5 any:1 shorter:2 quant:1 wavepacket:3 units:2 relatively:4 breakdown:1 independent:1 investigated:1 singapore:1 trajectories:1 effect:7 hand:2 moment:1 moving:1 purpose:1 potentials:1 recent:1 joos:1 off:1 center:1 minimize:1 studies:1 well:5 deal:1 without:1 contact:1 position:9 dimension:4 bodies:1 left:1 distances:4 just:1 less:4 increasingly:1 connell:1 accurate:2 isolated:1 press:2 cease:1 aspect:1 part:2 useful:1 λi:2 rotates:1 macroscopic:8 eigenstates:3 mittelstaedt:1 letting:1 note:1 rapid:2 density:6 thinking:1 regarded:3 seems:1 mathematically:1 spread:6 nato:1 corresponds:1 versa:1 theorem:1 stable:6 momentum:9 opt:1 b59:1 aspects:2 easily:2 rules:1 louisell:1 results:3 possible:1 period:1 ciencias:1 vacuum:1 wojciech:1 world:1 emergence:1 σc2:1 loss:2 appearing:1 particle:2 lost:1 δp:1 translates:1 specific:1 giannoni:1 indication:1 fully:1 evolutions:1 become:4 reduced:2 accessible:2 right:2 neumann:3 classical:31 absolutely:1 some:4 back:1 competition:1 therein:2 towards:1 respect:1 expression:1 happens:1 provided:1 scale:4 lead:1 sufficiently:5 measurements:3 comments:1 does:1 eliminate:1 provides:1 tends:5 prog:2 unstable:9 fragments:1 proc:1 philadelphia:1 minimal:1 dittrich:3 scientific:1 power:2 arbitrary:1 quantified:1 translated:1 heq:3 although:1 instability:3 eye:1 approximating:1 dictated:1 hilbert:2 takes:2 unruh:1 about:4 polynomially:1 usa:1 origins:1 universe:3 dependence:1 o:5 essential:1 indeterminacy:2 range:2 plus:3 consequently:4 hotly:1 soc:1 own:1 keeps:1 h2:3 into:14 within:1 steady:2 negative:1 nothing:1 appropriate:1 because:4 ppw:1 determine:1 operator:2 amsterdam:2 σp2:1 hellmann:1 shrinking:3 physical:1 significantly:1 fill:1 log:1 few:1 suffice:3 initial:11 transform:1 long:4 dispersion:7 los:2 facultad:1 way:1 astrophysics:1 was:6 opposed:1 function:7 north:2 complete:3 form:4 enough:2 fundamentals:1 becoming:1 regard:1 but:7 ford:2 idealized:1 failure:2 ho:1 squeeze:1 true:2 naturales:1 coupling:7 compute:1 nonlinearity:1 versions:1 whether:1 characteristic:2 us:3 until:1 record:2 liouville:4 limit:6 reflects:1 continuously:1 fluctuations:1 problem:4 similar:1 called:4 expect:1 mechanics:4 b62:1 constant:6 lcrit:2 hdot:2 defined:4 flow:4 abstract:1 describe:1 influence:2 general:4 conserved:1 our:4 perez:1 gradients:2 distributions:1 internal:1 regime:4 2dt:1 predictability:1 compared:1 nm:1 no:5 nonlinearities:2 wavefunction:6 when:10 preventing:1 ny:1 narrowing:1 other:4 role:1 spatial:3 test:1 approximated:1 theor:1 2di:1 shrink:1 immunity:1 picture:1 briefly:1 wheeler:1 superposition:2 hilger:1 preceding:1 berman:1 nonclassical:1 prepared:1 commutator:1 generated:3 important:2 b256:1 yields:1 needed:1 correlated:2 longer:4 vice:1 2mkb:1 physics:7 required:1 d24:1 rule:1 d26:1 transient:1 time:8 far:1 σci:1 decoherence:38 quantity:1 roy:1 rep:3 coherently:2
|
quant-ph9503001.txt |@word sci:3 chain:1 results:1 four:1 fig2:1 fig1:3 gn:6 disk:8 gk:1 centers:1 scr:1 whose:1 depend:1 veq:4 technique:3 micrometers:1 finally:2 critical:1 ny:1 under:3 shielding:2 transducers:1 cantilever:3 very:7 frequencies:2 rise:1 wave:1 electron:2 resonant:4 condition:2 vector:1 small:5 enforce:1 configurations:1 prevent:1 smaller:2 force:20 machined:1 estimates:2 measurable:1 approximation:1 second:2 theory:1 appear:1 apparatus:4 section:1 tabor:1 thickness:1 current:7 above:3 waals:1 new:1 method:2 pioneering:1 actuators:1 respectively:3 component:6 reported:1 operating:1 based:1 observing:1 galilei:1 extreme:1 obtained:4 shift:1 study:4 changed:1 allows:2 vibrating:1 simultaneous:1 resulting:1 pick:1 resonance:4 fourier:11 diameter:2 via:1 useful:1 buser:1 instr:1 plenum:1 braginsky:3 vac:1 modulated:1 decrease:1 aimed:1 motor:1 nxp:1 planck:1 unit:2 use:4 νr:3 physics:1 few:1 therefore:1 averaging:1 means:2 resonator:17 until:1 more:1 flat:2 optimizing:1 giovanni:1 about:1 tested:1 particular:1 cases:1 1µm:3 high:3 mm:2 der:1 work:1 oscillator:2 london:1 kaminsky:1 values:1 dn0:1 making:1 mx:1 control:2 dedicated:1 νp:2 figure:5 give:1 relativistic:1 table:3 sample:1 application:1 performed:2 tab:2 amplitudes:1 times:1 information:2 redundancy:1 end:1 sensors:1 verify:1 get:4 far:1 instrum:1 parameter:1 circular:1 mar:1 fv:3 modulation:6 fc:3 snr:1 fg:1 monitoring:2 law:1 parallel:2 types:1 physical:1 dynamical:4 third:1 light:1 quadrant:1 generic:1 ultimate:1 allow:3 first:3 order:7 cutoff:1 fft:4 stability:1 paper:1 through:6 existence:2 its:7 burleigh:2 acknowledge:1 lateral:7 khalili:2 fruitful:1 detected:3 fig:10 suspension:2 main:1 decades:1 versus:1 non:2 affected:2 greater:1 ya:2 propose:2 outlined:1 introduce:1 scaling:1 band:1 penetration:1 now:1 february:2 2d:1 vibrations:1 mode:2 acoustic:2 universit:1 d40:3 side:2 illuminati:1 displacement:2 related:1 insulation:1 frequency:11 static:4 measure:2 quantum:2 our:4 thick:1 out:2 shown:6 driving:4 factors:3 electronic:1 furthermore:1 rev:4 increase:1 acting:2 europhys:2 istituto:1 term:2 induced:3 ref:1 conti:2 linear:2 fisica:2 possibility:4 quite:1 approaches:1 base:1 advantages:1 york:1 besides:1 put:3 org:4 detecting:1 carugno:1 geometry:1 determining:1 could:3 10µm:1 motion:1 turn:1 plane:1 assumed:1 view:1 permit:1 origin:1 informations:1 already:2 manuscript:1 upper:2 rydberg:1 explored:1 improvements:2 done:1 least:2 type:1 xr:19 xp:15 quality:6 angular:1 biasing:2 equating:1 given:5 dipartimento:1 2ωr:3 2ωp:3 their:2 quadratic:1 fn:2 eqn:1 white:2 scheme:6 relationship:2 100nm:4 relative:1 akad:1 park:1 optical:2 believe:1 than:4 png:8 oscillate:1 steel:1 distance:11 holland:1 microresonators:3 roberto:1 absence:2 editors:1 transducer:6 amplitude:3 polishing:1 hunklinger:2 m2:1 spectrum:4 israelachvili:1 levitov:1 close:1 seem:1 unaffected:1 orders:3 depending:2 uncorrelated:1 latter:1 proportional:1 gravity:1 instance:3 forces:18 schematically:2 electric:3 most:1 detect:2 connected:2 rationale:1 preliminary:2 phase:1 future:1 measured:2 manifested:1 kc:4 sinusoidally:1 consequences:1 calculated:1 detectors:1 physica:1 typeset:1 astonishing:1 part:2 mechanical:19 left:2 tubes:1 ned:1 spaced:2 show:2 probe:1 feasibility:1 friction:1 purely:2 gauge:1 corner:1 d4:1 uniform:1 d0:30 piezoelectric:8 ratio:2 parameters:1 dissipative:2 written:1 should:8 only:3 candidates:1 factor:6 hope:1 dn:1 plate:1 di:4 dependent:2 de:1 db:1 beam:3 ones:2 report:2 during:1 2mm:2 submicron:1 aluminum:1 arxiv:5 acknowledgments:1 microscope:2 experiments:2 predicted:1 levin:1 including:1 fixed:1 inside:2 voltage:14 mandatory:1 sensitivity:5 coccia:1 up:4 detection:11 see:2 result:1 discussions:1 terms:1 observed:2 best:1 techniques:3 surfaces:7 exploited:3 speed:1 review:1 opening:1 6mm:1 µm:1 enough:2 determined:3 various:1 heterodyne:1 between:12 tens:1 drawn:1 reading:1 approach:2 wide:1 available:4 recently:2 ability:2 nature:4 weak:1 however:2 analyzer:1 vanishing:1 configuration:1 suppressed:1 suggested:1 both:4 cos:6 last:1 limits:1 many:1 region:1 equal:5 sensitive:1 figures:1 casimir:24 expression:1 masses:3 among:1 cm:1 point:1 reasons:2 inc:1 harmonic:1 respect:3 indefinite:1 cv:1 ps:4 pp:1 described:1 kinematic:1 atomic:1 due:3 been:9 pc:1 reduction:1 interest:1 ph:5 prototype:3 systems:1 corresponding:2 observable:1 concerning:1 formed:1 requires:1 gap:3 observe:3 1mm:1 present:2 case:5 flexural:1 unlike:1 appearance:1 arnold:2 rectangular:1 will:3 while:2 suppose:2 tunneling:14 pessimistic:1 cylinder:2 larger:2 pzt:3 drawbacks:1 thus:2 surface:2 ii:2 bias:6 electromechanical:5 technology:1 different:1 italy:2 estimate:1 suggest:1 lett:4 same:4 quant:5 schematic:1 plates:4 finite:1 independent:1 used:8 http:4 peaks:1 retarded:1 upon:5 hand:1 driven:2 conductors:1 supposing:2 infinite:1 stack:9 recent:1 simulates:1 lower:2 center:2 nucleare:1 calibration:4 well:2 without:1 components:10 simulated:1 quantitative:1 bodies:3 usual:1 distances:5 proposed:1 less:5 being:3 when:3 accurate:4 obtain:2 shape:2 plagued:1 spatially:1 alternative:1 macroscopic:2 clamped:1 previous:2 tables:1 vibration:2 simple:1 other:8 attractive:1 wet:1 tests:2 around:3 format:4 bands:6 possible:1 corresponds:2 vacuum:4 press:1 using:5 apart:1 like:2 exploiting:2 signal:3 sezione:1 become:1 4mm:1 because:1 nm2:1 rigidly:2 understood:1 deduce:1 moreover:1 oscillations:2 provided:2 scale:2 measurements:1 integration:1 per:3 conservative:1 magnitude:5 provides:1 proc:2 biased:1 noise:10 2µm:2 equivalent:3 onofrio:1 revtex:1 although:1 repeating:1 gained:1 comparison:1 conducting:3 geometries:1 eqns:1 discussed:2 dependence:1 deduced:1 reduced:1 practical:2 range:9 observation:1 micromechanical:1 rooij:1 considerations:3 soc:1 contains:1 letter:1 presence:4 instruments:1 lenght:2 within:1 three:2 references:1 cent:1 amsterdam:1 van:1 devices:1 area:1 transfer:3 long:1 detectable:3 low:3 way:2 1khz:1 function:3 survives:1 north:1 ruoso:1 differences:1 but:2 marzolo:1 neutral:2 gain:1 true:1 proposal:1 padova:3 made:5 ωp:20 gravitational:5 ωr:17 maximum:1 us:1 below:2 gaps:2 limit:3 ruling:1 spectroscopy:1 problem:1 piece:1 similar:2 constant:6 minutes:1 abstract:1 measurement:4 proper:1 single:1 nazionale:1 check:1 regime:1 compared:2 no:1 tip:3 detail:1 field:2 valid:2 electrical:1 test:2 techn:1 nice:1 excitation:2 welcome:1 problems:1 allowing:1 studied:1 dissipation:1 seismic:1 implies:1 resonators:2 assume:1 d20:5 required:1 curve:1 300v:3 mass:5 parallelism:2 time:2 4b:2 4a:1
|
quant-ph9503002.txt |@word 2kµ:4 nato:2 four:6 fig1:3 consists:1 whose:1 const:1 aug:1 segments:5 exponentiation:1 tween:1 restriction:2 under:9 worth:4 divergent:1 connects:1 distort:2 p1:26 every:11 summarized:1 affect:1 enard:1 dominator:1 clothed:1 convenience:1 vector:3 succession:1 indices:3 ǫi:3 japanese:1 second:12 rigorous:3 implemented:1 even:7 established:3 errors:1 supplied:2 above:8 supplies:2 net:4 increasing:1 consisting:1 coefficient:1 8a:1 simultaneously:4 behavior:4 never:1 residual:5 here:16 represented:11 logarithmic:8 contraction:2 obtained:21 property:19 mintchev:4 employees:1 changed:1 dri:1 drj:4 california:5 suitable:1 spacetime:13 cancellation:3 9a:1 9c:3 explained:1 replace:2 unitary:6 rω:8 unit:1 charge:10 would:23 kinematics:1 therefore:5 m2:78 type:32 until:4 separated:8 pinching:5 separates:2 ward:1 hold:3 must:15 springer:1 join:1 rights:1 work:19 theories:4 henry:1 ero:5 root:1 example:5 conf:1 indicated:2 give:11 cited:3 validates:1 malgrange:1 involve:4 indicates:1 magnitudes:1 times:6 absolute:1 end:27 thing:1 provide:3 imprecision:1 feature:1 how:1 significance:1 classify:1 replacing:1 earlier:5 containing:1 diagram:15 stipulate:1 law:5 parallel:1 types:1 third:3 eliminated:1 summing:2 green:2 enter:2 order:25 operations:3 origin:3 interpretation:1 office:2 over:24 satisfied:2 japan:1 before:8 manageable:1 writing:1 destroyed:1 production:1 fig:12 them:2 combination:2 amenable:1 break:1 effects:5 they:13 singularity:45 represents:12 reasonable:3 each:87 side:12 inserts:1 meets:2 series:8 principles:3 laboratory:6 extract:1 restricted:1 crucial:1 singling:1 particles:24 re:4 multiply:1 ra:2 rb:5 conjectured:1 rn:2 ri:7 rj:38 foundation:1 linear:1 written:3 free:8 standard:3 detecting:1 incorporates:2 enormous:1 r1:18 r2:3 created:1 starts:2 creates:1 wiechert:1 incorporated:4 corrections:4 generalizations:1 separable:8 already:4 features:1 primary:1 thereof:3 nonperturbative:1 another:2 service:1 needed:11 zeros:3 ordered:3 iδ:2 collapse:1 zeroth:5 direct:1 peculiar:1 begins:1 distance:5 princeton:3 conforms:1 approximations:2 zero:20 regulator:1 powers:9 minus:3 extracting:1 bridge:2 entail:1 modern:1 spectrum:1 manner:1 emphasizing:3 seem:2 lbl:4 relatively:1 convenient:2 latter:5 responsible:1 instructs:1 shall:12 denominator:17 simplify:1 involving:2 phase:4 frautschi:3 vertices:23 bracket:4 principle:16 section:32 reserve:2 labels:1 infrared:27 iǫ:1 gauge:5 d8:1 subtle:1 d4:23 pki:12 d3:4 explain:1 topological:1 integrate:1 adequate:1 do:19 dj:5 establishes:1 di:11 de:3 dx:2 new:2 report:3 dr:2 runs:4 contributes:1 fields:4 interspersed:1 discs:1 pµn:1 pµi:9 pµj:7 clarified:1 detection:3 depends:2 result:24 fail:1 subject:3 away:6 propagates:1 symmetric:1 µn:7 µi:9 µj:2 approach:3 terms:42 positron:3 nature:2 however:12 pµ1:9 essentially:5 ill:1 contribution:13 suggest:1 appeared:1 had:1 factorize:1 γσi:13 commutative:1 basis:1 simplification:1 three:36 been:12 much:2 interest:4 basic:3 expected:3 ann:3 θj:1 θn:7 argument:13 coherent:2 applied:3 exception:2 remaining:10 aim:1 euclidean:1 near:4 suppose:12 applies:1 aid:1 endpoints:2 leaves:1 procedure:2 n2i:4 ki2:8 tions:1 ii:2 disjoint:1 im:2 cone:1 io:3 interacts:1 disappear:1 confirmed:2 perform:1 things:1 make:5 quant:4 split:1 several:1 independent:4 i0:27 differing:1 hand:9 kij:13 potentials:1 opportunity:1 mentioning:1 fourier:3 possibly:1 changes:1 preceeding:1 contact:2 quantitative:1 left:9 opinions:1 just:12 photonic:4 transforms:1 scattering:24 yet:2 adding:2 enters:1 regarded:2 character:5 easy:1 apart:3 gave:2 9b:1 possible:11 objective:1 distortion:4 grenoble:1 occurring:3 dµj:5 appearing:7 specific:1 follows:6 mahanthappa:3 right:12 theorists:2 deal:2 formulas:3 deflection:1 embodied:1 ici:3 fop:12 colloque:1 electromagnetic:12 propagators:12 everything:2 substitutes:1 dropped:3 arbitrary:7 constructive:2 properties:9 proceed:1 numerator:15 o:4 nonvanishing:1 ensure:1 emilio:5 propagate:1 down:2 lies:5 refined:1 initial:4 approximate:1 class:2 accordingly:1 conservation:6 way:18 was:21 form:40 becoming:1 idealized:1 failure:3 responding:1 attached:2 devices:1 complications:1 proved:4 computing:1 upset:1 abstract:1 covers:2 convergent:4 conserved:2 proves:1 dλ:10 internal:4 constructed:2 nj:1 no:26 whereas:3 when:6 vanishes:2 schwinger:2 setting:1 role:1 papers:2 preceding:1 ckr:1 uniformly:1 zwanziger:2 variable:11 regime:6 factorized:1 coulomb:1 assume:1 interval:4 packets:4 together:8 storrow:1 time:1 serious:1 backward:1 logarithms:1 concept:1 focus:3 leads:2 computation:2 bremsstrahlung:6 depend:3 graph:39 technique:1 quasi:1 weakening:3 osterwalder:1 analogous:5 division:1 choice:1 liability:1 emphasized:1 exact:2 level:1 did:1 turns:2 leave:1 discrete:1 recall:1 attracting:1 upper:3 nordsieck:3 says:1 dealing:1 sign:2 stands:2 comparable:1 contracted:3 foregoing:1 current:3 goes:1 international:2 satisfy:1 concepts:1 smearing:2 address:1 along:15 appears:3 change:1 incoming:1 masslessness:1 institute:1 shift:3 studied:1 usually:1 conveniently:1 studies:1 useful:3 extra:8 merely:2 logical:3 ipz:6 ipx:1 employer:1 prove:6 covariant:1 positive:4 rω2:8 predictions:3 associated:35 compactly:2 theoretical:2 diagrams:1 dxµ:1 apparent:6 validity:4 appendix:1 virtue:3 cases:4 originally:1 modified:1 values:3 following:10 making:4 trans:1 figure:9 sense:2 performed:3 allowed:2 unphysical:1 counting:7 occur:4 verlag:1 rays:3 requirements:2 s3:1 s2:1 s1:1 write:3 fourth:1 endorsement:2 plus:2 dominance:1 product:11 mar:1 may:11 neat:1 residues:6 produce:7 sectors:2 so:15 verify:1 sc:7 representation:5 typical:2 indeed:3 displayed:2 course:4 motions:3 omitting:1 differs:1 still:1 coordinates:2 forms:1 coordinated:1 main:3 correspondence:15 non:9 thereby:2 views:1 matches:1 qs:2 introduce:8 half:13 now:8 nor:4 term:31 name:1 drop:1 σ2s:2 domain:12 square:3 ei:1 ed:1 entering:2 σ2j:2 ev:1 eq:4 shown:17 space:51 squared:1 cancels:1 increase:1 contained:5 suggesting:1 formula:10 correct:4 shows:10 after:4 theory:20 suura:2 derived:1 divergence:5 complicated:1 org:3 remainder:8 e2:1 qj:2 language:1 ministry:1 dλn:2 favoring:1 transition:3 dλj:7 dλi:9 motion:2 turn:2 place:8 massive:1 qn:1 neglect:1 first:32 xj:2 xi:5 onm:1 omitted:1 variables:25 transform:1 multiplying:1 specifically:4 directly:6 carry:1 open:2 angular:1 size:1 interchange:1 given:16 necessarily:2 indicate:1 constants:1 speaking:1 gives:23 cope:1 proving:1 accurately:2 transverse:1 x2:19 x3:17 rightmost:1 x1:19 representing:3 than:11 png:6 sections:9 propagator:39 were:13 decompose:1 subprocesses:2 correction:4 premier:1 locations:6 generalization:5 say:2 distorted:6 recover:1 any:29 conversion:1 computationally:2 efficient:1 ideas:3 converges:1 note:2 sciences:1 potential:2 take:1 interior:2 destroy:1 coincide:1 ωj0:1 begin:2 multiple:3 normal:4 falls:1 pair:2 inserted:11 interacting:1 phic:1 considered:10 later:1 feynman:15 quantity:3 show:7 jµ:9 subprocess:1 obtains:2 enough:2 analytic:14 only:22 explicitly:2 correctly:1 get:1 conjunction:3 geometric:3 yield:4 predicted:1 nonrigorous:1 ignored:2 physically:4 2ps:2 cin:6 relative:4 lausanne:1 surfaces:12 fails:1 commutation:1 ways:8 definite:1 sites:2 kj2:5 outside:2 jth:1 radiated:6 between:16 justified:1 across:2 multiplied:4 notice:1 deliver:1 analyzed:1 article:2 n1i:3 σj:5 many:3 region:1 according:11 contract:1 called:3 propagation:5 σs:4 expression:5 comes:4 among:3 colons:1 pole:46 cancel:2 moreover:3 considering:2 combines:1 mounting:1 combined:1 differently:1 6a:1 6b:1 formed:4 photon:78 fortschr:1 observe:1 external:11 jǫ:1 evidence:1 those:8 case:36 cast:1 cancelled:2 situation:1 coupled:6 bros:2 iagolnitzer:4 converts:2 technology:1 different:7 verified:1 d11:1 same:11 shifts:2 arguments:8 physical:10 events:1 breakdown:2 extended:1 companion:4 director:1 running:1 arose:1 invariance:1 relies:1 takahiro:1 severe:1 components:1 coordinate:17 model:1 grounds:1 d1i:6 charged:42 kawai:5 being:2 generally:2 actions:1 pσj:3 aspect:1 villars:1 photons:59 seems:1 except:1 interested:4 treatment:9 enjoys:1 momentum:41 real:3 aspects:4 around:4 rules:4 decomposed:2 vacuum:2 confined:4 using:7 decomposes:1 76sf00098:1 particle:39 reduces:2 serves:1 either:11 integrals:5 always:2 multiplicative:1 ie:2 reduced:1 specified:5 nonzero:8 provided:5 extensively:2 legal:1 decomposition:5 provides:2 measuring:1 scientific:2 power:18 kyoto:2 wavefunctions:1 notable:1 b211:1 eiφ:1 manufacturer:1 comparison:4 discussed:4 generated:7 practical:2 stand:1 kµi:2 act:1 mixed:1 inclusion:1 references:3 operator:29 log:25 assumed:2 strictly:2 there:21 start:1 low:1 labelling:4 assumes:1 complete:1 aµ:2 longer:1 ωi:4 ωj:13 ωn:2 ωa:2 ωb:5 connect:1 ab:9 ad:2 ai:2 certain:1 describe:3 am:2 direction:4 general:10 ap:2 examine:2 formulation:4 controlled:2 again:2 completeness:1 d2i:6 field:28 juin:1 regents:3 massless:3 polar:3 separate:4 symbol:3 vertex:53 representable:1 important:8 bounded:2 included:1 insertions:7 perturbatively:2 pseudo:1 mass:9 once:1 starting:1 original:14 represent:5 consider:13 caused:2 commute:5 follow:1 causes:1 tr:3 nonlocal:3 program:1 th:1 enjoying:1 amplitudes:4 straightforward:1 very:4 fall:9 iǫi:1 difference:6 newly:1 condition:11 treating:1 hamiltonian:1 large:15 small:14 study:3 abbreviated:1 neighborhood:9 direc:1 rate:1 displays:1 pass:2 further:1 residue:20 what:6 sub:2 advantageous:1 sum:20 method:2 contrast:2 outgoing:1 full:15 component:3 answers:1 behaviour:2 inverse:1 berkeley:6 directions:4 ignore:1 strong:3 generalizing:1 antisymmetric:1 allows:4 amount:1 advertising:1 action:15 uniquely:1 establish:1 conventional:1 takes:1 probabilities:2 contains:8 finally:3 nucl:1 ψi:1 taken:4 entails:3 more:5 initiated:1 operators:19 emission:2 basically:3 particular:4 known:3 producing:1 none:2 endpoint:12 science:1 equation:5 arrangements:1 specialized:1 states:9 numbers:4 arise:11 concordant:2 information:2 goal:1 rather:6 acts:3 simplicity:1 fr:2 singularities:39 reflect:1 fa:3 fb:1 coming:12 fj:3 short:1 departure:1 assign:1 generic:1 responsibility:1 fundamental:3 developed:2 trade:1 held:3 paper:8 through:3 signs:4 kibble:3 its:18 energies:2 actually:3 detected:1 strange:1 disclosed:1 travelling:1 focussed:1 good:1 framework:3 formulating:1 easily:1 document:1 2r:1 fully:1 delicate:1 radial:2 found:1 2n:2 2k:9 formulate:1 mesoscopic:2 energy:14 hard:27 idea:1 expect:1 measurement:1 quantum:71 http:3 beyond:1 travels:2 dominates:1 nuovo:1 since:2 research:4 flowed:2 denoted:2 issue:2 occurs:3 lawrence:5 difficulty:1 reason:1 imagine:1 asi:2 definition:2 bring:2 positioning:2 nonnegative:1 exhibited:2 integrand:7 number:12 least:26 passes:2 inapplicable:1 perturbation:4 introduction:3 interact:1 construct:1 assumption:3 identity:1 calculations:3 rates:2 recovered:2 shifted:5 kµ:1 relationship:1 part:52 authors:1 separability:1 kind:4 double:1 determined:1 contrary:1 treated:11 electrodynamics:27 orders:7 lie:3 generalizes:1 depending:1 lim:5 self:3 k3:2 k2:14 k1:38 stapp:7 generalized:32 analogy:2 play:1 added:1 most:6 sponsored:1 plan:1 extremely:1 appear:1 kb:1 ka:1 ke:1 kj:81 clear:2 cover:2 kn:18 physica:1 ks:6 electrons:5 exp:3 velocity:7 physics:11 lying:10 sector:2 particularly:2 admittedly:1 find:2 parameters:2 technologically:1 increasingly:1 factor:55 morchio:3 triangle:36 spurious:3 express:1 closely:1 during:2 transitional:1 sources:4 arxiv:4 wightman:2 factorization:13 switzerland:1 set:23 culture:1 see:4 individual:8 close:2 materially:1 contour:6 analog:3 smallest:2 various:8 subscript:1 conditions:5 available:5 unobserved:1 initially:2 iky:8 ikx:3 incident:11 interface:1 relying:1 both:11 last:6 reverse:1 connection:2 context:5 perturbative:5 experimental:2 arbitrarily:3 eiky:2 point:34 simple:12 others:2 corresponds:2 subgraphs:4 simply:5 bν:1 indefinite:2 ps:8 complication:2 described:8 px:14 due:4 annales:1 dropping:1 pk:13 ph:4 pi:50 lett:1 else:1 determination:1 p2:59 p3:17 replaces:1 p6:10 p4:14 p5:12 solid:1 ǫj:1 straight:2 expanded:1 empirical:1 while:1 replaced:8 evaluating:1 couplings:17 loop:12 vectors:5 century:1 herein:2 reads:1 itself:4 vanish:1 currents:1 grant:1 γµn:1 belong:1 problems:5 modification:1 resulting:3 ray:4 used:11 flows:1 domains:2 levels:1 moving:4 purpose:4 recent:2 lower:2 pµ:19 analysis:2 edge:1 machinery:3 distances:8 λp:1 abbreviation:1 atomic:2 λk:12 λj:14 λi:30 λn:8 letting:1 tables:1 cut:4 empirically:2 signals:2 source:3 k0:2 location:2 theorem:5 absorbed:1 transformation:2 format:3 couple:2 integer:1 nakanishi:1 pertinent:3 differentiations:2 λx1:1 λx2:1 λx3:1 manifest:1 separately:9 exploiting:1 experimentalists:1 essential:3 mathematical:5 pertaining:1 methods:1 creation:3 some:11 back:1 strongest:4 redefining:1 scale:3 though:4 integration:23 behave:1 connecting:1 eliminate:1 tends:2 proc:1 inserting:11 step:1 hilbert:1 superpositions:1 integers:1 anything:1 entailed:1 pθ:6 range:1 consequently:7 block:6 computational:3 into:61 within:3 integral:18 ensue:1 appropriate:2 primarily:1 proportional:3 reabsorbed:3 institut:1 classically:1 question:5 long:2 forward:2 translate:1 theory2:1 theory3:1 theory1:1 subgraph:5 gauss:2 cloud:1 properly:1 delta:1 line:71 directed:1 intuitive:2 up:1 cim:4 cir:2 verification:1 planes:1 similar:7 ki:41 constant:4 defined:27 single:15 numerators:1 formalism:2 defines:1 analyticity:1 dashed:1 application:1 points:18 department:1 draw:1 clean:1 lend:1 nonclassical:1 prepared:1 meaning:1 graphically:1 sides:4 structure:7 vs:2 required:4 equivalently:2 implied:1 far:2 requires:1 having:4 normalized:1 ambiguities:1 partial:2 results:14 illustrated:2 eds:2 go:1 contributions:42 compact:2 ac03:1 concerned:1 factoring:1 glaser:1 contours:8 excluded:1 stable:3 include:2 confirmation:1 wave:4 electron:7 zµ:1 entire:4 positions:3 notes:1 try:1 epstein:1 dealt:3 inspection:1 noted:1 disclaimer:1 velo:2 smaller:1 zk:4 imply:1 insertion:11 d7:1 dynamics:1 index:1 apparatus:1 giving:1 analogously:1 expressed:11 henceforth:1 experiment:2 poles:7 flowing:5 renders:2 led:1 degree:9 respectively:4 gathered:1 diagramatic:1 commercial:1 desired:1 separation:14 eikx:1 consideration:3 convert:1 rdr:3 larger:1 contradiction:1 products:1 makes:2 involves:2 examining:1 formulated:2 fieldtheoretic:1 integrations:9 privately:1 sgn:2 summation:4 apply:1 orderings:1 manipulate:1 standing:3 use:7 asymptotic:5 commun:4 remains:1 next:3 calculation:6 examination:2 themselves:4 rearranging:1 becomes:3 occurred:2 carrying:1 labelled:2 iii:1 account:2 integrating:1 ρi:2 electrodynamic:1 ρj:2 drops:3 proof:6 control:1 weaker:5 reserved:1 process:17 purposes:2 high:2 dominant:19 weaken:1 united:4 six:4 regions:2 located:2 instead:6 counterterms:1 singular:3 factored:2 tack:1 multiplication:1 efficiently:1 kulish:2 light:1 lines:22 correspond:3 element:1 asserts:3 discussion:1 holds:6 move:1 interpreted:2 produced:4 including:1 mentioned:2 buchholz:1 bridges:1 exclusion:1 chosen:1 li:6 papanicolaou:1 greater:1 landau:11 cutting:2 front:1 articles:2 february:1 university:6 identified:3 sufficiently:5 few:1 dωj:3 related:5 constitute:1 measure:1 separating:3 our:17 special:11 out:19 matrix:5 rev:11 behaviours:1 strocchi:2 lecture:1 ref:11 integrated:1 math:8 interactions:19 8b:3 8c:1 discontinuity:6 approaches:1 tied:3 interaction:28 could:1 keep:7 hence:13 diagrammatically:1 owned:1 intuitively:1 precisely:5 reliable:1 reference:4 ordering:4 behaves:2 system:2 relations:1 their:11 intermediate:2 travelled:1 final:5 denominators:4 shell:2 completed:1 exactly:5 diminish:1 observed:3 cimento:1 submitted:2 amplitude:5 distinguished:3 separations:1 unchanged:2 qˆ1:1 qˆ2:1 qˆ3:1 need:4 viewed:1 acceleration:1 ohlich:2 pursued:2 agency:3 decomposing:1 concerns:1 bakshi:1 accuracy:1 unless:1 axiomatic:2 connected:9 segment:13 why:2 stronger:4 graphs:15 mechanical:1 superscript:1 normally:2 fact:6 2pµ:9 supported:1 purely:1 trivial:1 q1:8 q3:9 q2:8 based:1 controls:2 should:8 bernard:1 local:3 means:8 familiar:1 simplest:2 overall:2 wiggly:1 ones:1 procedures:1 symbols:1 processes:4 differential:2 contain:3 qi:5 fixed:10 pertains:3 view:2 2p1:6 2p2:6 computed:4 finiteness:4 p21:1 usefulness:1 p22:4 quantumclassical:1 qµ:3 extend:1 nuclear:1 tend:5 state:3 difficulties:2 closed:10 neither:2 mainly:1 meromorphic:33 ends:2 attention:2 importance:1 emitted:6 p2i:17 key:4 2pi:6 2pk:36 limits:3 taking:1 equal:3 etc:1 regimes:4 otherwise:2 cj:9 ci:10 relevant:2 dependent:2 addition:2 trademark:1 alters:1 treat:4 define:4 arises:5 corresponding:23 commutes:1 sufficient:5 c3:1 present:12 subsets:1 value:6 will:26 frameworks:1 vi:4 thus:31 surface:19 positrons:3 examined:3 vx:1 cjn:1 perhaps:2 eaµ:1 divergences:6 radiation:4 cross:3 unity:3 parts:32 pauli:1 finite:10 infinity:5 upon:20 effect:6 v1:5 v2:6 v3:6 infinite:4 cµ:1 destruction:2 off:12 well:11 arising:6 usual:7 moments:1 accurate:3 obtain:7 cutkosky:1 momenta:7 macroscopic:10 supply:1 mathematically:1 reasons:3 add:1 valid:1 combine:6 maintaining:1 ought:1 identical:1 asymptotically:1 government:4 yennie:4 increases:1 press:1 immediately:1 necessary:5 like:5 excluding:1 sizes:1 alternatively:1 28d:1 qm:6 become:5 works:7 soft:40 replacement:4 because:9 qed:6 classical:57 sequence:1 discontinuities:1 recommendation:1 proper:1 star:7 proofs:1 lead:8 avoid:3 does:8 deflections:1 slight:1 σij:3 ensures:1 expansion:6 qˆ:1 imaginary:2 stage:1 about:2 carried:1 introduces:3 dependence:5 recognized:1 carries:2 evoke:2 insufficient:1 introduced:5 loops:5 create:1 warranty:1 iµj:1 previously:1 functional:1 en:1 chung:3 artifacts:2 vac:2 naturally:2 function:44 triangular:3 but:35 neutral:1 convergence:13 he:2 count:2 made:5 compute:2 whether:1 wish:1 placed:4 below:1 converted:3 limit:5 problem:12 mechanics:2 int:1 contribute:10 linearity:1 operand:1 relates:1 education:1 identities:3 functions:18 compared:1 variety:1 detail:6 virtual:3 other:22 details:1 branch:3 theor:1 conclusion:1 kinds:1 coupling:17 factors:38 rule:2 4n:1 portion:2 4k:2 4b:3 4c:1 4a:3
|
quant-ph9503003.txt |@word consider:2 proposed:1 violation:1 when:1 lack:1 dynamic:4 unacceptable:1 osi:1 course:1 argued:1 hungary:1 conservative:1 its:1 kp2:1 rmki:1 violate:1 chosen:1 seems:1 naturforsch:1 coordinates:1 should:2 supported:1 leibniz:4 quasi:4 potential:1 board:1 easy:1 mail:1 might:2 momentum:2 happened:1 applied:1 them:1 his:3 march:1 di:1 couple:1 budapest:1 obtain:2 effects:1 leads:2 evolution:1 like:1 particle:2 hamiltonian:1 qx:2 arxiv:1 yields:1 references:1 mathematical:1 square:1 another:1 classical:5 energy:1 approximation:1 differentiation:2 see:1 result:2 quantum:4 eq:1 aleksandrov:3 canonical:3 even:2 fails:1 total:2 interacting:1 nuclear:1 since:2 rev:2 research:1 favor:1 enough:1 above:1 kfki:2 invariant:1 ref:2 justification:1 backreaction:1 theory:3 nature:1 preserves:1 quite:1 reason:1 diosi:1 although:1 calculate:1 both:1 antisymmetric:5 institute:1 similar:1 36a:1 motion:2 admit:1 opinion:1 expression:1 otherwise:1 comment:1 via:1 lajos:1 traschen:2 had:1 variables:3 cf:1 system:1 qp2:2 hermitian:1 promise:1 controversies:2 directly:1 xq:3 pob:1 derivatives:1 takes:1 would:2 failed:1 initial:1 due:1 been:1 anderson:6 too:1 realization:1 notices:1 ph:2 hardly:1 consistent:1 lett:1 questionable:1 himself:1 acceptable:1 departures:1 but:1 hu:1 construction:1 maddox:1 derivative:2 translation:1 hold:1 proposal:1 p2:1 boucher:2 was:1 equation:2 work:1 maximum:1 will:2 my:1 example:1 mechanics:1 abstract:1 proper:1 conserved:1 good:1 arise:2 formalism:1 occur:1 different:1 ing:1 otka:1 author:1 generally:1 antisymmetry:1 kp:1 quant:2 instead:1 really:1 hermiticity:2 mar:1 antihermitian:1 derived:1 shown:1 algebraic:1 letter:5 variable:2 choice:1 recent:1 no:1 especially:1 consequences:1 calculated:1 grant:1 well:1 rule:4 obviously:1 bracket:6 time:4 serious:1 first:2 physics:2 bulletin:1 fact:1
|
quant-ph9503004.txt |@word consider:1 rev:3 brownian:2 leads:1 commute:1 eckern:1 remarkably:1 whose:2 γy:4 menzel:1 ρst:9 equivalence:1 tr:8 ts:4 nonlocal:1 environment:4 violation:1 pˆt:8 under:1 stochastic:7 analogous:2 include:1 tb:1 tc:1 divergent:2 attempts:1 hibbs:1 returning:1 frequencies:2 emphasizes:1 wave:1 valued:8 decide:1 difference:2 entire:2 ρs0:3 tro:2 hamiltonian:10 turns:3 trb:3 differentiating:1 solution:3 leave:1 solved:1 phase:1 math:2 trs:6 outstanding:1 consistent:1 arnimallee:1 approximation:2 zero:1 evaluated:1 further:1 canonical:5 spectral:1 turn:2 ˆs:11 ˆt:10 rate:1 sum:2 expressed:2 ˆb:3 version:1 goes:2 new:3 consisting:1 contrast:3 temperatures:3 2kt:3 exponentials:3 respectively:3 never:1 preserves:1 here:1 canonically:1 represented:2 path:21 along:1 equations:9 appears:1 box:1 algebra:2 averages:3 study:1 larger:1 reason:1 example:1 products:1 action:18 suitable:1 regardless:1 adjoining:5 possessing:1 replace:2 sliced:1 coinciding:1 nonequilibrium:1 orderings:1 total:4 planck:2 unit:1 eiωt:1 use:2 expresses:1 dωω:1 working:1 prove:3 remains:2 contains:1 tightly:1 chp:1 comparing:1 linear:1 going:2 taken:1 type:1 theoretical:1 possible:1 more:2 introducing:2 treated:1 becomes:2 operators:21 ti:1 odinger:5 berlin:4 observations:1 pˆx:1 known:1 iii:2 must:3 springer:1 ρb:4 ibm:1 fulfils:1 collision:1 recall:1 equation:61 oscillator:6 values:2 ρt:2 freedom:2 following:2 making:1 my:2 mx:2 decoupled:2 performed:1 f0:6 indicated:1 expanding:1 high:1 ready:1 ρˆb:7 allowed:1 dxd:2 yη:3 verlag:1 end:2 noises:1 rather:1 verify:1 holds:1 xˆ:3 write:1 how:2 nontrivial:1 ordinary:4 ihˆ:1 product:3 mar:1 description:4 minus:1 may:3 oscillators:6 after:1 derived:4 containing:1 dx1:1 consequence:3 plane:1 lax:1 physik:1 representations:1 data:1 ot:4 quasiclassical:1 dynamical:1 effective:5 resemble:1 counter:1 explicit:3 st:10 so:4 allow:1 correlation:8 representation:8 integrand:1 order:1 prefactor:2 imagining:1 acts:1 played:1 dx:11 produces:1 numbers:2 indeed:2 over:8 satisfied:1 course:2 thermal:4 paper:1 through:1 statistical:2 y0:1 satisfies:3 its:2 supplemented:1 derive:7 chosen:2 temporal:10 unity:1 coordinates:5 complex:1 degrees:2 dp:1 defining:1 puzzle:1 versus:1 combination:1 processes:1 slicing:1 hamilton:4 iht:6 they:2 half:1 insisting:1 now:4 yt:6 maintaining:1 easily:2 february:1 equality:2 reasonable:1 each:1 found:1 universit:2 2i:1 mean:2 differential:2 series:1 gaussian:4 toda:1 frequency:3 remove:1 quantum:46 laboratory:1 approximated:1 drude:1 eq:11 eiht:2 out:3 large:4 shown:2 matrix:18 driving:1 factors:1 res:1 furthermore:1 since:5 crucial:2 denotes:2 mazur:1 replacing:1 acting:1 dxdy:2 wick:1 ref:6 correct:2 independence:4 shows:1 performing:1 theory:1 gardiner:1 divergence:5 standard:1 pleasant:1 completely:5 york:1 institut:1 rewritten:1 definition:4 interaction:3 derivation:1 transition:1 times:1 motion:7 unitarity:5 length:1 place:1 leading:2 hence:2 onto:1 think:1 first:5 initial:6 humboldt:1 upper:1 xc:2 variables:8 timeindependent:1 number:2 xd:1 system:32 clear:1 xx:9 xy:5 directly:4 carry:1 precisely:1 xt:14 size:1 given:3 temperature:5 introduction:2 unknown:1 eqs:2 theoretische:1 relations:2 their:4 brevity:2 kleinert:2 calculations:1 iat:2 ordered:1 leggett:1 gives:1 moscow:1 yield:1 part:3 somewhat:1 lehr:1 branches:2 x0:4 x1:5 than:2 iωt:1 determines:1 accordance:1 prevent:1 distinguishes:1 see:8 annihilation:1 determined:1 were:2 powers:1 russia:1 descriptions:1 exhibit:2 rewrite:1 fluctuation:3 argument:2 generalization:1 say:1 conjugate:1 seen:1 element:3 apparently:1 any:5 issue:1 mapping:2 mechanism:1 contour:3 note:4 potential:2 analogy:2 coincide:1 heisenberg:17 subscripts:2 trace:4 shall:2 systems:1 most:2 boltzmann:1 xω:1 remarks:1 plays:1 benguria:1 takes:1 surprising:1 average:9 coincides:1 physica:2 feynman:11 accounted:2 exp:18 mechanical:4 superscript:1 physics:4 section:2 fact:2 momenta:1 absorbing:1 random:1 friction:7 xω2:1 relation:10 solutions:2 substituting:5 longer:2 find:6 schmid:3 help:1 aω:2 dissipative:1 specified:1 only:4 explicitly:3 ambiguity:2 hamiltonians:1 local:5 pointed:2 equilibrium:1 do:1 above:1 dh:1 means:1 dependent:4 between:1 expectation:2 nearly:1 aη:5 dy:1 dt:22 subscript:3 coth:1 alexander:1 evolution:20 resolve:1 arxiv:1 comprising:1 dpy:1 dpx:1 ffl:3 characteristic:1 fixed:2 valid:1 coefficient:1 set:1 exists:3 notational:1 hγ:1 hη:2 ωt:6 collectively:1 shabanov:1 sec:1 result:3 converting:1 nonlocality:3 quantizing:1 caldeira:1 satisfying:1 setting:2 commutation:11 ways:1 written:1 closed:1 simplest:1 without:1 invariant:1 boundary:5 conditions:4 terms:8 anti:2 however:1 hill:1 vernon:9 key:1 demonstrate:2 anticommutator:1 both:4 cos:1 parentheses:1 last:1 repeating:1 desired:1 many:1 taking:1 infinitely:1 equal:6 agree:2 fulfilled:1 hρ:1 xˆt:2 experimental:1 space:1 point:2 simple:1 harmonic:2 121a:1 simply:3 tˆc:1 lagrange:1 constant:4 ensures:2 ket:1 described:5 commutative:2 second:1 would:1 px:9 py:11 due:5 been:5 defined:6 describes:4 treat:1 ph:1 define:2 obtained:4 arises:1 corresponding:3 ordering:5 observe:2 general:1 fokker:2 case:1 look:1 exponential:2 value:3 will:1 while:3 fub:1 behavior:5 shift:1 property:2 procedure:2 polymer:1 unitary:1 coupled:2 phenomenological:1 von:1 thus:5 iv:1 ii:2 canceled:1 reads:1 itself:2 pileup:1 ia:1 different:3 develop:1 perform:1 make:2 same:3 freie:2 parts:2 quant:1 arguments:2 modification:1 proved:1 finite:4 development:1 independent:2 used:3 zwanzig:1 singapore:1 trivially:1 upon:3 hand:3 kubo:14 purpose:1 potentials:1 infinite:1 identity:1 eigenvectors:1 break:1 lower:2 schr:5 edition:1 well:2 obviously:1 academic:1 contact:1 solve:1 consistency:2 coordinate:1 position:1 arising:2 usual:2 just:2 being:1 obtain:6 effects:1 positions:1 alternative:1 preprint:1 density:15 regarded:1 conclude:2 guaranteed:2 interested:1 lett:1 theorem:1 guarantees:1 momentum:1 identical:2 fluctuating:5 rules:2 replaced:1 iγ:2 term:14 corresponds:2 using:1 formal:1 appearing:1 like:5 particle:2 identifying:1 follows:2 reduces:1 velocities:2 specific:1 integrals:7 arbitrary:4 become:1 reduced:1 iˆt:2 kac:3 right:2 neumann:3 classical:14 what:1 successfully:1 some:1 calculated:2 respect:3 proper:1 resolutions:1 happens:1 pronounced:1 slice:1 avoid:1 footing:1 langevin:22 integration:2 linearly:1 assuming:2 three:1 inserting:1 noise:44 scientific:1 power:1 equivalent:5 agreement:1 expansion:2 step:1 although:1 2m:1 properties:2 noisy:8 pt:1 world:1 mcgraw:1 tracing:1 discussed:1 dependence:1 o:45 side:1 cancelation:1 involving:1 obeys:3 ρˆt:7 introduced:1 ρˆs:1 cutoff:1 presence:2 into:10 within:1 integral:22 functional:14 encircling:1 bath:21 down:1 dissipation:7 ηt:23 determine:1 operator:43 ηy:1 statistics:1 hep:1 ωd:1 assumed:1 there:7 much:1 low:2 way:3 jinr:1 forward:10 was:2 u0s:1 iˆ:1 function:7 hx:1 creation:1 annals:1 form:3 ht:5 ford:2 heat:5 ho:2 removed:1 true:1 observation:1 absent:1 temp:1 whether:1 ut:3 up:1 us:3 ur:1 liouville:5 limit:3 fluctuations:2 distribution:1 similar:2 called:3 mechanics:5 ab:3 associated:5 ad:27 ai:4 contribute:1 influence:8 fellow:1 tˆ:4 pˆ:10 rule:3 formulation:1 dη:1 proceeds:1 physical:2 again:2 functions:4 no:4 whereas:3 when:3 other:4 role:2 picture:1 stat:4 elements:3 denote:3 generates:1 symbol:1 kt:11 helpful:1 deriving:1 commutator:1 important:1 variable:9 sides:1 implies:1 coupling:2 dω:6 interval:1 governed:1 having:1 equivalently:2 time:32 backward:8 requires:1 original:1 once:1
|
quant-ph9503005.txt |@word represent:5 reversibility:1 four:4 roy:3 computation:8 fig1:3 factorizing:2 whose:4 simon:1 languages:1 answered:1 finally:2 bakker:1 include:1 economical:1 very:1 matrices:2 ibm:1 school:1 bypasses:1 solution:1 fewer:3 prototypes:1 large:2 minimal:1 optics:1 deutsch:4 direct:1 likely:1 enhancement:1 qualitatively:1 iσ1:3 what:1 above:1 new:4 method:1 contrast:1 pioneering:1 edited:1 margolus:1 respectively:3 teleportation:1 here:2 reported:1 them:1 represented:1 appears:1 interpret:1 box:3 great:1 institute:1 study:1 changed:1 contradiction:1 schumacher:2 action:1 suitable:2 changes:2 cancellation:1 extra:2 logical:4 replace:1 addressed:1 total:1 alamitos:4 would:3 toffoli:4 tabulated:1 classically:1 automata:1 call:1 simpler:1 more:2 composite:1 becomes:1 operators:7 apparent:1 carrying:1 particular:2 known:3 foundations:1 producing:1 states:1 springer:1 room:1 science:3 equation:2 work:5 dev:1 labeled:3 obvious:2 following:3 making:1 example:3 control:4 figure:3 process:1 bennett:3 involve:2 numbers:3 want:1 sense:1 awkward:1 verify:1 six:7 feature:2 machine:2 how:2 gate:38 sin:2 inputs:1 may:1 after:3 realized:2 physical:1 third:2 eats:1 inquire:1 complexity:1 cannot:2 so:1 fundamental:1 representation:1 order:2 operations:2 indeed:1 fredkin:17 satisfied:1 course:1 through:3 mentioned:1 ieee:4 its:4 superior:1 group:1 interesting:1 systems:1 might:1 theo:2 non:1 motivated:1 combination:4 ekert:1 introduce:2 they:2 symposium:4 rotation:1 now:3 realize:1 february:1 2b:1 found:2 entirely:1 series:1 idea:2 society:4 quantum:31 our:6 operation:2 eq:3 out:4 divincenzo:5 shown:2 matrix:3 res:1 since:3 rev:7 replacing:1 performs:2 ref:2 correct:1 foundation:2 theory:2 barrier:1 interactions:1 vazirani:1 complicated:1 york:2 dynamics:1 ask:1 org:3 earliest:1 jozsa:2 milburn:2 could:1 computers:2 programming:1 int:2 first:4 diagrammatically:1 coding:1 lond:3 done:4 another:2 impossible:1 wilczek:2 similarly:1 system:2 construct:4 realization:3 bits:4 recovered:1 gives:2 shifter:4 authors:1 natural:1 believe:1 than:3 png:6 unfortunately:1 princeton:1 wiesner:1 require:1 second:1 annihilation:1 classes:1 doubly:4 toward:1 dash:2 manner:1 seem:1 weinfurter:1 clearly:2 constructions:2 built:1 efficient:1 convenient:1 consequentially:1 note:1 sciences:1 potential:1 generalized:1 algorithms:1 accuracy:1 investigations:1 denoting:1 price:1 who:1 most:2 involving:1 adder:2 significant:1 phase:8 probabilistic:1 class:1 constructed:3 gather:1 typeset:1 feynman:3 proceedings:5 iassns:1 mechanical:1 physics:1 laws:1 shor:2 show:1 supported:1 discovered:1 solutions:2 find:1 o:1 popescu:1 implementation:2 commutators:1 explain:1 behind:1 completes:1 only:4 explicitly:2 bernstein:1 do:4 explorations:1 his:1 de:2 overall:1 ones:1 acm:2 arxiv:4 remove:1 summary:1 34th:1 mapped:1 body:19 set:1 modulo:1 unpublished:1 see:8 computer:10 result:1 unaltered:1 preparation:1 mechanically:1 state:4 various:1 closed:1 between:3 available:3 recently:1 importance:1 however:1 residual:1 sleator:1 both:3 σi:1 last:1 reverse:1 taking:1 annual:4 relabel:1 figures:1 logic:7 inspired:1 passing:2 ci:3 relevant:1 co:3 simple:2 had:1 ca:4 leeuwen:1 corresponds:2 maintained:1 polynomial:2 table:4 ps:3 basis:3 addition:2 three:12 been:3 defined:1 yao:1 much:1 combined:3 basic:1 ph:6 abstract:1 fig:15 obtained:1 determinant:1 controlled:6 sufficient:1 cos:2 demand:1 denote:2 spin:2 case:1 pacs:1 leave:1 rectangular:3 will:3 while:2 35th:2 leaves:1 seven:1 unitary:6 thus:2 site:1 different:1 perhaps:1 grant:1 perform:1 acknowledgments:1 make:1 same:1 any:3 quant:6 pauli:1 finite:1 composition:1 used:3 http:3 trivially:1 numerical:1 upon:1 i6:3 running:1 arrived:1 delicate:1 identity:1 relies:1 makes:1 well:1 simulated:1 olden:1 drawing:2 gates:14 proposed:1 less:1 true:1 proposes:1 advertised:1 alternative:1 previous:1 tables:1 preprint:3 generator:2 seems:1 capabilities:1 improvement:1 passive:1 lett:5 easy:1 input:5 extensive:1 transformation:3 around:1 format:3 possible:6 know:1 using:16 bit:15 accepted:1 advanced:1 mod:2 like:2 qualitative:1 performing:3 specific:1 output:5 works:1 classical:6 sequence:1 creation:1 some:1 choosing:1 provided:1 eiθ:1 does:1 provides:2 proc:3 demonstrated:1 core:1 truth:2 power:1 bc:1 problems:2 bo:2 bi:3 revtex:1 references:1 bz:1 stage:1 actual:1 extension:1 recognized:1 simulation:1 act:1 block:1 soc:3 computational:3 garbage:1 down:1 nothing:1 accounts:1 operator:4 coppersmith:1 hep:1 log:1 there:1 question:2 approximate:1 los:4 workshop:1 way:2 was:2 naturally:1 conditional:9 elsewhere:1 smolin:2 jun:1 but:1 change:1 construction:13 90er40542:1 line:2 fg02:1 irreversible:2 proposal:1 partially:1 25th:1 whether:1 characteristic:1 uv:1 up:5 us:3 record:1 problem:1 similar:2 called:1 mechanics:2 sometimes:1 computing:1 ai:4 universal:8 ao:3 evidence:1 substantially:1 chau:2 doe:1 defines:1 again:1 nj:1 no:1 fixing:1 whereas:1 wavefunction:1 when:5 application:1 other:4 details:1 outputs:1 nice:1 elements:1 reversible:7 convincing:1 meaning:1 important:1 variable:1 sides:1 building:1 lane:1 regime:1 algorithm:1 write:1 time:1
|
quant-ph9503006.txt |@word consider:7 remarkable:1 crucial:1 magnetic:27 results:3 leads:5 scalar:3 bergmann:1 consists:2 gn:10 localized:3 peshkin:1 bremsstrahlung:2 clarification:1 nonlocal:1 those:1 excluded:2 ρdρ:4 presentation:1 case:28 string:4 straightforward:1 orthogonal:2 implicitly:1 choice:1 electron:1 stays:1 exact:1 fakult:1 condition:8 hamiltonian:1 bn:5 cause:1 michael:1 solution:4 solved:1 leninsky:1 quick:2 relation:2 der:1 configurations:1 work:1 force:1 pragmatic:6 dealing:1 prediction:1 go:1 konstanz:6 enhancement:2 follow:1 further:1 selfadjointness:1 even:1 aim:2 what:1 developed:1 appear:1 section:3 uniform:1 above:2 fractional:2 values:9 method:5 satisfy:2 full:1 lee:1 pm3:1 respectively:1 realizations:1 component:4 here:7 cylindrical:1 ansatz:1 represented:1 along:1 standard:3 equations:9 appears:1 calculate:1 obtained:3 institute:2 involved:1 study:1 studied:2 allows:4 approaches:1 orthogonalization:2 p2:4 resulting:2 usually:1 hospitality:1 fourier:1 changes:1 mutual:1 orthonormality:1 projection:2 explained:1 modifying:1 sgi:1 liml:1 apply:1 use:1 takes:2 remains:1 positive:2 eφ:1 eρ:1 negative:3 next:1 ψj:5 nucl:1 approach:7 msk:1 therefore:10 relativistic:1 aϕ:1 type:3 theoretical:3 reflects:2 more:4 becomes:4 operators:3 odinger:16 berlin:1 particular:4 known:2 trait:1 must:3 obeying:1 springer:1 vladimir:1 equation:16 fµν:1 modified:4 remain:1 obvious:2 thin:4 following:3 fulfill:2 ulf:2 example:6 asymptotic:1 dxi:2 give:2 anomalous:1 organized:1 states:4 numbers:6 want:2 arise:2 axis:2 information:1 respective:3 s3:1 interacts:1 discussion:2 olariu:1 carries:3 located:1 nontrivial:7 pure:17 shortens:1 verlag:1 parameter:7 sin:2 pρ0:9 product:1 mar:1 description:1 singular:1 replacing:1 after:1 derived:2 containing:2 applications:1 demonstrating:1 wave:6 parallel:1 realized:1 spectra:1 correspond:1 su:1 rather:1 complexity:1 so:4 sm:3 sl:6 representation:1 juergen:1 order:6 exotic:2 interpretation:1 produces:1 ep2:1 over:1 course:1 paper:3 differs:1 satisfies:1 still:3 its:5 before:2 group:1 xl:1 fiz:2 fix:3 inclusion:2 coordinates:1 fruitful:2 attraction:1 choose:3 mail:3 them:1 return:1 thereby:1 integral:3 popescu:1 practice:1 evolution:1 landau:1 mention:1 hamilton:8 effects:3 they:3 now:4 discuss:4 easily:1 term:2 dirac:14 always:1 university:1 orthonormal:1 academic:2 l2:1 mode:1 reasonable:1 radial:19 accompanied:1 universit:2 spinor:3 domain:4 adjointness:6 series:3 energy:3 ea:2 related:3 manifests:1 tsov:1 sketched:1 quantum:14 our:4 happen:1 rl1:1 out:2 shown:2 precisely:1 factors:2 rep:1 interference:2 particles:9 may:5 contained:1 vector:1 rl:30 formula:2 rn:2 issue:1 occurs:2 shows:3 inevitably:1 theory:4 found:1 quite:1 reason:1 complicated:1 york:1 members:1 put:2 definition:1 interaction:10 nonnegative:1 int:1 consequence:1 first:3 origin:1 already:1 physik:1 probability:1 variables:1 number:2 peculiarity:1 approximately:1 directly:1 fluxes:1 open:6 angular:4 aharonov:9 illustrate:1 given:3 exists:1 needed:1 introduction:1 adjoint:25 least:1 their:2 too:1 calculations:1 scheme:1 gives:1 ryzhik:1 moscow:1 eliminates:1 direct:2 part:6 than:1 coefficients:3 require:1 second:1 limiting:2 matter:1 express:1 determined:2 were:1 treated:1 russia:1 decompose:1 result:1 prospect:1 function:3 hagen:3 unchanged:1 modern:1 deutsche:1 manner:1 need:1 seen:1 cumbersome:2 saw:1 orders:4 indeed:2 zero:3 depending:3 lim:2 self:29 responsible:1 polarization:1 gφ:6 potential:13 take:1 interior:1 correlating:1 explanation:1 transparent:1 cl:1 unless:1 electric:1 index:1 collaboration:1 denominator:1 most:1 regular:4 germany:1 gradshteyn:1 phase:1 why:3 don:1 observation:1 considered:1 clear:1 irregularity:1 yang:1 electrons:1 exp:1 subsequent:1 charged:6 physics:2 lying:1 lebedev:2 show:2 lewis:1 supported:1 scattered:1 attempts:1 gauge:1 solutions:16 find:7 rev:7 based:3 knowledge:1 parameters:16 situations:5 explain:2 appended:1 state:2 completes:1 only:4 going:1 postfach:1 specify:1 factor:3 integrable:4 adequate:1 local:1 do:2 his:1 goes:1 de:3 cannot:4 new:3 combinations:1 dr:1 processes:2 fields:2 arxiv:1 fixes:1 remove:1 acknowledgments:1 investigate:1 contain:1 fixed:1 ignored:1 set:2 reference:1 physically:1 j1:1 lett:2 opposite:1 see:5 radius:5 bordag:3 p23:3 discussions:2 phases:1 µz:1 distinctive:1 away:1 definite:1 diverge:1 symmetric:1 outside:2 µh:6 between:1 invariant:1 boundary:3 conditions:9 solenoid:10 emitted:1 terms:4 reproduced:1 extend:1 modify:1 attention:1 however:1 jl:2 vanishing:6 analyzed:1 problem:15 thank:1 both:2 essentially:3 irregular:13 newly:1 many:2 space:1 called:1 approximative:1 uni:2 eaϕ:2 finds:3 experimental:1 point:2 simple:3 coincidence:1 ii:1 table:1 indefinite:1 pp:4 described:4 solenoids:1 addition:1 due:2 been:2 defined:1 much:1 combined:1 yad:1 ph:3 attractive:1 arises:3 corresponding:2 tonomura:1 cos:1 forschungsgemeinschaft:1 gal:1 external:1 spin:4 present:6 applied:2 intriguing:1 pacs:1 solid:1 straight:1 appearance:3 value:2 will:6 near:2 behavior:2 applies:1 situation:7 procedure:10 identical:1 cylinder:1 unitary:1 sousa:1 vol:1 thus:6 non:1 surface:1 couples:1 canceled:1 reads:3 properties:1 reports:1 exterior:1 turns:1 vanish:1 ie:1 regression:1 fulfilled:1 different:15 combination:2 circumventing:1 make:3 radiation:1 cross:1 same:11 any:1 beside:1 parts:4 quant:2 pauli:1 units:1 products:1 dimensionless:1 constructed:2 status:2 independent:1 used:1 effect:8 hand:1 domains:1 moment:9 purpose:2 normalization:3 electromagnetism:1 mρ0:4 schr:16 modes:2 framework:1 whole:2 well:3 analysis:2 bohm:9 patterns:1 without:1 components:2 model:6 possesses:1 usual:1 just:1 accurate:1 underlying:1 thanks:1 using:3 alternative:1 scattering:3 eigenstates:3 note:1 preprint:2 infinitely:4 ramakrishnan:1 nonrelativistic:1 mathematically:3 wu:1 treatment:1 easy:1 relevance:1 momentum:4 gave:1 real:2 spinless:1 depends:4 read:1 possible:4 increases:1 helicity:1 press:2 integer:1 mod:3 particle:12 follows:1 collective:1 audretsch:4 specific:3 flux:6 integrals:2 arbitrary:6 stationary:1 reduces:1 mathematical:4 because:7 methods:1 oriented:1 phenomena:2 back:2 pρ:18 matching:1 nonzero:2 lead:5 electromagnetic:2 shall:1 integration:1 critical:2 exposition:1 provides:1 assuming:1 bessel:8 refer:1 inserting:1 bl:10 equivalent:2 each:2 shifting:1 although:1 2m:6 hilbert:1 bz:2 simpler:1 comparison:1 about:1 urgen:1 extension:23 extending:1 discussed:2 dependence:1 recognized:1 practical:1 range:2 extensions:1 obeys:1 connected:1 contains:6 presence:1 jδ:2 into:1 splitting:1 bound:2 cylindrically:1 square:4 references:1 jasper:3 sov:2 operator:10 spinors:2 additional:5 support:1 there:4 ehz:1 long:2 class:1 accordingly:1 describes:1 way:4 was:6 sφ:4 hz:1 complete:1 form:3 enough:1 but:9 reed:1 hl:12 removed:1 made:1 evident:1 characteristic:2 inside:2 us:2 ur:1 below:1 limit:9 distribution:2 similar:1 calculated:1 detailed:2 ab:27 ai:2 abstract:1 contribute:1 influence:3 general:3 separating:1 exist:1 deed:1 physical:18 again:3 functions:10 eq:1 wavefunction:2 when:1 detail:3 field:12 other:1 role:2 details:1 papers:1 rl2:1 conclusion:1 electrodynamical:1 draw:1 lpi:1 separate:2 describe:2 meaning:3 important:1 allowing:1 simon:1 suffers:2 interval:1 fact:5 time:2 original:6
|
quant-ph9503007.txt |@word logarithms:1 chinese:1 caused:1 alternatives:1 results:4 entropy:3 computation:7 fig1:2 follow:1 increase:1 certainly:1 depend:1 calculate:2 alamos:2 editors:3 factoring:9 anglin:1 environment:20 uniqueness:1 edward:1 th:1 stable:1 suffered:1 dramatically:1 presently:1 advantage:1 md:1 very:2 focus:1 every:1 difference:1 matrices:1 paz:2 obvious:1 hamiltonian:1 turns:1 notes:1 solution:1 damped:1 large:3 discrete:2 phase:1 small:2 upper:1 smaller:1 periodicity:1 regained:1 fragility:1 discover:1 approximation:2 second:3 design:1 gaithersburg:1 further:1 machines:1 even:2 index:2 what:4 xor:1 ˆx:1 sum:1 expressed:1 experiment:3 goes:1 fractional:2 new:2 net:1 method:1 contrast:3 satisfy:1 simultaneously:1 lee:1 loose:1 here:4 met:1 asymmetry:1 relaxation:3 represented:1 ratio:1 sieve:1 implicit:1 digits:2 great:1 study:2 allows:1 trial:2 amount:4 resulting:1 hamming:1 implement:1 fourier:4 involves:1 york:1 useful:5 smax:3 plenum:1 decrease:1 org:2 total:1 establish:1 linearly:1 use:1 takes:2 usa:3 probabilities:2 positive:1 until:1 chooses:1 next:1 leaks:1 program:1 therefore:6 memory:1 taken:2 simpler:1 patashnik:1 theoretical:2 today:1 more:1 separated:1 becomes:4 visibility:1 clue:2 opposing:1 particular:3 known:3 foundations:1 must:1 evolves:3 springer:1 ed:1 science:3 oscillator:2 remain:1 values:1 temperatures:2 ms:1 tracing:1 believed:1 example:2 proof:1 ions:1 august:1 figure:6 give:3 process:2 states:5 indicates:1 slit:1 purity:1 verlag:1 information:4 verify:1 algorithms:1 how:1 pure:2 significance:1 answer:3 instead:1 parameter:2 ensemble:1 succinct:1 inputs:2 mar:1 building:1 huge:1 may:6 oscillators:3 factored:1 applications:1 wrong:2 lenstra:4 destructive:1 efficiently:1 elusive:1 third:1 computations:1 register:1 τdec:3 so:2 allow:3 keeps:1 representation:1 order:3 nearly:2 operations:2 exclusive:1 ρred:1 help:1 numbers:3 over:2 murray:1 interpreted:1 course:1 thermal:1 through:1 statistical:1 differs:1 cold:1 still:2 pointer:5 its:5 perfect:3 thank:1 la:1 ln:2 coordinates:1 better:1 degrees:1 choose:1 decreased:1 correspondence:1 them:2 crucial:1 greater:1 conversations:1 practice:2 investigated:1 effects:2 they:2 optimal:1 nov:1 now:2 nop:3 realize:2 bank:1 february:1 always:2 university:1 factorizable:1 fringes:2 l2:3 reasonable:2 l1:3 found:1 2n:1 there:2 energy:2 hard:2 idea:1 interferometer:1 frequency:2 measurement:5 quantum:55 laboratory:2 operation:6 eq:5 monitors:1 out:3 divincenzo:1 shown:3 accomplish:1 matrix:3 factors:8 restricted:1 interference:6 b288:1 hill:1 lecture:1 induced:1 issue:1 correct:2 shows:1 linear:1 enforcing:1 diagonal:4 possibility:1 labs:1 difficulty:2 completely:2 term:1 put:1 hep:1 estimate:1 remainder:1 inevitable:1 card:1 enormous:1 interaction:3 could:1 computers:13 messages:1 david:1 threat:1 assumed:1 hence:1 first:5 xk:3 already:1 probability:11 xa:5 powerful:1 number:18 executions:2 computing:1 another:1 xr:1 message:1 given:8 temperature:3 likely:1 needed:1 introduction:1 unknown:1 system:8 unruh:1 their:2 statement:1 realization:1 siam:1 perfectly:1 bits:2 sensitivity:1 gives:5 imperfect:2 inefficient:1 mostly:1 trapped:1 wavelength:1 continuous:2 part:1 predictable:1 than:5 png:4 distance:2 fuelled:1 isolation:3 rate:1 submitted:1 final:1 inversely:1 determined:1 amplitude:2 providing:1 comput:1 remained:1 correction:1 modern:2 argument:1 substantial:1 acknowledgment:1 seen:1 any:3 relatively:1 mountain:1 ρout:2 realm:1 zero:4 academic:1 efficient:1 studying:1 isolated:2 mechanism:1 note:1 high:2 causing:1 build:1 finding:1 performance:1 mit:1 accuracy:1 spectral:1 broglie:1 fundamental:1 ieee:1 viscosity:1 systems:2 most:1 beta:1 decohered:2 device:1 hu:1 class:2 sf:2 principle:2 exp:6 mechanical:1 typical:1 physics:2 calculates:1 fact:1 saying:1 emerging:1 show:1 chances:1 encrypted:1 random:2 attempts:1 chuang:1 lloyd:1 trivial:2 find:4 feng:1 based:2 spite:1 ment:1 written:1 operational:1 only:3 factor:8 employed:1 hamiltonians:1 above:1 cryptography:1 get:5 zurek:4 de:1 preferred:1 cannot:3 fastest:1 report:1 prime:5 runs:1 arxiv:3 attitude:1 factorization:3 investigate:1 common:2 qn:2 coefficient:2 modulo:1 national:1 depends:1 computer:29 result:5 terms:1 uncorrelated:1 best:1 subject:1 mechanically:2 interacting:2 macroscopic:1 label:4 state:25 difficulties:1 τrel:3 between:11 available:2 publishers:1 recently:2 ability:1 initially:1 screen:1 however:4 interfere:1 δaa:2 problem:3 undermine:1 suggested:1 both:1 kluwer:1 many:1 taking:1 pauli:1 equal:1 σz:1 involve:1 expression:1 finds:1 unitarily:1 cn:1 timescale:1 bell:1 appeared:1 ca:1 leeuwen:1 corresponds:1 scully:1 polynomial:3 superselection:1 suppressing:1 broadening:1 ensures:1 basis:4 arbitrary:1 been:4 secret:1 much:5 ph:3 universal:1 fig:5 obtained:1 corresponding:2 frontiers:1 coherence:7 uncommon:1 coherent:5 determination:1 external:1 irrelevant:1 case:3 ǫa:3 exponential:3 value:1 will:9 while:1 behavior:2 error:1 aid:1 35th:1 leaves:1 landauer:1 annual:1 almost:1 thus:10 non:2 good:1 elsevier:1 ave:1 different:1 anymore:1 make:1 format:2 answers:3 adverse:1 quant:3 arguments:1 widely:1 largest:1 knuth:1 difficult:2 development:1 fairly:1 calculation:1 used:1 http:2 peaks:5 see:4 paths:1 effect:9 uses:3 unpublished:2 task:1 off:2 modes:1 largely:1 zoller:1 well:2 concrete:1 exceedingly:1 without:1 solve:1 model:2 paradigm:1 gates:1 λq:1 proposed:1 less:1 being:1 obtain:1 identify:1 world:1 yamamoto:1 speed:2 drexel:1 cut:1 preprint:1 integer:2 density:3 nonequilibrium:1 simple:3 valid:1 transformed:1 maintaining:1 easy:3 theorem:2 input:2 euler:1 take:3 rev:3 skeptical:1 digital:1 possible:4 harmonic:1 know:1 press:2 using:6 bit:2 execution:1 mod:6 loss:3 necessary:1 like:1 lost:4 follows:1 qualitative:1 lose:1 nonintegrability:1 become:1 security:1 essential:2 shor:3 because:4 often:2 classical:13 sequence:1 some:3 deduce:1 reasons:1 happens:1 provided:1 scale:1 per:3 critical:1 λdb:2 provides:1 pattern:1 proc:2 demonstrated:1 measuring:1 destroys:1 run:1 ps:2 equivalent:1 each:2 agreement:1 constructive:1 wesley:1 step:4 although:2 superpositions:2 about:1 would:4 freedom:1 fringe:1 discussed:1 o:7 reduced:1 practical:2 distinct:1 consequently:1 functions:4 cutoff:1 own:1 significant:1 communication:2 into:3 obtaining:2 bound:1 bath:2 remarks:1 right:2 references:1 determine:1 proportional:1 your:1 van:1 log:7 few:2 transfer:3 suffice:1 initial:1 transform:3 long:1 los:2 workshop:1 handbook:1 low:1 way:2 crucially:1 astrophysics:1 was:1 assumes:1 function:4 designs:2 certificate:1 complete:3 form:3 but:5 sophisticated:1 volume:1 failure:1 hn:2 delta:1 encoded:1 line:1 nutshell:1 partially:1 count:1 inevitability:1 stanford:2 whether:1 characteristic:1 smooth:1 up:2 us:1 ur:1 limit:1 verification:2 distribution:6 called:2 cirac:1 constant:4 moore:1 addison:1 defined:1 abstract:1 measure:2 reliability:1 our:5 graham:1 approximated:1 physical:1 again:1 nj:1 codes:1 dotted:1 no:4 trials:4 wavefunction:1 when:6 field:1 other:1 outputs:1 np:2 mathematics:2 pratt:1 arithmetic:1 symposium:2 superposition:6 problems:1 chance:1 important:2 peak:1 ubc:1 source:1 cryptographic:1 correlated:3 implies:1 coupling:1 algorithm:16 assume:1 required:3 mass:1 time:8 far:1 understand:1 decoherence:24 once:5
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.