text
stringlengths 0
190k
|
|---|
quant-ph9506037.txt |@word is0:2 partial:2 sch:6 ljl:1 magnetic:1 results:6 leads:8 eε:1 concept:2 llm:1 parameterization:1 whose:1 lkl:1 lkm:1 const:1 calculate:2 tx:1 tu:1 tr:2 finally:5 program:1 those:1 under:6 iνj:1 rise:2 translations:1 wave:3 ovsiannikov:1 every:2 nµ1:5 matrices:1 ιj:2 condition:8 four:2 iν2:2 17th:1 hamiltonian:1 turns:2 t2:2 solution:19 damped:1 leave:1 vector:9 math:4 small:1 relation:2 linearizing:5 yf1:1 grateful:1 2k2:1 consistent:7 eλs:2 direct:2 sign:1 φrs:2 φrr:1 zero:1 further:1 dynamics:1 theory:3 subscripts:1 established:1 nonlinear:33 appear:5 invertible:1 euclidean:1 giving:2 d2:1 section:14 current:1 aperiodic:2 above:1 new:6 change:1 boost:1 acknowledgments:1 clausthal:8 full:2 led:3 degree:1 copernicus:1 respectively:1 mizrahi:1 here:6 lu:1 inverse:2 ansatz:1 groups:4 depend:1 equations:42 annales:1 galilei:2 obtained:6 remark:2 antisymmetric:1 rigorously:1 institute:1 leaves:3 reason:1 reports:1 resulting:1 action:5 hospitality:1 foundations:1 zhdanov:2 equivalence:2 useful:1 classification:6 requiring:1 explained:1 plenum:1 private:1 replace:1 texts:1 rσ:1 apply:1 planck:1 σss:2 derivatives:4 baumann:1 would:1 lemma:1 covariant:1 positive:1 next:4 approach:1 kinematics:1 therefore:2 m2:1 taken:1 associated:1 type:7 theoretical:3 definition:1 becomes:1 odinger:13 malomed:1 particular:4 known:2 projective:4 cases:8 derivation:1 springer:1 valued:3 mc:1 integrating:1 deformed:2 equation:55 oscillator:1 modified:2 labeled:1 values:2 galilean:1 following:4 root:1 initial:2 f1:6 f2:6 indicated:1 give:1 calculation:1 december:1 weinberg:3 states:4 µj:2 νj:1 information:1 s3:1 s2:2 aff:11 acts:1 nontrivial:3 pure:1 champaign:1 simplifies:1 instead:1 ordinary:2 verlag:1 parameter:15 sin:6 classify:1 wolfram:1 map:1 product:1 description:1 algebra:32 schro:14 derived:2 φr:5 produce:1 waves:1 multiplication:2 representations:4 fj:1 choice:3 heidelberg:1 types:2 eight:1 natural:1 dynamical:2 third:1 correspond:1 st:3 like:1 so:8 allow:1 sl:4 representation:7 βk:2 diplomarbeit:1 order:5 se:6 restriction:2 s0:8 interpretation:1 produces:1 developed:1 interpreted:1 stability:1 paper:3 including:2 differs:1 still:1 its:7 linearizability:1 group:22 symmetry:46 ln:11 exact:2 fix:1 affine:3 toru:3 φc:1 choose:1 mail:1 τt:10 might:1 maximal:12 non:5 bo:1 salamanca:1 irreversible:4 fig:2 yf:9 scaling:1 hamilton:2 they:3 symposium:5 sσ:1 multidimensional:1 now:2 discuss:1 ushveridze:2 2t:2 articles:1 finite:13 2r:1 invariants:3 university:2 classified:1 arrows:1 appropriate:1 establishing:1 academic:2 l2:3 2c:1 found:4 universit:1 2h:1 2i:1 characterized:2 scherer:3 homogeneous:2 arxiv:1 ei:1 series:1 related:1 constitute:1 investigated:1 combining:1 quantum:16 our:3 nonlinearities:1 special:4 out:2 rt:3 simplify:1 sabatier:3 matrix:2 space:6 restricted:4 integrates:1 since:5 rev:1 research:1 particles:1 contained:3 postpone:1 integrated:1 rj:5 shows:1 linear:13 candidate:1 fisica:1 free:8 mapping:1 completely:1 york:1 consequences:1 asi:4 monographs:1 generate:1 r4:1 r5:2 pairs:1 r0:7 r1:1 r2:2 r3:2 determining:10 impose:2 excluding:1 quantummechanical:1 technische:1 plane:1 exponentially:1 hence:2 castle:1 βj:1 first:7 xj:11 xk:2 already:4 einer:1 probability:4 variables:4 φd:2 number:3 rank:1 dinger:14 restrict:2 fits:1 least:1 another:4 xu:1 given:1 zψ:3 kluwer:1 indicate:1 introduction:1 zφ:4 system:4 relations:3 their:8 constants:1 calculations:5 realization:1 scheme:1 ehrenfest:1 exactly:1 part:3 because:1 x2:3 july:1 representing:1 separability:1 coefficients:5 diffusion:3 kind:1 l47:1 subalgebras:2 was:2 second:3 limiting:1 winternitz:2 determined:1 were:2 treated:2 symmetries:16 generality:2 rewrite:1 hagen:1 ann:1 l53:1 eigenschaften:1 seen:1 admitting:1 viewed:2 lie:49 depending:1 εt:5 latter:1 note:4 k2:1 k1:4 without:2 square:1 generalized:2 analogy:2 k4:1 finding:1 εf:1 σrr:2 σrs:2 begin:1 continuous:1 serov:1 though:1 who:1 systems:5 most:1 germany:1 phase:3 represen:1 class:3 cke:1 volume:1 picture:1 observation:1 tpa:4 dordrecht:1 kj:1 calculated:1 dimension:1 proceedings:6 φss:4 exp:9 mechanical:1 thank:1 te:1 physics:7 sum:1 fact:2 show:1 german:1 functionals:2 purely:1 helv:1 gauge:20 solutions:14 yf2:1 trivial:3 find:2 struktur:1 parameters:12 semigroups:1 commutators:1 explain:1 written:1 analytic:1 only:10 explicitly:1 generators:15 summarizing:2 ambiguity:1 factor:1 local:5 abelian:2 notation:1 get:5 dependent:2 dg:16 de:2 subfamilies:6 ones:4 international:3 dt:2 gen:1 evolution:11 densities:1 fields:6 differential:8 expansions:1 yield:1 investigate:1 dodonov:1 qf:2 fixed:2 coefficient:2 requirement:1 set:9 tation:1 exists:1 δjk:1 testing:1 δjm:1 δjl:3 up:2 observed:1 mentioned:2 see:1 computer:1 arg:16 discussions:1 inequivalent:1 commutation:2 doebner:16 review:1 representatives:1 symmetric:1 state:2 future:1 various:5 irn:16 between:3 invariant:13 αj:3 conditions:6 available:1 publishers:1 terms:2 august:3 do:1 however:3 vanishing:3 comm:1 modulational:1 distinguish:3 configuration:2 topology:1 both:2 cos:1 last:1 goldin:16 always:1 ir1:1 stenflo:1 conclusions:1 laplace:1 fulfilled:3 hψ:2 und:1 σs:5 σr:8 pde:1 whole:3 σt:1 unitarily:1 among:2 diffeomorphisms:1 niederer:1 corresponds:1 dimensional:29 polynomial:4 diff:1 pr:2 described:1 transformations:24 pt:1 basis:1 addition:2 outstanding:1 due:4 been:6 int:2 workshop:1 pg:1 basic:1 pj:9 pk:1 ph:1 algebras:6 pl:1 pm:1 nattermann:7 corresponding:5 commutes:1 arcsin:1 am:1 sufficient:1 m1l:1 coherent:1 2im:1 systematic:1 derivative:1 fokker:1 manifolds:2 case:15 exponential:8 remaining:3 will:8 technical:1 while:1 olver:1 σxj:7 conformal:3 procedure:1 seven:1 unitary:1 vol:1 ir:12 thus:5 them:3 ii:1 characterize:1 mod:2 vanish:1 currents:1 different:7 φs:13 φt:1 φx:1 connection:1 φa:1 complex:6 quant:1 dilations:2 dimensionless:1 several:1 subalgebra:5 infer:1 independent:5 used:3 imply:2 singapore:3 sym:9 hand:4 purpose:1 infinite:17 invariance:2 six:1 schr:14 programs:1 nevertheless:1 adapted:1 no:5 well:6 roughly:1 analysis:2 obviously:1 barut:1 sche:3 solve:2 convenient:1 model:3 otherwise:1 arising:1 possesses:1 usual:3 λs:1 ny:1 world:3 mathematica:1 proposed:2 cj:2 obtain:13 rest:2 homogeneity:5 confined:1 via:1 immediately:1 polish:1 graduate:1 functionally:1 previous:3 nicolas:1 k3:1 intersection:1 preprint:2 family:13 generator:7 density:2 wei:1 seems:1 transformed:1 lett:4 theorem:1 formal:1 solvable:1 transformation:10 k6:3 real:13 acta:1 iλ:1 k5:1 depends:1 easily:1 dissipative:2 hennig:1 iγ:2 iε:1 possible:1 spanned:1 additivity:1 five:3 press:3 using:3 subfamily:25 apart:2 loss:2 ljk:6 necessary:1 semi:1 particle:1 systematically:1 exploiting:1 xe:1 separately:2 indication:1 follows:1 evolutions:1 stationary:2 reduced:2 mathematical:5 sketch:1 2ξx:1 methods:4 classical:2 formulas:1 madrid:1 some:3 sym3:3 sym2:6 sym1:5 sym0:4 respect:1 neglecting:2 ourselves:1 scale:1 dimensions:3 lead:3 centre:1 integration:2 decomposition:2 yields:3 conference:1 linearizations:1 scientific:3 bl:1 problems:1 arbitrary:2 oscillating:1 bj:11 bk:2 2m:1 imaginary:2 properties:4 commutative:7 kinematical:3 extension:2 constraint:1 discussed:7 dependence:7 o:1 compatible:1 ensure:1 diffeomorphism:2 act:2 mixed:3 connected:1 introduced:1 slightly:1 organizers:1 ηf:1 ciemat:1 previously:1 communication:1 into:2 functional:4 three:6 integer:2 en:1 references:1 laplacian:1 determine:3 φxj:7 operator:2 proportional:1 span:3 additional:5 there:9 u2:1 start:1 restricts:1 modifications:1 forward:3 dε2:1 sections:2 treat:1 function:3 considerably:2 complete:1 δkl:3 δkm:1 jun:1 but:3 hj:1 heat:3 lindblad:2 pdes:2 prolongation:1 fulfilling:2 smooth:3 deduce:1 us:2 dnx:2 ljm:1 xxvi:1 called:5 mechanics:5 fulfills:1 constant:1 defined:1 abstract:1 sym4:3 linearity:1 generating:1 general:10 single:1 interchanged:1 formulation:1 ax:1 inc:1 again:2 functions:5 variety:1 amounts:1 fushchych:1 whereas:1 wavefunction:3 detail:1 quantization:1 field:6 other:4 role:1 spatial:1 mathematics:1 er:2 ξx:10 polar:1 elements:1 kinds:1 generates:1 ξt:2 shown:1 covariance:1 commutator:1 generated:2 linearization:4 structure:3 independently:1 correlated:1 implies:2 longer:2 together:2 mass:2 time:4 observables:2 n2:3 backward:3 requires:1 furthermore:5
|
quant-ph9506038.txt |@word gu:1 concept:1 partial:2 peshkin:4 similarity:1 depends:2 lagrangian:1 magnetic:2 results:5 existing:1 four:5 roy:1 scalar:3 commute:1 edu:1 cases:1 causes:2 consider:1 fronts:3 ıu:1 afanasiev:1 alamos:1 qian:1 charge:1 critical:1 excluded:1 under:3 sound:1 confirmation:1 returning:3 very:3 p0:1 wave:34 electron:5 polytechnic:1 affect:2 difference:4 exact:2 condition:1 turns:1 solution:2 t0:7 large:1 solved:1 vector:5 small:4 relation:1 optics:4 commented:1 concluded:1 application:1 ten:1 measurable:2 zero:2 design:2 traveling:1 qualitatively:1 even:2 index:2 what:1 sub:2 cimmino:1 sum:2 uniform:1 version:2 above:3 allman:1 new:3 net:1 increasing:1 method:1 filled:1 condensed:1 full:1 calculations:1 respectively:1 never:3 certainly:1 here:5 reported:1 cylindrical:1 focused:1 directions:1 consideration:2 transformation:6 change:11 ref:1 thirty:2 institute:1 shift:2 study:1 changed:2 reason:2 p2:2 amount:1 periodic:1 published:1 usually:2 shaded:1 changes:1 hν1:1 elongated:2 named:1 formulated:1 merely:1 explained:2 unitary:1 logically:1 total:5 establish:1 use:2 feb:1 proceed:2 would:3 positive:1 until:1 motivate:1 negative:1 e0:1 going:1 m1:2 therefore:6 m2:1 taken:1 themselves:2 type:1 theoretical:4 today:2 more:6 henneberger:2 clearly:1 initial:1 dxµ:1 line:1 odinger:3 tested:2 department:1 basically:3 particular:2 known:2 ward:1 must:3 evolves:1 none:1 word:1 indicates:1 shielded:1 avoiding:1 equation:10 london:2 theories:1 values:1 growing:1 meet:2 refractive:1 my:3 example:3 figure:2 stated:2 calculation:1 topic:1 effectively:2 slit:8 minimum:1 want:1 counting:1 yang:2 information:1 goal:3 provide:2 discussion:5 six:1 conducted:1 arrangement:1 makes:1 far:2 rubio:2 vital:1 fourth:1 significance:1 verlag:1 circular:1 simplicity:2 description:1 huge:1 wu:3 after:5 01m:1 plane:1 designed:1 waves:1 verified:1 realized:1 natural:2 effective:1 ones:1 so:12 media:3 representation:4 order:8 typical:1 interpretation:18 shield:1 gauges:1 over:1 move:2 mainly:1 years:3 course:1 paper:4 through:5 experimentally:1 mentioned:1 existence:6 still:6 its:11 before:2 perfect:1 probability:2 how:1 rojo:2 dr:1 relativity:1 actually:2 b1:1 detected:1 fig:33 mail:1 might:1 happened:1 eventually:1 non:5 good:1 return:1 introduce:1 number:1 cutting:3 effects:10 they:8 front:18 now:3 yu:1 realize:1 represents:1 term:1 finite:1 dirac:1 hereafter:2 always:2 reasonably:1 normally:1 possibilities:1 applied:1 fringes:1 conflict:2 toroidal:9 each:4 found:1 side:3 heavy:1 doing:1 energy:1 revised:1 used:2 expect:3 vectors:1 measure:1 quantum:15 laboratory:1 happen:1 eq:1 special:3 out:6 travels:3 shown:2 space:1 tried:1 since:2 interference:8 particles:1 may:6 qb:1 reader:1 print:1 issue:3 math:1 complicates:1 theory:18 free:6 standard:3 completely:1 complicated:1 put:2 estimate:1 beginning:1 generate:2 arrives:1 additional:1 interaction:1 r0:7 derivation:2 created:1 geometry:3 starts:1 could:3 m20:1 m21:1 length:10 gordon:2 consequence:1 think:2 first:4 major:2 already:1 symmetry:2 reflected:2 channels:1 done:1 another:3 carry:2 open:1 aharonov:12 size:1 manuscript:1 start:3 behaves:1 their:8 appl:1 too:1 kµ:1 travelled:1 emphasis:1 speaking:1 gives:1 m0:3 mostly:1 wavelength:1 acquire:1 took:1 prediction:6 part:1 47a:1 eliminated:1 believe:1 than:2 relative:1 kind:2 double:8 qaµ:2 cimento:2 grey:1 matter:2 states:1 rensselaer:1 amplitude:2 interferometry:1 hologram:1 motivation:1 generality:2 nuovo:2 electrodynamics:1 correction:1 argument:1 generalization:1 talmi:2 say:2 chambers:1 need:6 magnified:1 seek:1 any:9 viewed:1 elsewhere:1 acceleration:2 strength:1 convenient:1 interferes:1 liu:2 ideal:5 potential:30 absorbed:1 detector:2 effectiveness:1 channel:9 begin:1 broglie:1 altered:1 opposite:2 connected:10 letter:1 phase:10 measured:3 causality:1 cause:1 kg:2 calculated:1 sometimes:1 cover:1 properly:1 electrons:1 principle:1 clean:1 fowler:1 charged:2 tubes:1 fact:1 inspire:1 intensity:1 show:1 agreed:1 troy:1 gauge:21 solutions:3 carefully:1 thickness:1 trivial:3 anandan:2 based:2 knowledge:3 title:2 explain:1 loinger:1 state:2 topological:3 should:10 only:6 experiment:9 factor:3 circle:1 local:7 pointed:1 do:4 klein:3 means:6 dependent:3 familiar:1 de:1 expectation:1 preferred:3 aα:1 beam:1 aβ:1 despite:1 report:2 represented:1 following:1 evolution:1 gauged:1 approach:2 arxiv:1 qa:4 influenced:1 experiments:5 though:1 including:1 set:1 hν:2 national:1 testing:1 notice:1 module:1 observed:1 see:4 computer:1 radius:1 result:8 captions:1 discussions:1 contains:1 frequency:2 closer:1 detect:1 pattern:3 away:6 dipole:1 propagates:1 enough:5 closed:3 between:6 conceptual:2 invariant:5 boundary:2 conditions:1 solenoid:8 discovery:1 comparable:1 terms:1 extend:1 opening:1 importance:2 modelings:3 screen:3 weak:1 however:3 incident:2 key:1 modeling:2 ferromagnet:2 topology:1 both:2 realizable:2 last:1 reverse:1 desired:1 many:1 region:18 uncertainty:1 according:3 propagation:2 connection:6 berry:1 logic:1 operating:1 argue:1 whole:2 schroedinger:2 experimental:4 among:1 supply:1 wall:1 whatever:1 alone:1 simply:8 path:6 cancel:1 respect:3 worthwhile:1 ensures:1 described:1 solenoids:2 puts:1 trajectory:1 due:4 been:3 much:1 deposited:1 interpret:1 ph:2 magni:1 ann:1 choose:1 direction:2 referee:2 easy:1 observable:1 am:1 gap:1 coherent:1 understand:1 angles:1 covered:2 spirit:1 present:1 case:4 multi:2 look:3 developing:1 solid:1 expanded:1 value:2 eigenstate:3 will:1 while:2 replaced:1 behavior:1 situation:1 revisited:1 property:1 inspired:1 resolved:1 larger:1 find:1 iq:1 simulations:1 designs:1 surface:2 equal:1 ii:4 canceled:1 itself:2 dual:2 ie:1 disappear:1 different:6 develop:1 sensitive:1 suggest:1 problems:2 same:4 archive:1 complex:1 quant:2 several:1 neutron:2 higher:4 literature:2 infinity:1 numerical:2 upon:2 effect:70 hand:1 oversimplification:1 moving:3 purpose:1 potentials:4 changing:2 invariance:6 expand:1 suitable:1 schr:3 center:1 disappears:2 analysis:1 obviously:3 bohm:7 solve:1 comes:2 components:1 wider:1 left:7 opinions:1 less:1 generally:3 shilov:1 rest:1 alternative:1 scattering:4 eigenstates:2 previous:3 speculate:1 generator:1 ny:1 regarded:1 point:6 seems:2 except:1 discuss:3 source:8 k0:4 combine:1 lett:8 versa:1 grating:1 submissions:1 remaining:3 momentum:9 divided:1 real:1 tests:1 rev:8 big:1 possible:3 possibly:1 five:1 know:1 coaxial:1 using:1 variants:1 unique:1 rotate:1 qaα:1 like:6 particle:10 follows:1 separately:2 flux:17 either:1 become:3 depend:1 mathematical:1 because:7 methods:1 classical:5 people:4 springer:1 rpi:1 scatters:1 extended:1 generates:1 nonzero:1 rarely:1 electromagnetic:8 tube:5 shall:2 everything:1 does:3 provides:2 propagating:1 proc:2 demonstrated:1 june:2 equivalent:1 tonomura:5 complication:1 notably:1 ehrenberg:3 shifting:1 although:3 transformations:1 about:4 central:2 impenetrable:1 discussed:3 o:1 ensure:1 introduced:3 slightly:1 soc:2 own:1 statements:1 presence:1 into:8 integral:1 three:2 device:1 right:5 references:1 determine:1 einstein:1 legends:1 area:1 artifacts:1 support:1 there:16 approximate:2 long:2 los:1 conservation:5 way:1 was:4 naturally:1 function:1 complete:1 attempted:1 shang:1 jun:3 but:8 hk:1 construction:1 aµ:1 optical:1 count:1 made:1 zhu:2 intuitive:1 born:1 whether:3 wish:3 inside:1 variations:3 maximum:2 us:2 ur:1 crystal:1 un:1 accustomed:1 minor:1 zhi:1 problem:9 similar:4 called:1 connect:1 mechanics:11 b62:1 ab:28 associated:1 resemblance:1 defined:1 certain:2 abstract:2 measurement:2 influence:1 covers:1 general:2 single:3 cure:1 exist:1 our:9 curl:1 check:2 physical:1 compared:3 dotted:1 no:8 naturwiss:1 when:4 casher:3 field:13 other:5 hν0:1 details:1 normal:2 becomes:1 test:2 conclusion:1 conclude:2 picture:2 exp:2 calculating:1 convincing:1 variation:1 generated:2 important:2 bounded:1 qφ:3 variable:1 inspiration:2 ago:1 backward:1 implies:1 coulomb:1 vice:1 assume:3 physics:4 dτ:1 percentage:1 diffraction:1 equivalently:1 implied:2 mass:3 incomplete:1 denies:1 starting:2 original:4
|
quant-ph9506039.txt |@word represent:7 monte:2 consider:3 limited:1 localizes:2 broaden:1 brownian:3 results:3 existing:1 illustrated:2 scalar:1 mile:1 computation:12 consists:2 expressions:1 adjustment:1 localized:3 sch:7 whose:6 heller:2 inverse:1 calculate:2 4ns:1 irrelevant:1 deterministic:2 including:1 presents:1 uniqueness:1 th:1 under:1 stochastic:4 include:2 easily:1 norm:1 applied:3 random:2 provides:4 advantage:6 very:7 supercomputer:1 percival:15 semi:1 wave:18 every:1 application:2 affect:1 difference:1 services:1 identity:1 osi:3 school:1 dio:3 δt:6 hamiltonian:9 knight:7 barchielli:1 solution:14 fewer:2 damped:3 large:8 solved:1 vector:5 small:10 markov:1 optics:7 caltech:2 lot:1 upper:1 approximately:3 force:2 ten:1 estimates:1 direct:2 qmw:1 modified:1 jump:6 second:15 concludes:1 further:3 dynamics:5 chem:4 carlo:2 linear:3 even:7 dissertation:1 what:2 nonlinear:7 developed:1 appear:2 advantageous:1 section:11 interactions:2 brief:1 cell:1 experiment:1 run:1 above:1 illustrations:1 suppose:1 learned:1 increasing:1 method:21 contrast:1 satisfy:5 condensed:2 full:2 lee:1 degree:2 q0:4 pushing:1 here:1 atoms:1 behaviour:2 separation:1 represented:9 along:3 strong:4 equations:12 appears:1 change:4 referring:1 obtained:1 solid:1 great:2 generalizing:1 shift:4 study:2 studied:2 commonly:3 significantly:1 delocalizing:2 simultaneous:3 products:1 situations:1 usually:3 complicated:3 conveniently:1 suitable:1 changes:1 pearle:3 uniquely:1 examining:1 schack:2 followed:3 clark:1 bounds:2 timestep:2 castin:1 natural:1 highly:1 expect:1 treatments:1 total:4 planck:4 2γx:1 environment:17 use:5 takes:2 would:9 freedoms:4 distinct:1 calt:1 next:1 occupying:1 few:1 going:1 therefore:2 memory:1 taken:2 doubling:1 meyer:1 type:1 more:18 ambiguity:1 guckenheimer:1 clearly:6 becomes:6 operators:20 savage:6 line:3 odinger:13 thompson:1 needed:16 carrying:1 normalized:6 particular:1 known:1 cases:5 compromise:1 must:3 high:1 springer:2 integrating:1 equation:40 work:1 oscillator:12 ρl:2 remain:1 fock:3 obvious:1 following:6 example:7 compare:1 challenging:1 figure:3 give:2 process:4 neglected:3 purposes:1 ann:1 dependence:1 states:49 effectively:1 minimum:1 numbers:7 particles:1 potentially:1 simulation:9 junctions:1 g2:1 needs:1 counting:1 end:1 straightforward:1 provide:3 mcneil:2 di:3 berlin:1 chemical:2 how:3 varies:2 criterion:1 pure:10 opt:2 instead:2 ordinary:2 verlag:1 ensemble:11 isotropic:1 product:3 de:1 may:2 earlier:2 confirmed:1 epsrc:1 top:1 applications:8 plane:1 prance:2 physik:1 multiplication:2 representations:1 choice:2 get:1 types:1 varied:1 proceeds:1 quasiclassical:1 dynamical:5 effective:2 computations:4 slightly:3 approximation:1 counter:1 lines:1 capacitors:1 processor:1 duffing:8 rather:2 complexity:2 so:8 automatically:1 fundamental:1 decreasing:2 representation:8 predominate:1 order:4 typical:1 spreads:1 wigner:1 dum:1 produces:6 electromagnetic:1 over:7 move:1 produced:3 wiener:3 london:3 statistical:1 during:1 satisfies:5 poincar:1 its:6 before:2 regions:3 thank:1 interesting:4 solving:2 expectations:7 exhibits:1 actually:1 detected:1 parts:1 degrees:2 systems:23 jacobi:1 pad:1 main:2 weber:1 correspondence:1 stability:1 them:3 good:2 affected:2 greater:6 delocalization:1 mølmer:1 practice:3 processes:4 records:1 walls:3 hamilton:1 effects:7 they:6 acta:4 liquids:1 ghirardi:1 nor:1 represents:7 february:1 several:2 always:3 university:2 presented:1 normally:1 establishing:1 realistic:1 2f:1 magnitude:4 l2:1 trap:1 each:9 done:1 mean:6 reactions:1 bridging:1 differential:4 england:1 another:1 generation:12 energy:2 reduce:2 principles:1 conventions:1 elementary:2 investigated:2 t0:11 todd:1 quantum:87 our:3 transitions:1 explicit:1 special:1 out:7 shown:8 matrix:2 driving:1 space:41 restricted:1 itˆo:4 since:2 crucial:1 chaos:7 research:1 increase:2 studying:1 denoted:1 constants:1 adaptive:1 illustrate:1 occurs:1 math:1 decoherent:2 numerical:20 theory:9 mσ:1 localization:35 hf:1 gardiner:1 contain:1 differ:1 standard:4 difficulty:1 approaches:2 advantages:3 york:1 put:3 salama:1 estimate:2 e1:1 inevitable:1 care:1 definition:1 pairs:1 interaction:13 retained:1 derivation:3 inspection:1 could:5 computers:2 programming:1 times:6 motion:6 int:2 produce:1 diffuses:1 circuit:1 twenty:1 hence:1 retain:1 view:1 onto:1 interact:3 first:3 origin:6 already:1 probability:8 widely:1 variables:5 thesis:1 number:36 clear:3 parkins:1 simplified:1 fast:1 directly:2 wilson:1 open:23 angular:2 size:3 given:6 ian:1 checked:1 likely:2 similarly:3 introduction:1 leading:3 adjoint:1 system:46 least:3 while:1 their:5 appl:1 rates:2 too:6 statement:1 2ωf:1 master:18 white:1 molecular:2 gives:3 shifted:2 calculations:1 geneva:1 centered:2 strunz:1 completed:1 continuous:2 environmental:3 optical:2 simulate:1 x2:1 attempt:1 representing:1 than:13 x4:1 modes:6 diffusion:20 detection:1 determines:1 jumps:3 double:2 require:2 rate:2 submitted:2 halliwell:4 annihilation:4 matter:2 computer:3 amplitude:1 were:3 treated:3 capacitance:1 published:1 rimini:1 fig:1 diagonalization:1 fluctuation:1 unchanged:2 measure:1 dynamically:1 yielding:1 width:1 variable:1 conjugate:1 need:4 rotors:1 orders:3 relatively:5 forced:2 generalizes:1 traditionally:1 built:1 zero:1 depending:2 efficient:2 convenient:1 latter:2 isolated:8 approximating:1 potential:5 generalized:1 analogy:1 δnm:1 essential:1 modulus:1 accuracy:2 heisenberg:3 spectral:1 towards:1 opposite:1 analyse:1 measures:1 molecule:4 prohibitive:1 most:5 optimized:1 errors:2 drummond:2 significant:3 quantitative:1 phase:32 mechanically:1 collaborators:1 extremely:1 duff:1 apparatus:5 considered:1 average:1 sometimes:2 disperses:1 drifts:1 traditional:2 karplus:1 points:3 rev:14 principle:3 exp:1 dispersed:1 penning:1 sum:2 fact:1 ritsch:1 particularly:4 show:2 queen:2 bub:2 si:3 relation:1 solutions:4 optica:3 schenzle:2 tend:1 find:1 ground:1 q1:2 current:2 ratio:3 simulating:1 parameters:5 dissipative:5 gases:1 histories:2 should:1 values:4 analytic:2 only:5 explicitly:1 molecules:4 factor:11 equivalents:1 employed:1 adequate:2 local:3 pointed:1 hope:1 equilibrium:1 do:3 intractable:2 his:2 gains:1 localizing:4 means:2 dependent:4 connections:1 simplest:4 udiger:1 expectation:7 preferred:3 dyn:1 ones:1 multi:1 competing:1 impractical:1 dt:6 geometric:1 carmichael:1 qp:2 evolution:18 conditions:1 arxiv:1 thermal:3 acknowledgments:1 hyperbolic:1 optimally:1 common:1 inefficient:1 recommendations:1 qi:1 through:3 fortunately:1 fixed:8 occupy:1 approaching:1 pioneering:1 set:2 computed:3 reference:1 physically:1 packet:8 up:3 relative:4 see:4 individual:17 college:2 result:3 localize:2 versus:2 pi:1 limiting:2 belavkin:1 best:3 techniques:1 surfaces:4 cutoffs:1 capacity:1 eminently:1 ways:1 away:1 ralph:3 consequence:2 continually:1 state:45 determined:2 various:2 jth:1 between:14 crude:1 invariant:2 boundary:4 approach:2 wide:2 commute:2 terms:5 initially:1 however:3 implementing:1 succeed:1 hypothesis:1 hundreds:1 distribution:6 suggested:1 both:6 prospects:2 improved:1 limits:1 tractable:1 many:10 region:2 conclusions:1 hours:2 equal:1 enviroment:1 etc:1 connection:2 variance:2 ωf:2 otherwise:2 strongly:3 adjusted:1 lm:12 fields:1 point:5 simple:11 asymptotically:1 corresponds:1 environments:3 semiclassical:4 non:1 applicability:1 respect:2 appeared:1 runge:1 considering:1 broadening:1 pq:2 described:6 transformations:1 leads:1 basis:65 addition:1 trajectory:9 due:3 been:10 quickly:1 pc:1 reduction:1 much:7 treat:1 basic:1 ph:2 extreme:1 mary:2 define:2 describe:2 corresponding:10 indeterminacy:2 qsd:42 quantities:1 coherence:1 photon:9 cos:1 new:1 gap:1 relevance:1 coherent:5 external:3 ultra:1 fokker:2 former:2 those:5 bifurcations:1 case:6 p0:3 p1:2 look:1 josephson:1 steinbach:2 variances:3 transformation:2 will:2 near:2 replaced:1 euler:1 applies:2 situation:1 property:3 guide:1 dλ:1 a21:1 unitary:6 chaotic:5 ip:2 simulations:2 thus:1 surprisingly:1 surface:5 itself:1 properties:1 baths:1 comparative:1 motivated:1 interacts:1 different:2 ing:1 verified:1 considerable:2 perhaps:1 make:3 sytems:1 radiation:1 tour:1 same:6 any:2 member:2 unity:1 complex:4 quant:1 coworkers:1 units:1 limitation:1 dimensionless:3 regime:4 showing:1 difficult:4 kutta:1 independent:3 used:18 lie:2 trajectories:4 effect:4 hand:1 driven:1 action:1 strength:1 moving:19 changing:3 invariance:4 six:1 normalization:2 simulates:1 lower:2 schr:13 traps:2 largely:1 minimize:1 studies:1 well:6 roughly:1 analysis:2 picks:1 bohm:2 savings:3 without:1 solve:1 components:1 simulated:4 position:4 model:2 plotted:1 dimension:4 usual:2 holmes:1 just:2 less:1 when:7 adjustments:1 obtain:1 valuable:2 atomic:1 useful:2 yet:1 reduced:2 adding:1 rapid:2 preprint:3 zoller:3 density:15 photons:1 had:1 reasons:1 spread:1 attractive:1 easy:1 theorem:1 constant:2 mod:4 excited:3 momentum:3 take:2 real:5 around:2 depends:1 alternatively:1 big:1 breaks:1 possible:3 harmonic:14 increases:3 preference:1 vacuum:1 using:18 part:6 unique:1 helpful:2 desire:1 dimensional:1 necessary:3 like:5 particle:5 follows:3 signal:1 lett:8 δp:3 δq:3 separately:1 communications:1 steps:1 either:3 arbitrary:1 rarely:1 qualitative:1 replacement:2 exceed:1 because:9 methods:12 classical:18 discrete:4 decoherence:2 creation:2 some:5 competition:1 self:2 understood:1 zheng:4 examples:11 qmc:1 oscillations:1 extended:2 bigger:1 happens:2 provided:2 scale:2 recently:2 lead:1 sufficiently:3 cavity:4 affects:1 avoid:1 measurements:1 langevin:3 integration:3 selfadjoint:2 does:1 centroid:1 economical:1 moderate:1 umi:1 mode:6 measuring:4 destroys:1 noise:5 forces:1 inaccurate:1 detuned:1 drift:2 equivalent:1 l1:1 broken:1 step:4 shifting:1 reduces:2 tcomp:3 imaginary:2 refers:1 hilbert:2 after:1 asymptotic:1 comparison:4 about:3 carried:1 extending:1 freedom:7 commun:1 theorems:2 discussed:2 factors:2 alber:3 practical:3 financial:1 range:1 a2:5 nj:2 futhermore:1 mixed:2 introduced:2 spiller:6 projectors:1 road:1 cutoff:7 mechanics:2 computational:2 tn:1 helvetica:1 into:4 numerically:5 down:1 lies:1 appropriate:2 exacerbated:1 references:2 operator:27 ei:1 reducing:1 often:9 unambiguous:1 statistics:1 additional:3 periodic:1 support:1 there:17 available:1 detuning:1 long:2 dispersion:6 brun:3 accordingly:2 describes:1 way:2 was:7 garraway:7 damping:1 function:4 considerably:1 runs:1 gaseous:2 form:5 adjusting:1 displacement:4 jun:1 but:21 gaussian:1 volume:1 heat:1 hi:1 gain:1 larger:2 dξm:6 lindblad:12 removed:1 true:1 proposal:1 absent:1 made:4 applying:1 algorithm:3 circuits:4 characteristic:2 cells:1 gravitational:1 devices:1 2πn:1 ul:2 note:1 frequency:3 limit:8 uk:1 continuously:1 fluctuations:5 problem:14 similar:2 called:2 gisin:17 detailed:3 proved:1 dalibard:1 computing:12 defined:5 physica:2 abstract:2 measurement:5 proven:2 general:10 dξ:2 single:10 together:1 formulation:1 formalism:2 graham:3 eigenstate:1 physical:2 functions:1 compared:2 no:8 eq:3 whereas:1 storage:3 detail:3 scaled:3 power:2 field:3 other:9 neighbourhood:1 papers:1 department:1 mathematics:1 theor:1 arithmetic:1 picture:11 elements:2 separate:1 problems:7 includes:1 a1:5 important:9 ξm:1 vectors:4 dissipation:3 mately:1 signficantly:1 westfield:1 feasible:1 coupling:1 dψ:1 physics:2 lowered:1 required:5 packets:8 interacting:1 rule:1 compete:1 time:24 far:5 signalling:1 requires:2 original:1 once:1
|
quant-ph9506040.txt |@word aˆb:1 concept:2 gr:10 focus:1 four:2 eds:2 decisions:2 consider:1 bˆ:2 deterministic:29 tr:8 helps:1 under:3 analogous:1 must:5 appleton:1 provides:2 very:3 frequencies:2 choice:10 decide:1 drinking:2 condition:3 switches:4 presented:1 turns:4 notes:1 solution:1 t0:5 large:1 item:1 vector:1 unexpected:1 sin2:4 conjunctions:2 konstanz:1 concludes:1 eating:2 machines:1 even:3 what:4 errors:1 experiment:8 new:2 nurse:10 evolving:2 full:1 notions:1 concepts:1 understanding:1 governing:1 situation:2 directions:1 consideration:1 standard:1 appears:2 interpret:1 violate:1 sending:1 institute:1 involved:1 until:1 action:5 opinion:1 studies:1 outcomes:4 stern:1 crime:5 univ:2 causal:2 indeterministic:6 prove:1 probabilities:9 ψs:1 predictions:1 symbolizes:1 call:1 therefore:1 scope:1 type:2 tell:1 more:4 sort:3 definition:2 becomes:1 berlin:1 popper:2 particular:6 baby:12 foundations:1 hold:2 circumstances:7 springer:1 morally:1 room:1 recall:1 learn:1 following:1 making:1 example:2 something:1 hutchinson:1 mackay:2 figure:3 stated:1 process:7 sense:2 purposes:1 accept:1 states:8 performed:2 allowed:1 needs:1 turn:4 acts:7 how:5 reducible:1 answer:1 speaks:1 parameter:2 ensemble:1 description:2 may:4 earlier:1 derived:1 law:4 data:1 janis:1 consequently:1 switch:4 so:8 allow:1 correlation:2 typical:1 horne:1 holds:2 interpretation:1 numbers:1 indeed:3 pointed:1 soon:1 argues:2 brain:4 paper:2 executes:1 statistical:9 ity:1 existence:1 satisfies:1 its:1 massey:1 offers:5 fig:2 mail:1 hidden:8 someone:3 food:2 auto:1 budapest:1 they:2 now:3 nor:1 fully:1 university:1 identified:1 arrow:1 each:3 found:3 entirely:4 mean:2 mental:6 doing:1 related:1 deterministically:1 magnets:1 measurement:4 quantum:26 relates:2 out:7 shown:1 space:1 since:1 particles:3 denoted:1 lecture:1 correct:1 philosophy:1 theory:18 causally:1 commits:2 given:3 free:12 quite:1 admits:4 base:1 york:1 members:1 imagine:1 ask:1 advance:1 derivation:2 could:7 times:1 thing:1 assumed:1 first:1 xj:3 xi:3 xn:5 probability:6 feel:1 variables:1 philosophical:2 done:4 another:1 open:2 little:1 rejects:1 system:5 least:1 their:2 assumption:2 brevity:1 too:2 essays:1 structures:1 gives:2 pittsburgh:1 universe:7 x2:5 x1:5 than:3 specify:2 population:1 distance:1 kind:6 depends:1 matter:1 future:2 contrary:3 were:2 feeling:2 entail:2 well:2 mind:1 argument:4 say:1 elte:1 any:1 foundational:1 responsible:1 instance:1 internal:1 take:4 objective:1 detector:4 sure:1 shall:1 arguing:1 eggs:3 who:2 connected:1 position:1 remarks:1 probabilistic:6 s28:1 consequences:1 clear:1 tautology:2 detectors:1 scrambled:3 definitely:1 principle:2 mechanical:2 physics:5 laws:8 show:1 universit:1 relation:2 gerlach:1 fine:5 find:2 writes:1 outside:1 should:3 only:8 going:1 believing:1 local:4 do:4 his:1 means:2 followings:2 cannot:5 words:2 neither:1 processes:3 arxiv:1 experiments:2 she:1 london:1 fixed:1 human:4 exists:2 unbaum:10 relative:1 see:4 individual:6 result:2 refrained:1 forthcoming:2 subject:1 hilbert:1 detect:1 draws:1 inequalities:1 ways:1 state:3 determined:2 various:1 between:6 geometric:1 attention:1 however:2 come:1 interpretations:2 polytope:1 repeating:1 many:1 taking:1 according:5 against:2 etc:1 admit:1 logic:1 whole:2 finds:1 otherwise:5 characterization:1 simple:1 acted:1 cf:1 community:3 represented:1 proved:3 testable:1 considering:1 pp:1 raise:1 basis:1 three:1 been:1 inadequate:1 ph:1 differently:1 direction:8 senses:1 corresponding:1 concerning:1 readings:1 determination:1 external:3 careful:1 spin:9 otv:1 case:7 conception:1 will:26 while:1 suppose:2 behavior:7 determinism:1 indeterminism:6 kolmogorovian:3 identical:1 century:1 sellars:1 equal:1 itself:1 different:5 inquire:1 things:1 connection:1 same:5 quant:1 arguments:1 widely:1 events:6 conflict:3 meets:1 commonsense:1 drink:2 robust:2 brussels:1 thoughts:1 lehrer:1 makes:1 locality:1 epr:3 analysis:3 obviously:1 thought:1 without:1 claims:2 model:7 left:4 just:1 being:1 observed:2 actions:1 aspect:7 campbell:4 regarded:1 bell:1 other:2 theorem:1 save:2 real:1 results:1 possible:3 admitting:1 exemplars:1 background:1 press:2 world:14 accepted:1 pitowsky:3 theor:2 like:5 particle:4 follows:2 arthur:2 individuals:2 either:1 arbitrary:1 szab:6 right:4 often:1 classical:6 some:2 earman:1 understood:1 nonetheless:1 thinks:1 provided:1 describing:1 avoid:1 counterfactual:1 does:12 eliminate:1 aszl:1 limitations:1 conference:1 run:1 reasonable:1 problems:1 although:1 accommodated:3 predictability:1 limitation:1 would:5 freedom:15 aˆ:5 o:7 compatible:3 sake:1 act:1 commit:3 os:1 projectors:1 cambridge:1 letters:1 into:6 within:1 nothing:1 beings:1 references:1 determine:1 einstein:2 argumentation:1 statistics:1 distinctions:1 support:3 there:1 question:3 alleged:1 long:1 strict:1 way:2 was:1 himself:2 form:1 offer:2 jun:1 but:11 hu:1 subjective:2 mechanistic:1 true:1 brans:2 he:9 directed:1 made:1 applying:1 whether:6 selects:4 up:5 us:2 theoretical:1 those:1 problem:4 agree:1 mechanics:7 rightly:1 int:2 certain:1 abstract:1 describe:3 doesn:1 clauser:1 exist:1 together:2 our:3 proceeds:1 no:2 objection:1 percent:1 terminating:1 details:1 you:1 really:1 sufficient:1 conclusion:2 draw:1 kinds:2 time:11 june:1 includes:2 important:1 variable:4 assume:4 governed:1 remarked:1 starting:1 decision:3
|
quant-ph9506041.txt |@word consider:3 broaden:1 desirable:1 results:4 four:2 facilities:1 broader:2 go:1 query:4 particles:2 certainly:1 deterministic:1 languages:1 quasi:1 program:4 device:1 petersburg:2 analogous:1 include:1 predicate:1 orthogonal:2 far:1 alternatives:2 choice:1 electron:5 orientations:1 summarized:1 trouble:1 solves:1 hamiltonian:3 positions:1 solution:4 large:1 solved:2 convenience:1 vector:1 enhance:1 upper:3 computation:6 deutsch:4 uef:1 zero:2 pass:3 further:1 odd:1 substitute:1 theory:1 even:1 what:4 projectors:1 gabbay:2 appear:3 apparatus:1 section:6 brief:1 experiment:5 above:1 new:3 acknowledgments:1 filled:2 simultaneously:4 whose:1 here:2 objects:1 irrespective:1 concluding:1 change:1 wait:1 obtained:3 search:1 incoming:1 studied:1 changes:1 options:1 formulated:2 projection:1 heart:1 merely:1 simulating:1 logical:3 outcomes:3 brought:1 flexibility:1 stern:4 counts:1 imaginary:1 unit:1 working:1 prove:4 remains:1 positive:1 finally:1 properties:5 calculation:5 depicted:1 call:2 encode:1 theoretical:2 more:2 sort:1 preparation:3 pavlov:1 bennett:2 outputs:2 operators:3 emission:1 rigid:1 virtue:2 particular:4 nodes:1 must:3 evolves:1 setup:1 values:8 starts:1 following:7 making:2 my:1 example:1 ions:3 figure:4 give:1 process:6 preserving:1 purposes:2 states:12 performed:1 arise:1 spb:1 end:1 processors:1 provide:1 meanwhile:2 dov:1 machine:4 how:3 pure:7 reject:1 answer:3 instead:3 inputs:2 description:2 may:5 after:2 lab:1 applications:1 plane:1 law:2 data:3 realized:3 outline:1 beam:11 whenever:2 register:7 corollary:1 st:2 so:9 fundamental:2 order:4 operations:1 produced:1 paper:2 through:4 looks:1 filters:1 still:1 its:6 before:2 mod2:1 mod4:1 chosen:4 solving:2 forms:1 detected:1 degrees:1 choose:1 derivative:8 main:1 versus:1 non:3 return:1 halt:2 outlined:1 fig:5 introduce:1 functional:1 mention:1 compelled:1 effects:3 they:2 supposed:1 oxford:1 now:2 transparent:1 february:1 verifying:1 always:2 university:1 possibilities:1 stopped:1 each:4 found:1 2n:3 series:1 hard:1 reduce:1 idea:5 society:2 measurement:7 quantum:36 organised:1 witness:1 juxtaposition:1 shown:1 space:8 since:5 crucial:1 denotes:1 looking:1 re:1 reader:1 formula:3 get:2 forth:1 gate:1 linear:3 zapatrin:3 free:1 clarify:1 complicated:1 put:2 jozsa:3 enormous:1 r2:1 launch:6 determining:1 could:1 computers:4 programming:3 filter:2 thing:1 there:11 xn:10 probability:4 striking:1 variables:3 number:6 iht:2 xz:1 done:1 another:1 impossible:1 passes:2 given:2 1r:1 qtp:6 service:1 their:2 introduction:1 adjoint:3 system:3 least:1 needed:5 intermediate:2 realization:2 postulate:1 scheme:1 final:1 tuple:1 continuous:1 proving:3 resulted:1 review:1 x1:10 unrealistic:1 coefficients:2 dynamical:1 polarized:3 accordance:1 require:1 namely:2 project:1 matter:2 polarizer:8 were:1 russia:1 unchanged:2 correspond:1 say:5 trembling:2 contents:1 sat:2 issue:1 self:3 responsible:1 able:3 ideas:1 oriented:4 equipment:2 emphasis:1 potential:1 absorbed:2 machines:1 detector:3 spectral:1 towards:1 trace:1 shall:6 object:6 most:1 satisfying:1 pair:1 accepting:1 measured:1 telecommunication:1 richard:1 clear:1 steady:1 proceedings:2 definitely:1 electrons:7 principle:10 exp:3 mechanical:1 physics:2 notion:1 fact:1 laws:1 drastically:1 show:2 violation:1 random:1 attempts:1 registers:1 gerlach:4 networks:1 proposed:2 parameters:1 enough:2 controls:2 should:2 entities:2 only:6 going:5 rich:1 factor:1 circle:1 oscillate:1 do:2 notation:1 means:8 beams:1 famous:2 ones:1 preparing:2 words:2 drawn:1 combinations:1 during:1 deductive:2 evolution:7 arxiv:1 experiments:2 london:1 fixed:1 view:1 set:2 ser:1 exists:1 frame:1 observed:1 depends:1 computer:2 result:4 alternative:1 analog:1 instance:1 hilbert:1 detect:1 define:2 away:1 complementary:4 definite:3 state:40 simplest:1 progress:1 sorts:1 checks:1 discovery:1 labelled:2 nature:3 emitted:6 however:2 enters:2 spare:1 extent:1 suggested:1 both:2 last:1 many:1 uncertainty:2 equal:1 against:1 roman:1 logic:1 reply:3 otherwise:2 among:1 cn:2 point:2 royal:2 polynomial:2 loaded:1 testable:1 described:3 due:1 reduction:2 basic:1 ph:1 pi:3 systems:4 describe:1 controlled:1 observable:5 influence:1 concerning:1 convert:1 observe:1 understand:1 installation:1 c1:2 case:2 splits:1 launches:3 value:14 will:26 while:3 suppose:6 situation:2 property:1 margin:1 unitary:1 thus:1 them:4 according:1 wave:2 grown:1 different:2 verified:1 anymore:1 perform:3 suggest:2 make:4 same:6 quant:1 split:3 reminder:2 finite:1 used:1 see:4 assignment:1 finitedimensional:1 moment:1 edges:1 opportunity:1 lower:1 kept:1 well:1 bohr:2 thought:1 machinery:1 position:1 model:3 latter:1 left:3 just:1 being:1 valuable:1 lds:1 press:1 prepares:2 questions:1 touch:1 yes:6 yet:1 previous:2 note:2 loading:1 conclusions:1 seems:1 realize:1 source:8 tuples:1 theorem:11 input:27 semigroup:1 eigenstate:3 take:1 tests:1 satisfiability:3 checking:3 replaced:2 decomposed:1 possible:7 test:5 grib:2 know:2 confined:1 imposed:1 like:2 follows:3 reduces:1 steps:1 output:13 works:1 reduced:1 mathematical:1 right:2 methods:1 deal:1 some:3 cathode:1 calculated:2 complementarity:1 nonzero:3 provided:5 confirm:1 affects:2 avoid:1 measurements:3 comments:1 does:2 unavoidably:1 measuring:3 elucidate:1 journal:1 constructive:1 propositional:2 emits:2 freedom:1 certainty:3 essential:1 mutually:1 introduced:2 processor:13 computational:3 statements:1 computes:2 into:7 within:3 bound:2 nothing:2 appropriate:4 references:1 rapid:1 operator:2 logics:1 classical:15 prepare:1 assumed:2 support:1 initial:12 question:2 automata:4 start:2 grasping:1 way:5 forward:1 was:6 function:1 form:4 sequel:1 jun:1 but:4 principles:1 repeated:1 removed:1 true:5 made:2 whether:3 inside:1 up:4 reversibility:1 international:1 converted:2 verification:1 continuously:1 problem:10 piece:2 called:3 eigenvector:1 mechanics:7 associated:8 ai:4 abstract:1 measure:3 am:5 denote:2 prover:3 enable:1 exist:1 pip:1 formalism:2 commuting:1 check:1 physical:4 friedmann:1 no:10 objection:1 whereas:4 wavefunction:1 when:7 other:3 remarks:1 np:1 you:10 clicks:1 node:1 happens:1 briefly:1 superposition:4 calculating:1 enterprise:1 problems:2 representable:1 prepared:6 tackle:1 structure:1 algorithm:2 assume:1 requires:1 required:1 4r:1 governed:1 time:6 observables:1 resolution:2 having:5 normalized:2
|
quant-ph9506042.txt |@word rev:10 alternatives:4 baby:1 entropy:1 houches:1 2n2:1 follow:1 c1:2 albrecht:1 environment:1 under:1 fatal:1 orthogonal:1 condition:1 school:1 hamiltonian:1 presumably:1 try:1 vector:1 eigenvalues:1 noted:1 zero:1 copenhagen:4 implemented:1 even:2 what:1 appear:1 selected:1 experiment:1 above:3 new:3 paradoxical:1 satisfy:1 edited:5 respectively:2 never:1 les:1 focused:1 equations:1 interpret:2 box:8 vectors:1 studies:2 uniquely:2 griffiths:2 extra:1 plenum:1 julia:1 conventional:1 vol:1 live:7 therefore:4 memory:1 themselves:1 until:1 today:1 odinger:8 normalized:1 eλ:3 known:1 foundations:1 iii:1 must:5 tokyo:3 equation:2 cat:30 following:2 refine:1 give:2 process:12 states:18 numbers:1 absolute:1 information:1 rather:2 technology:1 get:4 how:1 frontiers:1 answer:3 instead:2 coleman:1 tried:1 may:3 after:2 derived:2 cyanide:1 branches:2 light:2 correspond:1 element:2 complexity:2 branched:4 order:1 belong:1 interpretation:5 zeh:1 paper:1 including:1 statistical:1 argued:1 japan:3 satisfies:1 before:2 decay:1 ln:4 detected:1 systems:2 might:1 into:4 non:1 incompleteness:1 shibuya:1 kamefuchi:1 symposium:1 now:2 realize:1 nor:2 eigenvalue:1 february:1 always:6 university:1 2a:1 2b:1 each:10 found:1 d47:1 characterized:1 subset:5 society:1 measurement:6 quantum:8 our:1 eq:6 es:2 description:1 hartle:5 opened:3 squared:1 adhere:1 rn:2 issue:1 theory:2 attempt:1 reason:2 york:1 ask:1 interaction:3 derivation:1 collapsing:1 times:3 hence:2 xi:5 probability:3 sakaguchi:2 omn:2 another:1 necessarily:1 eqs:5 system:3 unruh:1 leggett:1 gives:1 releases:1 exactly:1 natural:1 representing:1 than:2 coefficients:2 princeton:1 require:2 submitted:1 determined:1 wheeler:1 sees:2 ann:1 measure:8 need:1 seen:1 cosmology:1 any:2 lim:3 able:1 note:2 sciences:1 modulus:1 continuous:1 though:1 who:1 gravitation:1 but:4 letter:1 sfi:1 nothing:1 cleared:1 probabilistic:1 why:4 branching:3 don:1 observation:2 considered:1 calculated:1 physica:1 typeset:1 proceedings:2 principle:2 ku:1 physics:2 show:2 relation:1 solutions:1 find:1 o:1 consciousness:1 should:1 only:2 do:5 his:1 means:3 zurek:8 preferred:1 cannot:4 nonequilibrium:1 international:1 evolution:4 arxiv:1 investigate:1 through:1 gell:2 view:1 set:1 observer:19 observed:1 see:10 αq:2 αp:2 αr:2 review:1 definite:2 consequence:1 state:17 between:1 αi:9 invariant:1 neither:2 reading:1 αm:1 notice:1 nature:1 ascribed:1 however:2 piran:1 distinguish:1 observable:1 according:1 whole:1 mann:2 otherwise:1 among:1 2ni:1 cm:2 conclude:1 cr:1 cq:1 cp:1 described:10 transformations:1 basis:2 been:2 naturwiss:1 ph:1 obtained:3 corresponding:1 quantifications:1 coherence:2 coherent:1 observe:2 understand:1 c2:2 2n1:1 those:1 look:1 value:4 remaining:1 will:9 while:1 superposed:1 viii:1 situation:1 property:1 identical:1 almost:1 zhang:1 ascii:1 sequentially:2 different:1 paz:1 scientifically:1 same:2 complex:1 quant:1 weinberg:1 singapore:1 everett:5 hand:3 moment:1 recent:1 eigenvectors:1 schr:8 object:4 bohr:2 thought:2 summer:1 proposed:1 being:1 obtain:1 dose:1 assigned:3 atomic:1 human:5 world:2 alternative:1 macroscopic:1 2nm:1 point:1 guaranteed:1 add:1 other:6 lett:2 theorem:1 eigenstate:1 resolved:2 disappearance:1 caldeira:1 showing:1 possible:2 know:1 press:1 using:1 mod:2 follows:4 yields:1 either:1 because:2 people:1 alive:4 complementarity:1 universes:1 ourselves:1 demonstrates:1 recorded:3 overlap:1 provides:1 peek:1 knew:1 scientific:1 wesley:1 revtex:1 includes:1 bz:1 about:1 recognized:1 practicable:1 ci:7 cambridge:1 puzzle:3 device:1 references:1 operator:5 prepare:1 indispensable:1 there:3 long:1 sealed:1 analyze:1 was:5 opens:1 function:2 complete:1 form:1 collapsed:1 jul:1 hu:1 dead:10 radioactive:1 collapses:1 applying:1 maximum:1 placed:1 limit:2 mechanics:6 addison:1 recognize:1 abstract:1 describe:1 linearity:3 single:1 formulation:5 physical:1 ni:14 paradox:2 nm:5 no:3 corporation:1 wavefunction:5 when:8 vanishes:1 interested:1 details:1 superfluous:1 stat:1 elements:3 superposition:9 prepared:1 correlated:1 correlates:1 time:4 n1:5 n2:5 having:2
|
quant-ph9507001.txt |@word secondly:2 similarity:1 mehra:1 desirable:1 four:2 fig4:1 localized:3 relationships:1 whose:3 violate:1 obstructions:1 under:2 dynamic:2 every:2 vast:1 limρ:1 suffices:1 conceive:3 solution:3 cma:1 correct:2 vector:4 force:3 consistent:19 direct:7 approximation:4 surrounding:1 second:3 implemented:1 established:4 incompatible:2 selected:1 pragmatism:1 above:4 new:18 ever:1 consisting:1 here:20 atoms:2 met:4 represented:1 interpret:3 referring:1 obtained:6 substance:1 study:4 calculations:1 adopting:4 suitable:1 mutual:2 magnifications:1 secure:2 explained:1 plenum:1 replace:1 elude:1 opportunities:1 total:2 univ:4 quasi:11 would:10 mexico:1 therefore:7 separated:1 standardized:1 successful:1 odinger:29 berlin:1 separates:1 must:35 springer:2 pursue:1 work:1 mi:1 mj:4 suggestive:1 concepts:2 root:1 example:7 renormalization:1 give:2 relativistic:5 preserving:1 generically:1 indicates:1 david:1 end:1 enquiry:1 verify:2 feature:1 recovers:2 how:6 significance:2 ordinary:1 description:1 replacing:1 reconciled:2 after:1 demanding:3 objectively:1 law:1 parallel:1 attempt:2 effective:1 appreciate:1 enter:1 order:2 restriction:6 interpretation:20 over:2 satisfied:2 satisfies:1 before:1 fix:4 exhibits:1 fig:12 renormalizable:1 hidden:1 strength:1 overcome:2 unrecognized:1 them:7 heinzen:2 effects:6 they:7 eigenvalue:7 each:12 d47:1 d45:1 directly:9 evolve:1 principles:9 used:1 combining:1 laboratory:5 restricted:3 particles:23 re:2 york:4 foundation:3 mφ:4 linear:18 written:1 mψ:1 free:7 standard:3 homologous:1 universally:2 cosmic:6 pang:1 tied:1 generalizations:1 separable:3 already:2 render:1 encouraging:1 restrict:1 wash:1 philosophical:1 another:1 illustrate:2 xii:1 needed:3 observations:6 xiv:1 postulate:5 variational:3 collapse:1 a39:1 serve:2 speakable:1 requisite:1 xj:11 princeton:2 tree:1 matter:2 classes:1 historical:3 enables:2 solely:1 minus:1 perturbative:5 fashion:1 sees:1 mind:1 spectrum:1 manner:6 seem:3 seek:5 traditionally:1 genuine:1 responsible:1 isolated:2 broglie:4 object:2 simplify:1 decohered:1 phase:2 treats:1 flow:2 orderly:1 bracket:1 principle:17 camb:1 notion:3 dot:1 dover:1 incorporate:1 subtly:1 rayleigh:1 probe:1 radii:1 gauge:3 solutions:13 substituting:2 analogue:2 d3:4 proposed:1 explain:3 judged:1 integrate:2 hamiltonians:1 predecessor:1 do:6 localizing:5 di:3 df:1 dg:1 de:4 perceive:2 yielded:1 dx:4 dt:12 homogeneity:1 normalizable:1 runs:1 δφi:1 fields:42 acknowledgments:1 analytical:1 δφr:1 observer:25 emergent:7 observed:1 depends:4 radius:1 result:2 discussions:2 λi:1 subject:1 away:1 symmetric:1 simplest:1 conceptual:3 drawn:2 approach:5 discovery:1 terms:4 parallels:1 nature:8 weak:5 however:17 bose:2 suggested:2 essentially:1 eyeball:1 against:2 logic:1 30th:1 suppress:2 wider:3 testable:3 strong:1 basis:7 observing:3 radiative:1 three:1 tiny:1 extraction:1 much:1 interest:3 expected:1 derives:1 deeper:2 itzykson:4 rescalings:1 coherent:1 applied:2 tudor:1 exception:1 excited:4 employ:4 viii:1 applies:1 property:4 leaves:1 procedure:2 ix:1 played:1 linked:1 iv:1 ii:3 conf:1 overstated:1 containing:2 suggest:1 make:2 clearly:1 complex:29 quant:1 split:2 avoids:1 several:1 grows:1 independent:4 numerical:5 counterparts:1 amplified:1 potentials:3 hartree:6 opportunity:1 scenario:10 feshbach:1 unified:1 consciousness:1 ideas:3 assigned:1 spherically:1 eigenstates:3 previous:2 nǫ:2 candidate:10 regarded:1 character:1 spread:3 easy:1 take:8 rescaled:1 breaks:1 posed:2 possible:8 unification:2 unique:1 advanced:3 brought:1 appearing:1 specific:1 arbitrary:2 wavepackets:1 deal:1 dead:2 born:2 gˆ:1 indistinguishability:1 dense:1 electromagnetic:1 properties:3 o:5 essential:1 probabilities:4 ensure:5 efforts:1 lieb:3 soc:1 dilemma:1 presence:1 wineland:2 bound:3 son:1 down:1 lies:2 hermitian:1 amsterdam:1 often:1 support:2 initial:4 transform:1 conservation:10 way:5 was:3 lowest:1 form:8 offer:2 magnificent:1 denoting:2 idealized:3 encoded:1 true:2 surprising:1 dordrecht:2 cosmos:2 ψe:1 adopt:2 inclusive:3 configurational:1 conserved:1 xiii:1 dθ:2 hydrogen:2 check:3 physical:36 eventual:1 locality:5 whereas:1 wavefunction:13 when:5 ne:1 reality:9 role:6 papers:1 test:3 vanished:1 node:1 picture:3 reconsider:1 superposition:5 models:1 preceding:1 felt:1 jones:12 coulomb:3 dφ:2 packets:1 together:2 dρ:4 time:12 observables:3 nuclei:1 quantity:3 restored:1 concept:3 chain:3 global:2 focus:1 osi:3 foundations:2 devoted:1 certainly:1 depend:1 environment:2 finally:2 promoting:1 analogous:2 brown:5 string:1 unfamiliar:1 geometrical:1 entries:4 forked:1 emphasized:1 exact:2 presented:1 discrete:10 upper:1 occurrence:1 discover:1 literature:1 sign:3 theories:30 spectral:8 xψ:2 appear:2 favour:2 current:6 possibilites:1 appeal:2 filled:1 prescriptions:1 unobserved:1 understanding:1 contemplate:1 tangent:2 address:2 along:4 appears:1 change:4 trial:1 poisson:3 ngm:1 studies:5 genuinely:1 useful:3 problematic:1 merely:1 prefer:1 logical:3 additive:1 covariant:1 predictions:4 live:1 scope:2 australian:3 selects:1 theoretical:1 today:1 introducing:1 duality:1 afford:1 apparent:1 ruffini:2 rigid:1 virtue:1 easiest:1 insights:1 valued:10 cat:5 fock:4 values:8 hope:2 following:1 making:2 modifies:1 arrive:2 gravitationally:1 grained:3 choice:3 permutations:2 agent:2 council:1 allowed:1 counting:2 distinguishable:2 occur:2 verlag:1 criterion:1 pure:3 parameter:1 divides:1 map:1 product:2 huge:1 may:38 applications:1 4th:1 data:2 compatibility:2 stress:1 natural:9 remember:1 whenever:2 explicit:5 ordinarily:1 cosmology:6 provide:1 so:17 sa:1 talk:1 typical:3 canberra:1 nucleon:1 constituents:1 entity:1 course:1 experiments:2 differs:1 equip:2 cold:1 pointer:5 observational:5 solitary:3 thank:1 interesting:3 coordinates:2 forms:1 main:3 correspondence:10 non:23 etotal:3 evolution:3 introduce:7 scaling:2 identically:1 nov:1 now:14 discuss:2 term:6 drop:1 instability:2 weighted:1 ed:4 happen:1 monitors:1 shown:3 readouts:1 space:30 greeks:1 furthermore:1 lagrangian:8 seriously:1 dominate:1 viable:1 reformulation:1 theory:66 possibility:2 treatments:1 lump:1 advance:2 language:1 transition:4 motion:1 thing:1 place:6 massive:3 suffice:1 first:7 origin:1 xi:6 xn:8 symmetry:1 conform:1 reductionist:1 variables:2 approximate:2 long:2 suspended:1 open:4 affords:1 size:2 given:6 necessarily:1 encourages:1 chem:1 structures:2 gives:1 continuous:3 x1:8 representing:2 than:1 intrinsically:1 unfortunately:1 accordance:1 require:2 susan:1 modelled:1 were:3 outcome:2 decompose:2 pre:1 fork:2 addressing:1 ann:4 argument:3 generalization:1 13th:1 say:1 recover:6 occupied:1 any:10 symmetrized:1 lumps:3 aside:1 ideal:2 potential:17 idealization:1 forming:1 objective:12 begin:1 trace:1 cordoba:1 track:1 algebraic:1 importantly:2 rationale:1 pair:3 nonlinearity:14 considered:2 later:3 kozameh:1 beables:5 laws:8 precise:1 show:2 atom:2 obtains:1 imagined:1 ground:4 gulf:1 histories:1 analytic:1 only:17 black:1 thompson:1 coherences:1 legendre:1 viewpoint:5 expectation:2 simplistic:1 cannot:1 2mj:1 2mi:2 clearest:2 differentiating:1 hinges:1 yield:1 summary:1 scientist:2 scott:1 ignored:1 physically:3 j1:1 relative:2 namely:2 ignores:1 unaltered:1 concern:1 invoked:5 eigenfunctions:1 ways:2 excitations:1 review:3 definite:1 functionals:2 behind:2 between:4 reproducible:1 diagonalized:1 screen:1 jn:1 concentrate:2 jj:1 virial:1 embraces:1 reaction:1 successes:1 many:31 according:3 contract:1 embedding:1 expression:1 mann:3 among:7 d35:1 characterization:2 lagrange:2 decohere:1 caricature:1 mark:1 workshop:2 combined:1 abstract:2 indirect:2 restrictions:1 offered:2 observers:3 observe:3 external:6 diffuse:1 those:3 pilot:1 case:7 chap:1 situation:1 coupled:3 metric:2 motivated:1 binary:1 different:7 verified:2 reminded:1 admit:1 same:3 arguments:2 events:3 status:1 extended:1 assigns:1 closest:1 singapore:1 entanglement:2 paradox:2 invariance:4 electromagnetism:8 supports:1 modes:1 macro:3 no:14 severe:1 without:6 solve:3 coordinate:6 model:7 dimension:1 justify:1 manifold:1 being:3 generally:7 guided:1 rest:1 aspect:1 guides:1 presumption:1 legitimately:1 thinking:1 seems:1 except:2 instrument:3 treatment:11 eigenstate:2 momentum:2 real:12 aspects:1 eigenfunction:1 represents:2 read:1 replaced:5 early:2 preference:2 world:7 ruled:2 particle:27 collective:6 serves:2 discarded:1 either:2 characterizes:1 stationary:4 reduced:11 obstruct:1 reidel:2 intervene:2 competition:1 deduce:1 specified:1 a10:1 provided:4 dimensions:3 eiθ:1 toto:1 extensively:1 conservative:1 partials:1 critical:4 decomposition:1 provides:2 measuring:3 assembly:3 scientific:1 power:1 wavefunctions:7 notable:1 broken:2 meets:2 found:4 stong:1 conducting:1 central:3 smear:1 discussed:1 meaning:1 practical:3 greatly:2 act:2 cambridge:1 communication:1 speculates:1 references:1 determine:2 einstein:7 operator:7 nowadays:1 intervention:1 her:1 assumed:1 there:15 dispersion:7 stars:1 decisive:1 assumes:1 complete:7 newtonian:13 jul:1 applying:1 flato:1 minkowski:1 quantitatively:1 assume:1 expect:1 ag:4 conundrum:1 certain:2 describe:9 am:2 general:14 examine:3 associating:1 postulating:1 formulation:1 again:4 ideally:1 stationarity:1 field:33 spatial:1 mathematics:7 unobservable:2 separate:1 thirring:2 subsume:2 important:2 queensland:1 d24:1 d26:1 inhibited:1 mass:9 parallelism:2 resembles:3 decoherence:6 original:1 represent:1 consider:10 founded:4 scalar:4 generalize:2 adhere:1 content:4 preserves:1 remarkable:1 extraneous:1 spirit:1 program:2 stochastic:3 norm:1 subtleties:1 straightforward:1 returning:1 very:8 plausibility:1 interpreting:1 condition:7 treating:1 leads:2 hamiltonian:11 t2:5 applicable:1 t1:5 large:1 small:1 past:1 pass:1 further:6 haag:2 canonical:4 bilinear:1 what:6 nonlinear:55 brackets:1 section:3 associate:2 mitter:1 version:2 method:4 contrast:1 component:1 behaviour:7 ansatz:2 concluding:1 ascending:1 equations:19 search:4 inspired:1 allows:1 experience:2 prior:1 pick:1 action:6 options:1 via:18 followed:1 family:4 vii:1 ask:2 thought:1 research:1 select:2 readily:4 subsumes:1 proceed:1 distinct:2 charge:2 ψj:2 a50:1 mcclelland:1 qcd:1 taken:2 entails:1 more:3 flat:1 gm:1 operators:7 instrumental:3 tested:4 particular:1 known:4 projective:3 endpoint:1 quantized:8 recall:3 equation:24 canonically:4 cosmological:3 states:11 numbers:3 arise:1 exclude:1 species:1 g2:1 information:2 respective:1 goal:2 rather:2 maps:1 simplicity:2 intended:1 communicating:1 wiley:1 derived:2 mapping:3 sophistication:1 fe:2 waves:3 develop:2 readout:2 resemble:1 onto:1 spectra:1 departure:1 perhaps:3 extrapolation:1 negligible:1 fundamental:8 exclusions:1 september:1 soon:2 paper:2 through:6 existence:3 kinetic:2 kibble:9 avenue:3 its:17 environmentally:1 energies:2 solving:1 boson:1 microscopic:1 systems:4 bypass:1 differed:1 schrödinger:2 argentina:1 might:7 alter:1 good:1 return:1 number:6 framework:3 oxford:2 easily:2 2r:2 always:5 level:15 d3n:22 micro:6 inequality:1 radial:1 2m:8 2n:1 characterized:1 referred:1 breakdown:1 formulate:1 energy:19 reduce:3 idea:4 engaging:1 connect:1 measurement:12 quantum:80 operatorial:1 beyond:2 item:2 since:18 denotes:1 acting:1 hill:2 induced:1 issue:1 localization:7 difficulty:1 imagine:1 put:1 earliest:1 beginning:1 generate:2 recast:1 just:10 persists:1 enforce:1 consequence:1 major:1 probability:5 relate:1 thereafter:2 reflected:1 done:1 construct:5 differ:3 introduction:2 leading:1 5th:1 least:3 assumption:5 passed:1 scheme:3 recovered:1 too:1 option:4 needle:1 immediate:2 appreciation:1 part:2 jordan:2 differentiate:1 schr:29 separability:1 kind:2 critically:1 double:1 aims:1 annihilation:1 determined:4 pairwise:1 fˆ:3 falsification:1 treated:2 motivation:1 outstanding:1 electrodynamics:3 conjugate:4 elsevier:1 null:2 dynamics:24 lie:2 generalizes:2 lim:1 self:45 reliance:1 onset:2 empirically:1 internal:1 generalized:5 analogy:2 finding:1 commentary:1 play:2 albert:1 most:6 experiences:1 significant:1 extremely:2 clear:4 traditional:1 exp:2 physics:32 lying:2 tenet:1 relation:1 find:3 causality:2 dividing:1 1994a:4 iet:1 brisbane:1 factor:1 his:6 notation:1 dependent:2 zurek:10 closely:1 during:1 reprint:1 resolve:1 continuum:35 arxiv:1 doubled:1 investigate:1 gell:3 locating:3 redefine:1 set:8 achieved:2 plausibly:1 plausible:1 see:16 individual:3 gravitation:15 ritz:1 conditions:10 available:2 a40:1 attention:2 vanishing:1 remaining:2 both:7 prescription:5 quantization:5 sensitive:1 connection:1 context:2 whole:5 experimental:4 bell:18 simple:8 asymptotically:1 dimensional:6 simply:2 ensures:2 described:2 due:6 laplacian:1 pb:2 reduction:4 naturwiss:2 coarse:14 collected:1 ph:1 meeting:1 lett:3 wheeler:1 gas:1 demand:8 gausterer:1 microworld:1 replaces:1 conception:2 look:8 expanded:1 empirical:3 while:2 superposed:1 guide:3 resolved:1 unitary:1 vol:1 binding:1 encountered:2 reads:1 rid:1 currents:3 around:4 bollinger:4 grant:1 higher:1 development:1 weinberg:11 suggestion:1 levels:3 purpose:2 necessity:2 aggregate:1 recent:3 finesse:1 gsw:1 analysis:1 obviously:4 concrete:2 consistency:5 speculative:1 comprise:1 eigenenergy:1 notional:2 atomic:1 questions:1 using:6 elect:1 alternative:5 source:4 theorem:3 relevance:1 mod:2 transformation:1 euler:2 australia:1 demands:4 couple:2 game:1 entangled:5 pacheco:1 helpful:1 imposed:2 follows:2 interestingly:1 manifest:2 mcgraw:2 reduces:1 mathematical:7 methods:2 creation:1 some:14 back:3 strongest:1 scale:14 describing:3 measurements:3 novelty:1 integration:4 friedberg:4 behave:1 proc:3 contrasting:1 jumps:2 agreement:1 step:3 santa:1 δg:2 hilbert:3 constraint:2 tracing:1 block:2 into:16 within:11 appropriate:3 zuber:4 primarily:1 statistics:3 fluctuate:1 question:6 specifically:1 bosons:3 sections:2 elsewhere:1 properly:1 delta:1 subsidiary:1 line:2 observation:7 directed:1 characteristic:1 stumbling:2 up:1 us:2 sum:3 fluctuations:2 similar:5 called:1 associated:2 defined:5 detectors:1 transl:2 single:6 formalism:8 defines:1 heinemann:1 analyticity:2 points:3 department:1 confine:2 elements:2 generates:1 gross:3 problems:5 lucia:1 generated:1 sides:2 structure:6 ago:1 antecedent:1 independently:1 algorithm:2 required:1 graining:11 reprinted:5 introductory:1 once:5 partial:2 edn:2 results:4 existing:1 enjoyable:1 gf:1 go:3 psycho:2 simon:3 deterministic:1 stable:1 microscopically:1 include:5 indicating:1 presently:2 outside:1 implicitly:1 wave:19 reinterpret:1 electron:2 entire:3 notes:1 hartle:3 dealt:1 eigenvalues:1 optics:1 noted:2 jump:1 subtle:1 copenhagen:26 plays:1 unavailable:1 apparatus:1 morse:2 expressed:1 consistently:1 3n:5 3e:1 body:37 led:2 lee:1 degree:1 jointly:1 identifications:2 objects:1 consideration:3 deduced:1 remark:1 indivisible:1 involved:1 larger:2 leaving:1 suggests:1 resulting:1 submerged:1 guidance:2 composed:4 examining:2 showing:1 formulated:3 app:1 addressed:1 condensates:1 apply:1 causal:1 standing:1 superpositions:2 commun:3 remains:8 few:4 eds:6 totality:1 panel:3 reflects:1 becomes:6 normalized:1 koonin:3 discreteness:1 iii:1 entangle:3 ρj:2 obvious:5 freedom:1 meet:2 control:2 continuity:3 process:5 inaccessible:1 high:1 effectively:1 something:1 sought:2 invoke:1 sit:1 precessing:1 inaugural:1 evidently:3 frontiers:1 sin:2 stand:2 superluminal:1 philosophy:2 factored:1 computations:3 gleiser:1 realizes:1 asserts:1 subsequently:1 wigner:4 meter:1 interpreted:5 including:1 parameters:1 chosen:2 masses:1 relativity:6 h2:1 itano:2 choose:3 instruments:1 derivative:1 defining:1 greater:1 orthodox:2 material:1 determines:1 outlines:1 dirac:8 university:1 traced:2 identified:1 magnitude:1 uninteresting:1 constraints:1 homogeneous:1 elementary:5 static:1 our:7 transitions:1 nonlinearities:5 special:3 out:8 respects:1 kerman:3 matrix:4 defend:1 rev:11 reformulate:1 lecture:1 technically:1 cause:1 math:3 interactions:11 diagonal:6 surely:1 collection:1 interaction:10 geometry:2 determining:1 could:6 times:1 hence:9 phil:1 ancient:1 unknown:1 condensate:3 system:10 adopted:2 their:11 fermions:1 explanation:2 exactly:1 environmental:2 adjusts:1 constituent:1 july:1 dynamical:5 colleagues:1 holland:1 penrose:7 isolation:3 measured:1 distinguished:1 exhibit:3 fail:1 enforces:1 need:8 st:1 apparently:2 iφi:1 viewed:2 mappings:1 gravity:17 mechanism:5 instance:5 cosmical:2 accuracy:1 heisenberg:4 allow:1 device:3 intrinsic:2 class:3 afresh:1 stronger:1 sciama:1 absurd:1 constrain:2 normally:1 fact:2 selection:1 supported:1 anyway:1 purely:3 principal:1 based:3 knowledge:2 commutators:1 entangling:5 should:3 entities:2 ambiguity:1 indeed:4 employed:3 isham:3 local:3 achieve:2 beable:1 means:6 familiar:11 joint:1 aforementioned:1 gm2:3 processes:2 densities:2 fixes:2 contain:1 fixed:3 view:3 predictive:5 requirement:1 computed:1 correlations:4 packet:4 interacting:1 participant:1 state:14 difficulties:5 closed:5 invariant:1 boundary:3 sole:1 labelled:2 importance:1 physicist:2 hypothesis:7 key:5 precious:1 configuration:18 problem:10 bonazzola:1 observable:21 interpretations:2 instant:1 limits:1 freely:1 taking:4 gilbert:2 equal:2 attributed:1 etc:2 hψ:1 figures:1 bristol:1 otherwise:2 comment:2 relevant:1 cf:4 decreases:1 respect:3 copies:1 poured:1 treat:2 proposal:1 define:3 corresponding:7 route:2 sufficient:1 cos:2 bulk:1 ensuring:1 c2:1 present:9 prospect:1 novel:1 unlike:4 value:1 will:10 determinism:3 vi:1 thus:27 quantize:1 examined:1 demanded:1 compactified:1 φr:7 generic:2 geometrization:1 cross:2 parts:7 wavepacket:1 φi:6 finite:2 practice:2 infinity:1 absorb:1 upon:30 effect:4 iop:1 frequently:1 identity:1 off:1 fully:4 nevertheless:2 well:5 bohr:8 bohm:3 barut:11 insurmountable:1 sets:1 firstly:2 position:2 usual:5 1994b:3 less:1 obtain:15 sources:3 underlying:1 years:1 localize:1 momenta:1 macroscopic:7 gmi:3 conjugates:1 density:19 point:7 falsifiable:1 combine:1 attractive:4 beryllium:1 identical:4 tests:3 fluctuating:2 fate:1 unseen:1 press:6 immediately:1 necessary:2 like:8 lost:1 exploiting:1 δt:2 δm:2 δh:15 δi:10 become:1 therein:1 because:3 qed:7 classical:32 alive:1 neglecting:2 happens:1 avoid:1 philosopher:1 leap:1 does:3 assuming:2 locate:3 journal:1 pp:11 clarendon:1 although:7 imaginary:3 stage:2 gained:1 about:4 extension:1 universe:6 introduces:1 dependence:1 compatible:5 introduced:2 equally:1 own:2 previously:3 functional:9 been:3 mere:1 utility:2 additional:1 transfer:1 function:2 north:1 but:17 neutral:2 construction:2 bub:2 he:2 made:3 compute:2 whether:1 gravitational:21 variations:1 placed:2 limit:5 distribution:1 display:1 mechanics:9 int:1 recognize:4 universal:3 linearity:2 shooting:1 approximated:1 functions:5 percent:1 detail:1 other:7 quantities:7 conclusion:2 june:1 ultimately:1 foil:1 inspiration:1 coupling:3 persistent:1 rule:1 indirectly:1 unspeakable:1
|
quant-ph9507002.txt |@word represent:1 concept:1 partial:4 consider:3 funct:1 rev:4 global:1 blanchard:4 focus:1 existing:1 leads:1 perturbations:1 adjustment:1 contributions:2 compact:7 excludes:1 certainly:3 careful:1 const:1 ginibre:1 irrelevant:1 diffusions:1 uniqueness:4 those:4 excluded:1 under:4 stochastic:6 nodes:7 include:1 worth:1 norm:1 ingredient:1 interacting:1 belonging:1 preserved:1 g0:1 very:1 brownian:2 rise:2 intriguing:1 iii:2 choice:4 every:7 should:1 fall:1 verh:1 emphasized:2 fakult:1 encounter:1 gg:1 solves:3 level:1 issue:5 notes:1 developing:1 t2:33 solution:30 try:1 solved:2 interpolating:5 small:1 eigenvalues:1 markov:9 specified:2 enforce:1 degeneracy:9 prevent:2 employing:1 lecture:1 consistent:4 measurable:3 literature:1 sign:1 jump:1 fold:1 likely:1 displays:3 pass:1 further:1 dynamics:12 implemented:2 jamison:1 canonical:1 even:7 established:2 nonlinear:8 stands:2 celebrated:1 lαn:1 current:1 consistently:1 version:1 gn:1 above:10 sup:1 new:2 principal:1 method:1 ρt:8 make:1 philippe:1 nonlinearly:2 whose:1 symposium:1 respectively:4 pushing:1 equals:1 here:4 behaviour:2 met:1 simon:4 them:1 address:3 path:8 standard:1 equations:15 implicit:1 handle:1 dividing:1 forum:1 restrictive:1 institute:2 involved:4 study:2 allows:5 contradiction:1 accomplished:1 resulting:3 krohn:1 pick:1 usually:2 decouple:1 suitable:2 involves:2 boundedness:1 via:1 l1loc:2 investigate:1 elaborated:1 marginal:2 merely:1 limt:1 replace:1 first:10 coinciding:1 addressed:1 sgn:1 apply:1 glance:1 finiteness:1 establish:1 planck:4 select:1 derivatives:1 conventional:3 henri:1 would:7 commun:2 remains:1 positive:22 differentiability:2 negative:2 definition:4 next:2 scenarios:1 few:1 live:1 therefore:2 m2:1 generators:2 associated:11 mckean:1 type:3 theoretical:3 more:5 separated:2 difficulty:1 inaccessible:4 th:2 relax:2 started:1 apparent:5 odinger:27 validity:2 indispensable:1 berlin:2 everywhere:8 uniformly:3 particular:8 known:10 cases:3 hold:2 preserving:1 analogous:1 must:3 involve:2 springer:2 bernstein:1 permits:1 recall:3 equation:13 work:1 oscillator:1 reads:2 reproduce:1 mt:5 labeled:1 obstacle:3 obvious:2 publications:1 carmona:1 sci:1 conformity:1 example:8 define:3 impose:1 pushes:1 give:2 process:31 significance:1 arise:1 share:1 purposes:1 ann:7 sample:17 indicates:1 identified:1 assumptions:1 numbers:1 degenerate:2 allowed:4 sought:2 dxf:1 times:8 conversely:1 occur:1 verlag:2 itˆo:1 respective:9 notation:1 deserves:1 destroying:1 robinson:1 discussion:8 holds:8 utilize:4 ilin:1 write:2 how:1 nontrivial:3 modification:1 criterion:2 get:1 instead:1 field:2 happens:1 badly:1 kalashnikov:1 mat:2 singular:11 may:3 use:1 singularities:2 needs:5 olkiewicz:4 barriers:1 inst:2 physik:1 representations:1 wave:1 fixed:1 constants:1 namely:3 natural:2 duke:1 beurling:2 financial:1 explicit:2 chapman:1 st:1 interpolates:1 provide:1 integrability:1 green:8 block:1 fundamental:16 suggest:1 sc:1 looking:1 order:2 se:1 belong:1 interpretation:1 2md:6 considerations:1 indeed:2 over:1 spectral:3 mainly:1 major:1 interpreted:1 course:3 wiener:20 paper:2 through:2 looks:2 statistical:3 mentioned:2 existence:8 still:1 its:9 before:3 neither:1 exclusion:4 decay:1 chosen:4 interesting:2 temporal:1 solving:1 exhibits:1 ds:1 forms:3 usp:1 permanent:1 choose:3 bypass:1 persist:1 ours:1 main:1 might:3 subtlety:1 associate:3 non:5 motivated:2 than:1 processes:10 introduce:3 functional:4 framework:3 touching:1 repulsive:3 they:8 hands:1 anticipates:1 feature:2 singularity:9 now:2 realize:1 nor:2 qt:2 2t:1 represents:1 february:1 equality:1 2q:3 always:2 university:4 hamiltonian:2 2x:2 confining:4 oleinik:1 theory:7 academic:2 l2:5 breach:1 realise:1 each:4 crossing:5 inherent:1 universit:1 higher:1 decreasing:1 side:3 homogeneous:2 prohibit:1 domain:6 en:3 weight:1 fairly:1 ed:3 eg:1 journ:1 related:4 equivalence:1 f0:1 extended:2 expect:1 measure:19 quantum:6 our:19 approximated:1 beyond:1 event:1 special:1 out:3 ezawa:3 carlen:2 space:3 restricted:3 robert:1 since:6 crucial:1 discouraging:1 denotes:2 increase:1 replacing:1 investigation:2 formula:5 rn:1 ref:5 occurs:1 math:14 common:1 exploiting:1 after:1 linear:3 barrier:5 state:9 inessential:1 discontinuity:1 divergence:1 inapplicable:1 free:5 quite:3 completely:1 surely:1 york:2 intermediate:1 publ:1 anal:1 additional:2 dirichlet:5 r1:35 hg:2 authors:1 lincei:1 could:1 transition:6 success:1 nonnegative:14 motion:1 turn:1 expecting:1 gordon:1 leading:1 hence:10 generalizations:1 support:5 origin:1 intuition:1 there:12 features:2 probability:21 urich:1 xc:1 variables:2 number:4 peculiarity:1 another:3 comprises:4 unattainable:6 open:9 xt:3 received:1 given:6 necessarily:3 unknown:2 adjoint:8 inhomogeneous:1 system:24 least:3 pinned:2 their:10 quadratic:1 zeros:6 too:2 normalization:1 postulate:1 gives:1 originating:2 tool:1 continuous:25 proving:1 φsn:3 za:1 sizable:1 assumption:4 part:1 somewhat:1 centrifugal:10 x2:48 x3:1 eliminated:1 x1:1 completes:1 specify:1 pisa:1 gradual:1 qs:1 princeton:4 lnρ:1 older:2 imply:3 reconstructing:1 appealing:1 classes:1 supposed:1 were:3 providing:1 fits:1 motivation:1 rend:1 close:1 ikeda:1 respecting:1 boston:1 correction:1 argument:1 dynamically:1 substantial:1 tω:3 need:3 been:2 seem:3 constrained:1 clearly:1 viewed:3 paths:19 hopelessly:1 zero:9 depending:1 calogero:1 aside:1 thorough:1 definite:1 potential:15 obviously:3 interior:2 so:9 coincide:1 fukushima:1 kac:25 formulas:1 austr:1 unless:1 shall:1 friedman:1 measures:1 reach:2 birkh:1 most:1 diffusion:12 smoluchowski:2 but:9 pair:2 justification:1 probabilistic:2 involving:1 singled:1 picture:2 parisi:1 observation:1 considered:7 acknowledgement:1 traditional:2 feynman:25 accounted:1 principle:1 exp:60 kt:2 realised:1 germany:1 away:3 fact:2 impression:1 shepp:3 axes:1 phenomenon:4 restore:1 random:2 katata:1 analogously:1 appearence:1 3x2:1 spaces:1 solutions:25 kbn:1 data:23 availability:1 ground:9 chaos:1 zambrini:1 based:1 scuola:1 parameters:1 semigroups:1 eigenspace:1 situations:2 basel:1 outside:1 considerable:1 terminal:2 only:6 explicitly:1 candidates:1 x4:8 matters:1 developed:2 parabolic:34 integrable:4 mechanics:3 hamiltonians:1 local:1 combe:1 achieve:1 continuity:7 do:4 insight:1 hit:1 subspaces:1 viewpoint:1 means:6 dependent:3 familiar:4 simplest:1 overall:1 assumed:1 variate:1 geb:2 cannot:2 dz:1 streit:1 dx:14 dy:19 dt:2 finally:1 areas:3 hall:1 evolution:7 dewitt:1 densities:8 nicely:1 fields:1 arxiv:1 comprising:3 factorization:2 bad:1 difficulties:1 conflict:1 contain:1 including:1 ωs:3 view:5 kernel:22 set:22 modulo:1 confine:1 exists:1 achieved:1 freidlin:1 kolmogorov:2 generalisation:1 lett:2 see:4 lebesgue:4 result:4 effectively:1 terms:4 lng:1 dµ:7 points:4 appear:1 invoked:1 exponent:1 inappropriate:2 nondegenerate:1 subsequent:2 positivity:2 consequence:1 diverge:2 boundaries:7 importance:1 written:1 various:1 closed:7 between:5 propagated:1 boundary:27 conditions:5 taniguchi:1 x22:1 available:1 notice:5 never:1 recently:1 producing:1 extend:1 nature:1 premises:1 attention:2 weak:1 however:9 vanishing:2 concentrate:1 key:1 analyzed:1 come:2 aronson:1 infinity:2 motivations:1 both:8 hits:1 enables:1 last:1 reverse:2 0t:3 according:1 display:1 mathematical:2 propagation:4 admit:3 densely:1 context:6 oshima:2 contribution:3 whole:5 comes:2 otherwise:1 reside:1 among:2 relevant:2 extent:1 point:4 others:1 cf:5 ce:2 dimensional:3 distinguish:1 ii:2 simply:1 invariant:3 right:2 consideration:1 2t2:2 moreover:4 cv:1 cu:1 considering:3 kernels:17 second:1 capable:3 addition:2 prentice:1 create:1 locally:4 lα0:1 due:5 laplacian:1 appears:2 stora:1 interest:2 basic:1 expected:1 ph:6 algebras:1 sufficiently:3 pl:2 location:2 ergodic:2 arises:2 corresponding:11 relaxing:1 restrictions:3 nagasawa:2 subspace:1 prospects:1 rescalings:1 relevance:1 understand:1 proven:1 demand:4 receive:1 instant:5 albeverio:1 denote:1 fokker:4 høegh:1 present:5 case:22 exception:1 inquiry:1 bρ:5 subsets:1 pacs:1 nski:1 value:4 choices:1 will:1 invoking:1 while:13 replaced:1 stopping:1 situation:1 nonstationary:1 property:5 procedure:4 wroclaw:4 detailed:1 attains:1 coupled:3 almost:9 refs:5 communicating:2 thus:6 surprisingly:1 conditioned:1 respected:1 disjoint:2 regularity:1 itself:5 exterior:2 weakest:1 limit:2 orthogonal:1 vanish:4 inf:1 piotr:1 containing:1 anymore:1 grant:2 generic:2 things:1 granted:3 formulations:1 problems:1 connection:4 same:7 any:13 rules:1 complex:2 quant:2 arguments:2 units:1 physical:1 verw:2 composition:1 interpolation:1 independent:5 ball:1 singapore:1 upon:1 nj:1 hand:7 action:1 moment:1 auser:1 necessity:1 potentials:9 totally:1 cross:2 identity:2 destruction:1 pures:1 prescribed:2 fourier:1 schr:27 3x:1 mention:2 expression:4 poland:2 no:5 well:11 analysis:7 double:2 intervals:1 concrete:2 severe:3 without:3 solve:1 components:4 sets:9 redistribution:2 arising:2 dimension:2 left:6 comment:1 world:1 generalization:1 confined:1 criterions:1 vanishes:5 assigned:1 press:3 underlying:1 identify:2 questions:1 klauder:8 touch:3 followed:1 alternative:2 yet:1 previous:7 adv:1 preprint:1 generator:6 density:15 grenoble:1 regarded:1 conclude:2 had:2 except:4 exclusively:1 transparent:1 add:1 valid:2 transformed:1 garbaczewski:6 innocent:1 theorem:1 dµ0:5 input:2 semigroup:7 exit:1 polon:1 real:9 acta:1 aspects:1 eigenfunction:1 eigenvalue:6 read:2 evaluate:1 survival:1 results:2 possible:2 harmonic:2 possibly:2 game:1 indicative:1 know:3 confined:1 immediately:1 emergence:2 unique:9 stable:4 madelung:2 englewood:1 necessary:2 like:3 semi:1 identifying:1 follows:4 0c:1 temporally:3 admitted:1 separately:1 continue:1 integrals:1 arbitrary:3 multiplicative:1 output:2 stationary:1 quantal:5 accessible:1 because:3 deal:4 sequence:2 conditional:3 some:6 searching:1 born:1 strongest:1 zheng:1 acad:1 examples:1 b2:1 respect:4 duration:1 finite:5 establishing:1 nonzero:4 gradually:1 dimensions:1 lead:1 demonstrates:1 avoid:1 separate:1 integration:4 per:1 conservative:2 specific:3 does:10 decomposition:2 eliminate:1 provides:1 assuming:1 bratteli:1 proc:1 prob:1 eigenfunctions:2 differentiable:2 elucidate:1 bi:1 nauk:1 evolutions:1 step:2 bp:1 although:1 2m:1 properties:3 earlier:1 about:1 extension:2 instantaneously:1 meaning:1 o:2 nonvanishing:4 distinct:1 regular:4 stand:1 connected:5 introduced:1 consequently:1 other:4 automatically:2 subset:11 hypotheses:1 own:1 convergent:2 markovian:2 previously:2 communication:4 into:6 within:1 integral:13 bound:1 lα1:1 nothing:2 appropriate:7 bielefeld:2 references:1 selected:1 wahrsch:1 operator:4 harrell:1 subm:1 technically:1 seen:1 statistics:2 formulate:1 area:4 nodal:1 strictly:19 initial:13 long:1 strict:2 borel:4 manifested:1 way:2 forward:5 analyze:1 was:6 osaka:1 opens:1 function:30 trivializes:1 form:4 attempted:1 relaxed:1 identification:1 jul:1 volume:1 repeated:1 construction:2 link:1 intern:1 russian:1 line:3 true:5 borders:1 dist:1 he:1 vol:3 persisting:1 made:1 wise:1 instructive:2 inside:1 smooth:1 up:3 us:18 ur:1 below:3 un:1 complications:1 fluctuations:1 problem:29 invoke:1 called:2 poincare:1 strongly:1 diverges:1 constant:1 reconcile:1 ln:6 certain:5 abstract:1 combining:1 condition:4 covers:1 general:7 proves:1 exist:1 rule:1 research:1 encompass:3 formalism:2 indirect:1 constructed:2 again:2 functions:22 repelling:1 eventual:1 nonetheless:2 amounts:2 deserve:1 when:3 defined:12 invalid:1 arctan:8 field:1 priori:3 role:1 neighbourhood:3 nat:2 spatial:10 test:1 mathematics:1 defines:2 ny:2 node:9 polar:2 differential:3 relat:1 suppl:1 generates:1 parametrix:1 setting:1 drift:7 disclosed:1 2n:2 generated:1 bounded:9 allowing:2 variable:1 sides:1 building:1 implies:6 longer:1 assume:4 physics:5 dτ:21 interval:6 together:1 original:1 4n:1 scientific:1 nelson:1 time:27 appl:1 backward:1 having:1 once:2
|
quant-ph9507003.txt |@word consider:10 remarkable:1 mcgrawhill:1 interference:2 equalities:1 reversibility:1 results:1 leads:4 roy:1 ge:1 follow:1 ˆj1:1 contributions:5 compact:1 inverse:1 calculate:3 xxii:1 bx3:3 eˆ:4 presents:1 contours:1 under:2 stochastic:2 resources:1 84b:1 case:2 supported:1 amplitudes:3 hibbs:1 very:1 springer:1 wave:1 difference:3 exact:2 deformations:2 condition:8 four:1 hamiltonian:5 t2:1 solution:9 t1:5 solved:2 2b4:1 noted:1 upper:1 force:3 takhtajan:1 direct:2 approximation:3 zero:7 differential:3 theories:2 quite:1 linear:3 even:3 aim:1 what:1 nonlinear:2 d2:2 section:2 probably:1 guaranties:1 ˆe:1 above:2 new:14 ˆj:3 method:6 coefficient:1 lee:2 prescriptions:1 neveu:1 here:5 following:6 cylindrical:4 possibility:2 concluding:1 consideration:1 along:2 sine:1 equations:4 change:1 deduced:3 parameters:1 institute:2 losses:1 allows:4 experience:1 φr:5 suggests:1 published:1 action:10 opinion:1 linearised:1 suitable:1 cancellation:1 bx2:3 useful:6 projection:1 explained:1 plenum:1 sliced:1 total:10 reφ:3 causal:1 use:6 ht:11 asymptotic:4 would:1 sake:1 contains:2 ej:1 suppl:1 e0:1 classically:3 nucl:1 ψn:3 therefore:3 memory:1 taken:2 doubling:4 more:2 flat:1 formally:3 becomes:3 georgian:1 stable:1 introduces:1 correspondingly:1 rigid:1 eθ:5 breach:1 known:2 must:7 account:2 ih:10 science:2 equation:8 work:3 cancellations:1 extremum:1 remain:1 fock:2 values:1 canonically:1 im:1 my:1 example:1 subnuclear:1 proof:1 give:3 calculation:5 expanding:3 choice:2 arise:1 high:1 sphere:3 minimum:2 performed:3 want:2 sense:2 dxe:1 counting:1 axis:4 information:1 regularization:2 rescaling:2 end:4 recursive:1 get:1 xˆ:4 feature:1 how:3 nontrivial:1 surely:1 instead:4 verlag:1 explains:1 e2i:1 simplicity:2 product:3 de:1 description:3 may:6 after:2 dx2:1 dx1:1 complicated:1 isc:3 wrong:1 plane:3 waves:2 destructive:1 data:2 times:1 quasiclassical:7 dynamical:2 ss:1 spectra:1 correspond:1 so:5 sc:13 representation:3 order:2 operations:1 help:1 over:18 zichichi:1 paper:1 through:3 looks:5 omitting:1 mentioned:1 jθ:6 satisfies:1 excitations:2 ima:7 group:4 symmetry:2 img:1 maps:1 chosen:2 interesting:3 coordinates:5 absence:1 offers:1 degrees:5 systems:3 mail:1 hidden:3 main:1 h0:5 them:1 combination:1 irreversible:1 propose:1 peculiar:1 introduce:6 slicing:1 hamilton:2 they:2 half:2 now:3 transparent:1 teller:1 easily:1 term:1 2r:1 sin:4 x21:3 l2:1 2a:2 2b:1 fields:3 2n:1 side:4 mean:2 en:12 ei:4 eh:7 weight:2 2e2:2 series:7 energy:8 hard:1 idea:2 ec:7 expect:1 measure:14 quantum:30 our:8 eq:8 special:2 really:1 living:1 shown:2 matrix:3 space:9 rep:1 since:20 crucial:1 particles:1 re:2 investigation:1 dowker:4 rea:3 dxdp:1 shows:1 foundation:1 i2:1 theory:21 free:3 dtˆ:4 reason:2 cartesian:1 unwanted:1 york:3 usual:1 put:2 zs:3 remainder:1 generate:1 e3:3 e2:3 definition:10 interaction:1 transition:2 keep:1 motion:15 introduction:2 gordon:2 corrections:2 first:2 xj:2 already:1 xo:1 probability:6 xc:28 variables:16 powerful:1 number:1 least:1 another:1 carry:1 impossible:2 given:2 perturbation:17 width:1 unitarity:7 eqs:2 iaa:1 system:3 construct:1 perturbations:4 too:2 statement:4 dt2:1 dt1:2 scheme:1 exponents:2 gives:7 shifted:1 pare:3 kolmogorov:1 calculations:7 mostly:2 academy:1 explanation:1 exactly:1 ime:1 part:2 x2:14 x3:1 x1:15 than:1 dtj:2 colleagues:1 variational:1 determines:4 double:2 second:1 dte:3 final:1 amplitude:6 were:5 bargman:1 result:13 vector:2 fluctuation:1 ann:1 mind:1 spectrum:1 dθ0:1 conjugate:1 curved:3 cumbersome:1 demonstration:1 any:1 irreversibility:2 ax2:3 forced:1 angle:3 mills:2 ideas:1 mechanism:3 note:17 instance:1 potential:2 hasslacher:1 build:1 jacobian:3 green:4 coincide:1 canonical:10 accuracy:1 spectral:1 play:3 measures:1 kam:1 coordinate:9 regular:1 jul:1 formulae:1 phase:10 why:2 2εt:1 especially:1 considered:8 calculated:1 tautology:1 tbilisi:1 feynman:1 points:1 principle:3 exp:23 mechanical:3 dh0:1 physics:5 fact:5 quantity:1 marinov:1 show:5 random:1 spaces:1 map:1 solutions:3 torus:1 trivial:1 find:20 based:2 spite:1 much:1 should:4 analytic:2 only:9 rich:1 postulated:1 integrate:1 integrable:3 local:1 preliminaries:1 do:1 dl:1 closed:2 means:5 dependent:1 between:2 dc:4 ones:1 eiet:1 dx:6 despite:1 dt:17 dr:2 3a:1 dp:2 secondary:1 processes:1 determinants:2 ushveridze:1 conditions:10 arxiv:1 fixes:2 remove:1 inomata:1 propagators:1 noncanonical:1 contain:1 analytical:1 london:1 fixed:3 view:1 set:2 frame:1 hypersurface:2 j1:3 j2:2 observed:1 see:16 sec:9 us:12 discussions:1 jx:1 lnf:1 contour:3 exponent:5 symmetric:1 favor:1 correctly:1 simplest:1 invariant:2 boundary:10 approach:4 x22:3 sections:1 terms:6 str:1 extend:1 nature:2 eˆr:1 however:1 jr:9 jm:1 jh:6 key:1 demonstrate:1 article:3 jφ:6 thank:1 both:2 cos:4 last:2 repeating:1 many:2 taking:2 equal:4 ln:1 connection:2 symplectic:1 retarded:2 contribution:4 expression:5 mechanics:8 conclude:1 simple:4 continuation:1 harmonic:1 insist:1 2i1:1 dimensional:6 d30:1 path:26 moreover:1 considering:2 most:1 transformations:13 basis:1 trajectory:11 extraction:1 reduction:1 describes:6 dtdt:3 xδ:1 ph:1 2i:17 generating:2 adopted:1 corresponding:7 quantities:3 offered:1 gas:1 6n:1 argument:1 external:2 convergent:1 manifolds:3 applied:1 georgia:1 hat:1 conserved:1 arnold:1 will:34 technical:2 p2:3 eie:1 rotator:1 property:1 procedure:1 identical:1 unitary:5 ip:1 ivt:10 canceled:2 ik:1 ij:2 vt:2 ia:1 ie:1 different:1 d10:1 propagation:1 perform:4 demands:1 same:6 shifts:1 complex:1 quant:1 arguments:2 defines:1 independent:1 used:5 singapore:1 i1:1 trajectories:4 effect:2 hand:4 moment:1 purpose:6 infinite:2 changing:1 noticeably:1 kleinert:2 lower:1 acknowledgement:1 disappears:1 well:2 without:1 solve:3 components:1 firstly:2 organization:1 model:3 dimension:1 left:1 world:1 manifold:1 just:1 among:1 sources:6 formulated:1 farther:1 klauder:1 differentiation:1 scattering:1 previous:2 ny:1 point:3 character:1 arctg:2 source:3 add:1 valid:1 transformed:4 lett:2 theorem:4 role:3 guarantees:1 solvable:1 transformation:35 real:6 acta:1 fluctuating:2 aspects:1 desy:1 rev:3 loss:1 iε:6 possible:2 know:1 using:5 unique:1 advanced:1 insert:3 necessary:1 like:6 particle:2 follows:3 performing:2 unnecessary:2 δj:2 integrals:13 arbitrary:2 become:1 δe:2 stationary:2 reduced:2 mathematical:1 right:3 methods:3 classical:14 lagrange:1 some:1 austr:1 examples:2 choosing:1 proper:1 sufficient:3 simplectic:1 lead:4 operators:1 avoid:2 integration:5 manipulations:1 does:2 decomposition:2 eliminate:1 expressing:1 borel:4 proc:1 demonstrated:1 inserting:6 faddeev:1 scientific:1 equivalent:3 each:1 continuing:1 expansion:5 step:1 shifting:1 imaginary:1 bx:1 properties:2 hiding:2 extension:2 simplify:2 freedom:6 linearise:1 discussed:3 dependence:2 o:4 essential:1 cancelation:3 a2:2 simplification:1 introduced:1 converging:1 soc:1 eφ:1 statements:1 into:7 integral:21 functional:3 remarks:1 references:1 pathintegral:2 determine:1 sov:1 operator:7 accumulated:1 statistics:1 assumed:1 strictly:1 there:3 start:2 conservation:4 ed:1 hooft:1 was:9 strict:3 iˆ:1 function:17 complete:1 form:6 phenomena:4 but:14 2ht:1 hj:8 ho:1 atom:4 convergence:1 hc:3 true:1 he:1 compute:2 evident:2 up:1 quantitatively:1 dφ:2 limit:1 organize:1 fluctuations:6 problem:19 tricks:1 aa:2 constant:2 conserves:1 introducing:2 defined:6 abstract:1 describe:1 influence:1 general:2 single:1 initial:4 ax:2 duru:2 formalism:6 commuting:1 physical:2 functions:3 dashen:1 differentiable:1 national:1 extract:1 when:1 virtual:6 field:2 unambiguously:5 republic:1 er:4 naive:4 unobservable:1 deviation:2 picture:1 briefly:1 elements:1 intend:1 generates:3 symbol:1 problems:3 deriving:1 meaning:2 important:3 suppression:1 variable:2 structure:3 auxiliary:10 perturbatively:2 starting:2 dτ:1 required:1 4n:1 impossibility:1 reversible:6 time:30 vestnik:1 requires:1 restored:1
|
quant-ph9507004.txt |@word limited:3 saturating:5 consists:2 sci:1 mandelstam:6 whose:4 under:2 worth:1 connects:1 selleri:1 vector:10 levicivita:1 degeneracy:6 miller:1 consistent:1 estimates:1 pulse:1 second:20 rigorous:1 even:3 employ:1 above:5 ˆh:1 new:11 increasing:1 ever:1 ˆn:11 ated:1 notions:1 never:1 here:11 met:2 represented:3 path:16 logarithmic:1 obtained:6 study:2 fourier:4 changes:4 projection:6 plenum:3 replace:2 glance:1 total:3 unit:9 would:4 negative:3 noting:2 call:1 composite:5 δhh:1 odinger:1 berlin:1 excellent:1 must:12 kraus:1 springer:1 characterize:1 work:2 concepts:1 example:14 indicated:2 give:5 relativistic:1 involve:3 degenerate:12 times:2 end:2 provide:3 feature:2 how:6 answer:2 symposium:1 description:3 transforming:2 after:1 diagram:1 minimizes:2 meaningful:1 constants:1 third:2 ultimate:3 correlation:1 operations:1 restriction:3 interpretation:1 office:1 devote:1 diagonalizes:1 over:6 expects:1 xi:1 satisfies:4 before:2 fiz:1 writing:6 better:2 distinguishing:2 fig:2 maximal:1 them:1 combination:2 pegg:1 effects:1 they:8 eigenvalue:11 πre:2 each:6 mean:23 feinberg:1 displacement:29 combining:2 restricted:6 re:8 reader:1 turning:1 linear:2 associate:1 ntr:1 free:5 standard:9 ǫjkl:3 estimate:8 degeneracies:3 ds2:6 isn:1 incorporated:1 onto:3 already:1 restrict:3 illustrate:4 similarly:1 eqs:6 approximately:1 needed:1 compromise:2 too:2 wootters:3 centered:1 uhlmann:2 distance:7 princeton:2 e2iϕ:6 matter:2 sees:1 rao:6 modern:2 mind:2 spectrum:12 seen:2 unaffected:1 seek:3 convenient:4 oriented:1 absorbed:2 forces:1 ˆp:3 though:3 involving:4 phase:44 professor:1 points:1 quantifying:1 sum:4 dot:1 incorporate:1 labels:1 radii:1 gauge:10 d2:2 d3:1 sˆ:2 summarizing:1 integrate:1 do:5 dx:114 dt:16 ds:5 dp:3 runs:1 ˆk:1 fields:1 nα:2 riemannian:2 coefficient:2 observer:2 detection:1 depends:3 result:9 discussions:1 tensor:4 away:3 yet:1 symmetric:4 drawn:2 sorts:1 caves:13 approach:3 terms:13 nature:1 however:9 extent:1 improve:1 cos:8 cot:1 uncertainty:104 arkanihamed:1 variance:30 unm:1 nˆ:1 conference:1 basis:3 three:5 been:3 much:1 interpret:1 interest:3 basic:1 expected:1 tan2:1 helicities:1 quantities:6 arkani:1 worked:1 applied:3 transformation:9 aim:1 fubini:1 suppose:4 viii:1 applies:5 property:12 procedure:2 ix:11 spacelike:2 mexico:2 iv:4 ih:1 im:9 specialization:5 perform:1 make:7 complex:3 quant:1 split:3 avoids:1 dimensionless:2 several:1 independent:8 dǫ:6 hand:1 normalization:5 specialize:1 academic:1 contact:1 quantitative:1 just:1 rotated:6 aside:1 followed:1 rotates:1 eigenstates:33 unique:2 spread:1 transformed:2 opt:1 rescaled:1 advances:2 possible:3 depicts:2 advanced:1 specific:1 steps:2 schwarz:2 arbitrary:11 acad:1 deal:2 truncated:1 dense:1 electromagnetic:2 asking:1 ψx:63 illustration:1 rephase:1 super:2 properties:10 takes:4 dˆ:3 o:5 nonvanishing:1 considerations:3 soc:1 rotations:2 bound:27 rendering:1 hermitian:18 amsterdam:1 tamm:6 physicists:1 way:5 was:1 iˆ:2 form:20 differences:1 removes:1 removed:3 true:1 versions:1 distinguishability:4 achieving:3 discarding:2 abstract:1 covers:1 peres:3 dθ:2 distributions:1 constructed:3 nh:4 nj:7 nl:1 dotted:1 no:19 whereas:1 when:11 vanishes:1 nf:2 reality:1 ny:2 interested:1 role:2 permitting:1 preceding:1 ξn:3 variable:6 dφ:7 interval:8 together:3 time:55 n0:3 observables:2 chain:1 global:25 leads:10 devoted:1 inverse:1 depend:3 environment:2 analogous:3 orthogonal:9 choice:13 annihilated:2 level:1 leave:1 discrete:6 recall:1 equation:7 prevent:1 dealing:1 cosh:10 gibbons:1 appear:1 axes:3 uniform:1 overcomplete:1 appeal:2 boost:6 satisfy:10 burnett:1 tangent:1 cos2:3 address:2 xβ:1 along:8 xα:1 change:4 institute:2 shift:3 vectors:1 accomplished:2 studies:1 useful:4 bounds:2 eiφn:4 covariant:3 positive:2 weizmann:2 permitted:4 going:1 scope:2 associated:6 uffink:4 rehovot:1 apparent:1 cases:1 eα:2 valued:6 cas:1 oscillator:10 labeled:2 values:5 achieve:3 resembles:2 following:3 making:3 trans:1 figure:2 sample:5 allowed:1 rescaling:3 normalize:1 rays:1 requirements:1 discussion:4 xˆ:33 orthogonality:1 chemical:1 till:1 pure:10 optimal:57 parameter:71 displacements:4 edinburgh:1 product:9 may:1 ωe0:2 representations:5 data:10 stress:1 natural:3 dynamical:1 whenever:1 explicit:1 st:1 inform:2 so:8 sn:1 representation:19 indeed:4 pointed:1 displayed:1 raised:1 years:1 course:1 experiments:1 eiθn:1 statistical:9 snα:1 differs:1 still:1 ieee:1 derive:7 group:3 decreases:1 ours:1 non:11 planewave:1 introduce:7 identically:2 now:11 discuss:3 term:4 equality:11 lies:1 drop:3 appropriate:2 possibilities:3 entirely:1 quarter:1 square:5 ei:4 ej:10 ed:1 gaussian:10 γx2:1 approximated:1 eq:58 er:9 ultimately:1 space:31 investigation:2 formula:1 shows:2 theory:20 albuquerque:1 possibility:3 complicated:2 remainder:3 e0:5 milburn:4 hamed:1 derivation:1 turn:3 place:1 first:26 origin:1 simplifies:3 hθ:4 xe:2 specifically:1 directly:3 impossible:1 xp:2 angular:3 city:1 given:24 necessarily:2 gives:2 moscow:1 continuous:3 x2:2 anandan:5 than:4 coefficients:2 wide:1 accordance:1 require:3 decompose:2 generality:1 ann:2 occupies:2 say:1 any:17 efficient:8 ideas:1 note:1 emphasis:1 take:3 timelike:2 coincide:1 multiple:5 replicas:6 xest:22 ordinates:7 multiply:1 inequalities:4 surprising:1 dordrecht:2 adopt:1 typically:1 quantity:5 precise:2 show:5 ratio:2 written:12 only:21 explicitly:3 normalizations:1 get:2 samuel:1 expectation:5 satisfied:6 unimportant:1 cannot:3 nearly:1 symmetrically:1 differentiating:1 regarding:1 yield:1 summary:1 maximum:5 relative:2 considered:6 uncorrelated:1 belavkin:2 ωj0:1 commutation:1 ways:2 review:1 label:4 outside:1 between:8 notice:11 come:1 concentrated:1 many:7 according:3 ωjk:1 expression:6 comes:1 period:4 cancel:1 moreover:3 considers:1 specializing:1 sensible:2 aˆ:7 carruthers:1 direction:2 restrictions:9 optimality:8 irrelevant:4 those:2 case:23 dξ:5 eix:1 single:12 microphysical:1 fiducial:19 eif:30 squeezed:12 situation:1 shepard:1 metric:5 bias:3 different:2 develop:2 same:11 poincar:3 shifts:4 verifies:1 physical:3 status:1 extended:1 closest:1 singapore:1 2mǫ:1 invariance:2 σp:2 modes:9 sssr:1 x0:1 without:6 components:5 manifold:1 being:10 generally:9 speed:1 multiples:1 generator:15 ω0j:1 except:5 improvement:1 treatment:1 eigenstate:2 momentum:24 real:12 aspects:1 represents:2 rules:1 harmonic:9 vacuum:15 world:1 mod:1 particle:3 reduces:6 either:1 reduced:5 specifies:1 specified:1 provided:3 calculating:1 eiθ:3 provides:4 measuring:5 considering:5 biased:1 eiϕ:4 scientific:1 power:1 equivalent:5 biases:1 eiφ:9 sixty:1 lucia:1 central:1 island:1 discussed:3 develops:1 estimator:28 mixed:5 inclusion:2 accounts:2 determine:6 operator:66 removing:1 there:11 start:1 assumes:1 complete:4 regard:1 independently:2 jul:1 trying:1 dissipative:1 applying:1 minkowski:1 assume:4 eschew:1 detailed:1 diverges:1 describe:4 general:23 tˆ:2 associating:1 formulation:1 eralized:1 tedious:1 again:1 completeness:10 deserve:1 field:9 spatial:15 deviation:8 separate:3 includes:1 commutator:1 important:4 bounded:3 queensland:1 quantify:2 resolution:1 original:3 represent:2 schumaker:2 consider:6 lack:2 founded:1 research:1 scr:1 fellowship:1 tr:3 preserved:1 amplitudes:2 straightforward:1 very:2 translations:1 difference:4 condition:32 treating:2 hamiltonian:6 large:7 variances:1 small:4 periodicity:1 zero:9 further:5 canonical:21 what:4 nonlinear:1 sub:1 clock:1 diag:1 section:28 brief:1 contrast:2 component:2 directions:1 equations:2 search:1 antisymmetric:2 naval:1 allows:11 amount:1 periodic:6 contr:1 narrow:2 via:1 shorthand:1 requiring:2 put:1 conventional:5 proceed:5 probabilities:1 ψs:1 contains:1 ψt:5 entails:1 more:4 lowering:1 israel:1 operators:19 corrected:1 particular:8 known:2 foundations:1 science:2 der:1 specializes:1 pioneered:2 specialized:1 stated:1 states:75 unbiased:2 minimum:5 attain:1 sense:2 species:2 axis:3 information:13 goal:2 e2r:4 acts:1 derived:2 plane:8 generalizations:1 spectra:4 fundamental:2 developed:1 held:1 paper:5 through:2 existence:1 its:4 glogower:5 squaring:1 systems:2 might:5 seeking:1 framework:6 formulating:1 bigger:1 easily:3 gets:1 2r:14 always:2 presented:2 token:1 inequality:25 accommodated:1 2i:1 formulate:2 energy:37 idea:2 measurement:52 quantum:49 beyond:1 since:11 helstrom:7 denotes:1 izv:1 denoted:2 found:3 difficulty:2 reason:1 ask:1 beginning:1 generate:1 pairs:1 recast:1 relativistically:1 consequence:7 probability:11 feel:1 relate:1 number:24 defects:1 changing:1 introduction:1 leading:3 construct:1 assumption:6 master:2 exponents:1 akad:1 immediate:1 part:2 authors:2 translation:5 john:1 gotten:2 annihilation:2 determined:8 doubly:2 treated:1 motivation:3 defect:1 null:1 generalized:8 finding:2 measures:4 unused:2 most:5 nothing:1 measured:2 saturate:2 cover:2 braunstein:15 exp:6 velocity:6 physics:6 thomas:2 relation:60 carefully:1 ojk:1 parameters:10 generators:1 factor:9 his:1 gains:1 notation:1 remedy:1 arxiv:1 remove:1 investigate:3 common:1 approaching:1 sipe:2 set:7 ser:1 achieved:3 see:6 n00014:1 smallest:1 various:3 subscript:2 numerous:1 knowing:1 complementary:1 attention:2 vanishing:2 distinguish:4 both:8 last:1 connection:3 finds:3 experimental:1 arbitrarily:1 point:2 simple:1 asymptotically:3 corresponds:2 whatever:1 semiclassical:4 throughout:1 described:13 transformations:3 due:2 whom:1 describes:1 pj:11 pk:10 ph:1 lett:5 sanders:1 wheeler:1 covariance:4 dθ2:3 determination:4 p2:3 p0:1 replaces:1 solid:1 while:1 replaced:1 merwe:1 unitary:15 reads:2 itself:2 busch:1 vanish:1 underlining:1 grant:1 used:8 moment:2 uses:3 purpose:1 eigenvectors:2 lower:15 underlies:1 analysis:5 reviewed:1 using:13 alternative:2 hjk:3 kluwer:2 location:1 guarantees:1 excited:3 australia:1 loss:1 integer:3 bit:1 systematically:1 follows:6 signal:6 communications:2 yields:4 translated:1 mathematical:1 methods:5 creation:1 some:4 back:1 examples:13 describing:1 measurements:69 phasing:1 proc:1 minimal:6 eixp:1 obscures:1 confidence:1 restrictive:1 step:2 nowhere:1 hilbert:15 pβ:1 integers:6 pα:1 idx:1 2iϕ:1 deserves:2 range:3 regular:1 into:9 within:2 integral:3 retaining:1 carlton:2 frames:1 ellipse:4 ixh:5 statistics:4 uncer:1 probabilistic:1 question:3 long:2 ixp:4 considerably:1 line:11 infers:1 up:4 us:8 suitable:1 similar:1 called:7 sometimes:1 constant:11 defined:5 globally:1 chap:9 pˆ:46 formalism:11 defines:3 application:1 department:3 generates:6 excitation:1 problems:1 prepared:4 generated:7 allowing:1 fisher:12 dimensions:1 ago:1 lane:2 implies:5 required:1 overcompleteness:1 requires:5 having:1 illustrates:1 results:11 illustrated:1 eds:5 broader:2 contributions:1 uniqueness:1 chaps:3 saying:1 2re:6 wave:31 wishes:1 nieto:1 arrange:1 entire:1 pˆ2:1 dealt:1 eigenvalues:9 noted:4 lˆ:1 sin2:1 imply:1 concludes:1 greenberger:1 dynamics:3 plays:1 giving:3 gen2:1 expressed:2 find:8 expresses:3 multivariate:1 focuses:1 spacing:2 highly:1 explore:1 sinh:13 technical:2 dembo:2 suggests:1 resulting:5 makes:1 honor:1 involves:1 jˆj:1 formulated:3 addressed:1 sgn:3 apply:1 use:9 asymptotic:1 remains:1 hudson:2 next:1 cram:7 inthe:1 sort:3 becomes:15 normalized:2 discreteness:2 jˆ0:1 iii:5 account:2 integrating:1 insists:1 ρo:1 infinitesimal:2 obvious:2 proof:1 weaker:2 inaccessible:1 lorentz:13 something:1 tan:4 decaying:1 holds:7 located:1 varies:1 instead:2 sin:7 stock:1 relates:1 tied:1 povms:7 discard:2 realized:1 light:1 element:10 allow:3 saturated:2 produces:1 insight:1 symbols:1 saturates:3 including:1 boosts:1 contaminated:1 write:8 chosen:2 temporal:1 relativity:2 estimating:1 permanent:1 choose:1 derivative:5 defining:2 mention:1 rotation:15 february:1 university:3 traced:1 sufficiently:1 magnitude:1 l2:1 mode:3 references:2 barnett:1 related:7 measure:5 our:12 special:11 out:5 matrix:10 rep:1 rev:11 holevo:11 astronomy:1 geom:1 max:1 lorentzinvariant:2 aˆn:1 threedimensional:1 york:4 likelihood:3 geometry:1 determining:7 could:1 keep:1 length:1 derivations:1 hence:5 precisely:6 aharonov:3 strict:1 system:11 relations:41 their:4 mathematically:1 final:5 acquire:1 iθn:1 observed:1 holland:1 submitted:1 appealing:1 amplitude:1 stricter:1 cohen:2 spelled:1 need:2 iφn:3 angle:16 able:3 unless:1 class:3 consequences:1 neighboring:4 pˆα:1 mechanical:9 fact:1 supported:2 rotating:2 trivial:1 principal:2 pause:1 based:18 should:1 local:2 hope:2 means:12 familiar:1 overall:5 compute:1 lahti:1 evolution:3 conditions:6 differential:3 nauk:1 processed:1 fixed:2 dpj:3 view:1 shapiro:2 requirement:3 hδ:1 acquires:1 closer:1 phases:4 state:55 difficulties:1 invariant:8 boundary:1 ability:1 efficiency:1 key:1 distribution:5 observable:4 limits:5 equal:5 ln:5 estimation:21 relevant:2 co:7 cf:8 respect:4 addition:1 define:1 determinant:2 arises:3 corresponding:7 route:1 sufficient:2 coherence:1 subspace:2 zeilinger:1 present:5 multi:1 splits:1 contexts:1 value:10 choices:2 will:1 vi:6 thus:28 radiation:1 unity:1 parts:2 units:7 finite:4 infer:1 difficult:2 parametrizes:1 effect:1 parametrized:1 infinite:2 schr:1 center:1 well:1 thought:2 displacing:1 position:25 hˆ:1 routinely:1 less:1 half:2 adt:1 preprint:1 density:16 nonrelativistic:6 hall:2 add:2 identical:1 increased:2 elapsed:12 increases:1 know:1 immediately:1 dimensional:7 displaced:2 necessary:4 like:2 δx:14 δt:2 δs:4 δn:1 displaces:4 δh:5 become:2 poor:1 because:17 classical:6 choosing:8 orthonormal:4 lead:3 overlap:1 does:3 limitations:4 noise:4 expansion:1 although:3 imaginary:1 about:5 actual:1 freedom:11 recognizes:1 projectors:2 h2:2 attains:1 weighted:2 estimators:2 stam:2 van:1 additional:2 vac:10 restricts:1 quanta:4 inner:5 2m:2 naturally:1 function:39 but:11 reminds:1 construction:1 squeeze:5 made:2 wise:1 places:2 instructive:3 whether:2 smooth:1 below:2 converted:1 limit:2 tainties:1 problem:3 mechanics:3 povm:18 contribute:1 denote:1 replica:3 ink:1 functions:5 compared:1 susskind:5 detail:3 other:7 aˆ2:1 conclusion:2 hirota:2 shown:1 precision:5 else:1 factors:2 rule:1 4n:12 northholland:1
|
quant-ph9507005.txt |@word consider:1 results:1 gx:1 illustrated:2 constants:2 gn:2 expressions:3 whose:3 inverse:1 depend:1 calculate:2 show:1 anharmonic:5 applied:2 scienti:1 worse:1 rise:1 fat:2 electron:4 ective:1 entries:1 exact:8 treating:1 annihilated:1 hamiltonian:1 positions:1 ers:1 solution:3 plotting:2 large:5 interpolating:1 small:2 inspection:1 upper:4 strongly:2 speci:1 arnimallee:1 prediction:1 cosh:1 approximation:10 zero:2 evaluated:1 incidentally:1 further:3 b01:1 errors:2 lowest:2 bc:1 uniform:1 poles:1 fractional:1 supplies:1 3a:4 increasing:1 method:3 contrast:2 27a:2 full:1 respectively:2 spacing:2 desired:1 ansatz:1 path:4 extrema:2 equations:3 z1:2 obtained:5 sending:1 receive:1 larger:1 allows:2 reason:1 simultaneous:1 resulting:3 published:1 involves:1 plotted:1 followed:1 requiring:1 merely:1 explained:1 replace:1 visible:1 apply:2 pxa:1 unit:1 plot:3 use:1 asymptotic:2 uniformity:1 positive:1 next:1 discrepancies:1 few:1 bender:1 relativistic:1 type:2 const:1 validity:1 berlin:6 known:5 account:1 mf:3 mb:2 equation:3 oscillator:5 obvious:1 following:1 example:2 references:1 calculation:1 expanding:1 share:1 minimum:2 sharp:1 simple:3 presently:1 divided:2 holds:1 how:1 a173:1 optimal:2 parameter:1 mas:1 fu:2 fw:1 may:2 after:1 singularities:1 plane:1 physik:3 data:1 fn:1 short:2 natural:1 third:1 interpolated:1 extremal:1 so:1 fundamental:1 weakcoupling:1 order:9 terms:2 superscript:1 help:1 zek:1 displayed:1 approximants:5 course:1 thermal:1 including:1 looks:1 statistical:2 cuts:2 japan:1 its:1 before:2 rapidly:1 energies:1 interesting:2 writing:1 better:4 systems:1 constitutes:1 lq:2 erences:3 derivative:1 eventually:1 them:1 good:1 propose:1 scaling:1 band:2 they:1 now:7 dielectric:1 possess:1 term:1 always:1 2a:2 turns:1 found:1 2n:1 interpolation:9 side:1 en:3 series:2 energy:21 logg:1 frequency:3 static:1 ex:4 quantum:1 our:12 approximated:1 eq:2 es:1 out:7 shown:4 since:1 rev:1 denotes:1 nite:1 denoted:1 correct:3 math:2 shows:2 benjamin:1 earlier:1 turning:1 theory:1 8c:1 8a:2 governing:1 quite:4 nth:1 completely:1 statistics:1 york:1 institut:1 interaction:1 created:1 determining:1 times:1 turn:1 devreese:2 arccos:1 corrections:1 locating:1 first:1 render:1 omitted:1 possessing:1 powerful:1 number:1 theoretische:1 cients:14 directly:1 carry:1 electronic:1 size:1 given:6 perturbation:9 selyugin:1 temperature:2 extremizing:2 leading:9 behaves:3 system:1 approximately:1 their:2 brevity:1 types:1 variational:18 x_:1 a34:1 accurately:1 direct:1 optical:1 rst:3 than:6 second:2 determined:4 were:3 powers:5 extracting:1 polaron:13 w1:1 rewrite:1 correction:1 argument:1 curves:4 miyake:1 orders:1 min:1 latter:1 converges:2 note:3 potential:1 take:1 new:3 accuracy:3 shall:2 most:2 boltzmann:1 jul:1 successive:2 extremely:1 32a:1 url:1 calculated:1 partition:1 typeset:1 feynman:17 points:1 exp:1 typical:1 physics:2 fact:1 quantity:1 precise:1 spaced:1 ects:1 pwn:1 minimizing:2 solutions:1 trivial:2 ground:4 ratio:2 knowledge:3 parameters:3 conduction:1 written:1 only:3 explicitly:2 factor:2 equilibrium:1 his:2 di:7 dependent:1 de:3 overall:1 arch:1 2mb:1 famous:1 dx:1 3b:1 erent:1 2mh:1 him:1 expansions:15 encyclopedia:1 remove:1 calling:1 optimally:1 qn:1 set:1 pade:6 exists:1 bounds:4 see:3 radius:2 truncating:1 ignores:1 b300:1 close:1 exploited:1 phonons:1 review:2 c2b:2 state:4 smallest:2 between:6 approach:1 email:1 available:1 ayk:1 recently:1 extend:1 wn:10 weak:19 wu:1 article:2 2pm:1 both:3 cos:1 c21:1 last:4 many:3 taking:1 equal:1 fiz:1 coe:26 expression:3 among:1 cn:2 reasons:1 corresponds:1 dimensional:1 likes:1 universitat:1 respect:7 cq:1 cp:2 strong:31 described:1 publishing:1 suppressed:1 due:1 been:2 cient:10 much:2 ph:2 ak:1 fig:7 dots:2 corresponding:1 quantities:2 systematic:2 c3:1 c2:1 c1:7 convergent:1 spin:1 present:1 p2:1 p3:1 fur:1 reliable:1 value:5 will:3 forgetting:1 b03:1 b02:1 replaced:1 behavior:9 couplings:5 polymer:1 vg:1 refs:4 vk:3 thus:1 reads:3 result:6 author:1 make:2 any:2 freie:1 complex:1 quant:2 arguments:1 units:1 figures:1 higher:3 independent:1 erence:1 used:2 http:1 singapore:1 purpose:1 jkj:1 kleinert:12 lower:7 acknowledgement:1 frohlich:3 well:2 polarons:2 solve:1 model:2 xed:1 less:2 being:2 3p1:1 obtain:1 thanks:1 xes:2 based:1 tables:1 cut:1 preprint:2 integer:1 lattice:2 lett:4 easy:1 5a:1 momentum:1 identical:1 possible:1 increases:1 know:2 using:5 apart:2 theor:1 necessary:1 like:6 follows:1 yields:2 either:3 integrals:2 arbitrary:2 c1q:1 www:1 deal:1 some:1 searching:1 b4:1 growth:1 b0:7 examples:1 choosing:1 table:2 extended:1 jx:1 prof:1 inserting:1 janke:3 power:4 derivatives:2 bn:8 expansion:32 rossler:1 revtex:1 although:1 renders:1 approximating:1 properties:1 chapter:1 comparison:3 about:1 would:2 world:1 o:11 ppb:1 soc:1 into:1 integral:2 sol:2 three:1 lies:1 rising:2 cent:3 determine:3 einstein:1 operator:1 fub:1 hep:1 there:1 approximate:4 fast:1 dispersion:1 start:2 valley:1 was:1 assumes:1 function:6 considerably:1 form:3 forming:2 wnn:1 but:2 volume:1 convergence:4 hc:1 removed:1 true:1 coupling:40 up:1 us:3 limit:2 more:3 display:2 b1:2 mechanics:3 ac:1 constant:6 b2:1 abstract:1 b3:1 general:5 physical:3 again:2 functions:3 compared:5 completeness:1 dotted:2 no:1 dashed:4 whereas:1 nd:10 nal:1 really:1 stat:2 calculating:3 models:1 uniformly:1 a1:1 a0:1 important:1 bcn:2 auxiliary:1 algorithm:10 4v:1 required:1 curve:3 phonon:1 mass:11 n1:1 nxn:2 requires:1 4c:1 4a:4
|
quant-ph9507006.txt |@word dewitt:1 sci:1 consider:12 pointing:1 maximum:2 novelty:1 lack:1 existing:5 four:1 berezin:1 scalar:2 ciar:1 broader:2 go:2 psycho:7 research:1 seemed:2 whose:6 certainly:5 depend:5 calculate:1 college:1 paris:3 assigning:1 april:1 nonlocal:2 program:1 restriction:1 present:9 th:1 under:4 alberta:13 analogous:1 include:4 worth:1 solvay:1 nouvelle:1 amplitudes:2 worse:2 straightforward:1 outside:1 very:7 dispense:2 implicitly:3 reader:1 translations:1 myself:1 choice:1 every:1 trouble:2 difference:1 continued:1 entire:2 school:1 routledge:1 augment:1 solves:1 level:2 did:1 positions:2 auspices:1 solution:3 t0:13 viable:4 try:3 vector:1 alzheimer:1 indices:3 provided:1 onerous:1 talked:1 version:5 guaranteed:1 direct:4 past:2 second:2 value:7 uncomfortable:1 incidentally:1 further:2 copenhagen:1 linear:3 even:26 what:11 nonlinear:1 appear:1 clock:4 giving:3 imagined:1 sum:1 sous:1 expressed:1 access:1 experiment:1 suspect:6 above:9 sixth:1 obvious:2 except:5 contrast:1 satisfy:2 edited:6 full:2 degree:2 respectively:1 modify:1 glimpse:2 here:6 contemplate:1 objects:1 free:1 address:1 along:2 strong:3 equations:3 implicit:1 extreme:3 great:1 interpr:1 depended:1 institute:1 appraisal:1 study:1 allows:3 completely:4 experience:10 leaving:1 prior:9 accomplished:1 resulting:1 published:5 usually:2 opinion:1 suitable:4 makes:1 uniquely:2 useful:2 projection:1 extra:2 requiring:2 merely:2 imagine:1 prefer:3 natural:1 highly:3 psychological:1 pp:1 odinger:3 apply:1 total:1 planck:3 select:1 readily:2 derivatives:1 use:2 takes:2 would:32 probabilities:7 positive:4 spontaneous:1 predictions:1 nonsymmetric:2 properties:1 few:1 going:1 call:3 opposed:1 memory:4 taken:3 undivided:1 simpler:8 selects:1 historically:2 today:1 more:14 becomes:1 operators:21 apparent:1 ascribe:1 occurred:1 ap4:1 aware:1 ignorant:1 normalized:5 particular:13 known:1 cases:3 hold:3 ontological:1 must:3 me:7 states:1 none:1 valued:3 anything:1 divorced:1 complication:1 station:1 equation:11 work:1 oscillator:1 theories:32 remain:1 lorentz:11 values:3 hope:1 following:3 making:1 lockwood:2 my:8 example:2 history:3 beautiful:1 heart:1 compare:2 reasonably:2 cosmological:1 give:10 ontologically:1 allowed:1 share:2 high:1 weighting:1 assumptions:2 caused:2 something:5 typicality:6 sense:1 concordant:1 nonnegative:1 cushing:2 occur:3 string:1 information:6 needs:2 hoc:4 rather:9 conversely:1 discussion:1 means:3 write:2 far:1 nontrivial:3 pair:4 low:2 opposite:1 reject:1 answer:1 instead:1 ordinary:7 intelligent:1 ensemble:10 simplicity:8 product:1 description:6 algebra:3 may:10 earlier:2 different:6 perceive:1 applications:1 wrong:1 produce:2 lay:1 records:1 fits:1 wave:1 gauthier:2 refuse:1 branches:1 council:1 conscious:32 onto:1 approximation:1 june:3 cosmology:4 diffeomorphism:2 extrapolation:1 so:20 specifying:1 fundamental:3 suggest:1 order:2 talk:2 transformation:1 integrated:1 breaking:3 interpretation:1 september:1 developed:2 over:10 years:2 course:10 cambridge:5 including:1 hypersurface:1 existence:4 still:4 its:20 features:6 superior:1 du:2 group:2 symmetry:3 acknowledge:1 chosen:3 temporal:1 hypothesize:1 reluctance:2 coordinates:1 actually:8 forms:6 holland:1 systems:1 dxψ:2 main:1 might:15 ugly:5 overcome:1 interpretive:1 maximal:1 eventually:1 them:7 good:1 affected:1 greater:5 propose:2 outlined:2 practice:2 preserves:1 prejudices:1 break:1 framework:4 rank:1 they:8 hands:1 oxford:1 postulated:2 nov:2 now:1 chicago:2 finite:1 bruxelles:1 goldstein:5 university:13 hamiltonian:1 appropriate:1 crudely:1 possibilities:3 sufficiently:1 magnitude:2 mode:1 truth:1 each:27 found:2 entirely:4 mean:1 subset:5 differential:1 financial:1 another:4 weight:2 doing:1 energy:2 hard:1 idea:1 inhomogeneous:1 fraction:2 static:5 sketched:1 quantum:77 our:10 beyond:1 special:4 out:15 canada:2 large:1 fundamentally:1 space:30 gradient:3 god:1 furthermore:2 since:14 crucial:1 denotes:1 content:2 sociological:1 investigation:1 internet:1 cause:1 correct:3 disagreements:1 she:1 occurs:1 perception:31 theory:58 written:1 zurek:1 given:15 possibility:3 difficulty:1 reason:1 surely:2 besides:1 element:3 hep:1 estimate:1 pretend:1 likelihood:1 axioms:2 sbm:44 could:10 similarly:2 success:1 times:10 motion:3 turn:3 plane:1 prejudice:1 hence:2 contingency:1 july:2 generalizations:2 think:4 first:4 sanchez:1 initial:1 rooted:1 probability:11 feel:1 number:1 preservation:1 cbm:9 clear:2 enlarged:1 done:1 construct:2 directly:5 type:1 precisely:4 open:1 between:4 take:1 guess:1 necessarily:2 pronoun:1 physique:2 their:5 metaphysical:1 eqs:1 gravity:6 least:5 attach:2 assumption:3 zeros:1 observations:8 postulate:1 easier:1 speaking:1 gives:6 eyes:1 assign:3 collapse:1 mostly:1 moscow:1 albert:2 speakable:1 astrophysics:1 part:5 too:6 somewhat:1 attempt:3 x0:1 believe:1 than:19 specify:2 modes:3 observed:1 kind:1 determines:3 unfortunately:1 princeton:2 suppressed:1 bother:2 measured:3 depends:7 matter:1 determined:6 7th:1 historical:1 were:3 cards:1 merits:1 wheeler:2 adopts:1 russia:1 perspective:1 conseil:1 motivation:2 keiser:1 appreciate:1 measure:41 randomly:1 raw:1 say:17 need:4 seen:1 seem:9 unaffected:1 apparently:4 any:21 seminar:1 relatively:1 acceleration:1 lie:1 traditionally:1 zero:6 depending:1 convenient:1 latter:3 able:1 overcoming:1 sciences:1 fitting:1 contact:1 generalized:4 meeting:1 objective:1 new:1 canonical:1 ultimate:1 4th:1 broglie:2 unless:1 allow:1 shall:8 ıve:1 measures:2 techniques:1 most:8 connected:1 but:21 quantized:1 nothing:3 grateful:1 future:1 extremely:1 class:1 jantzen:1 subjective:3 don:3 especially:1 surprising:1 dordrecht:2 calculated:1 later:1 differ:4 disease:1 looked:1 proceedings:3 points:1 electrons:1 principle:4 urr:2 mechanical:1 velocity:6 typical:2 physics:16 technical:1 fact:6 bell:1 precise:1 incorporate:1 paul:1 particularly:1 show:1 sceptical:2 random:1 purely:4 inconsistent:1 earth:1 fine:1 find:5 ground:1 ualberta:1 rev:2 des:1 just:6 nonperturbative:1 explain:3 enough:1 topological:1 should:14 tries:1 held:1 only:17 explicitly:5 black:1 indeed:4 adequate:2 local:2 axiom:9 awareness:12 do:15 hit:1 closed:1 quantph:2 get:8 dependent:7 connections:1 de:6 expectation:8 preferred:1 cannot:4 listed:1 words:1 altogether:2 report:6 interpreted:1 object:2 eme:1 evolution:4 continuum:12 brain:2 fields:1 arxiv:1 consisting:2 qc:3 predicted:1 minkowski:2 london:2 fixed:1 qm:29 require:3 view:2 consciously:3 kernel:1 set:15 constructing:2 observer:1 creator:1 intelligence:1 frame:4 lett:1 sex:1 plausible:4 see:6 individual:4 bare:20 descriptions:1 discussions:2 dµ:1 nonstandard:2 best:2 subject:1 closer:1 evaluation:1 ways:1 definite:8 functionals:2 fulling:1 importance:1 state:25 connection:8 various:1 correctly:1 simplest:10 crude:1 probably:4 neither:1 before:1 conditions:3 tenu:1 wide:1 comparable:2 terms:2 unconscious:8 initially:1 however:13 sicily:1 pick:1 harvard:1 hypothesis:1 blackwell:1 configuration:23 come:1 distribution:3 motivations:1 both:2 essentially:2 perceptions:33 instant:2 many:9 la:2 against:1 called:2 etc:1 sketchy:1 les:1 context:1 concentrates:1 distinction:1 grossmann:1 whole:2 trajectories:22 nearby:1 mechanics:32 presumably:2 relativity:3 cm:2 point:5 simple:13 had:2 ca:1 harmonic:1 whatever:2 hollow:1 dimensional:1 superstring:1 instants:1 simply:9 invariant:6 experiencing:1 wider:1 constant:3 suppressing:1 sensible:12 ensures:1 described:4 transformations:2 puts:1 trajectory:58 claiming:1 three:2 been:3 appears:1 attaching:1 devise:1 reprinted:1 much:8 complicated:5 combined:1 interest:1 basic:3 expected:1 flexible:1 ph:2 hardly:1 define:3 wants:2 direction:1 arises:1 corresponding:15 drugs:1 linearity:1 sufficient:2 differed:1 subspace:1 bulk:1 maps:1 bohmian:65 understand:1 personally:3 bayesian:2 evidence:2 spin:2 those:2 case:9 multi:1 unlike:2 isolated:1 davies:1 suitably:1 engineering:1 premature:3 choices:2 will:8 frameworks:2 near:1 suppose:2 texas:2 situation:1 correspondence:2 almost:2 etation:1 thus:6 non:1 marcel:1 obeying:1 superstrings:3 itself:9 dual:1 cumbersome:1 result:1 containing:1 develop:2 lacking:1 suggests:1 perhaps:8 things:2 make:1 formulations:2 indistinguishable:1 same:10 metaphysics:1 shorter:1 quant:2 virtually:2 modification:2 survey:1 gets:3 higher:2 fairly:2 extended:1 closest:1 again:1 dynamique:1 numerical:2 upon:3 effect:3 hand:1 parametrized:1 action:2 moment:2 purpose:1 invariance:8 totally:1 identity:1 mentioning:1 lower:2 task:1 schr:3 subsets:1 thy:6 neural:1 nevertheless:1 spacetime:2 ıvely:1 tentative:1 well:7 roughly:2 analysis:3 bohm:3 academic:1 severe:1 without:4 components:3 sets:6 coordinate:3 position:6 lin:1 mind:2 consciousness:34 less:2 being:9 generally:1 edmonton:1 compound:1 rest:1 ideas:1 assigned:2 underlying:1 aspect:1 augments:1 flavor:1 yet:4 adding:1 villars:2 kluwer:2 density:19 photons:1 nonrelativistic:2 seems:13 entirety:1 pov:2 add:1 other:17 combine:1 location:1 dµ0:3 probabilistic:1 remaining:1 idealization:1 spinless:1 aspects:8 increased:1 2j1:1 read:1 admit:2 spatial:2 measurement:2 possible:6 munich:1 early:1 test:2 hiley:1 know:3 burden:1 vacuum:4 press:6 world:42 objectively:1 gr:3 like:4 loss:2 necessary:1 helpful:2 particle:2 admittedly:1 reduces:1 velocities:1 unnecessary:2 remind:1 yields:2 either:3 arbitrary:2 conclusion:1 page:6 mathematical:4 sketch:1 because:4 often:1 classical:5 absolutely:3 affects:1 conditional:1 some:11 understood:1 deduce:1 evaluated:3 choosing:1 table:1 universes:5 little:1 chalonge:1 nonzero:5 canonically:1 scale:1 describing:4 aesthetically:1 phenomenal:1 ones:1 though:14 nonclassical:2 sketching:1 everything:2 does:13 connecting:1 wavefunctional:1 assuming:2 heat:1 particles:2 refer:1 core:1 biased:1 who:2 scientific:2 slight:1 seconds:1 bm:31 equivalent:1 wavefunctions:3 agreement:2 how:7 although:5 relating:1 transported:1 hilbert:7 after:1 stage:1 comparison:2 about:5 postulates:4 actual:3 carried:1 extension:3 eaire:1 universe:14 discussed:3 dependence:10 o:5 range:2 greatly:1 rubakov:1 homogeneous:2 outset:1 own:6 ecanique:1 orders:2 into:1 within:6 integral:4 functional:8 negative:1 down:1 phase:3 beings:2 rapports:1 references:1 operator:11 relativistic:1 institut:1 additional:4 conceivably:2 comparing:2 assumed:1 support:1 there:15 question:5 shelly:2 long:3 spread:2 quanta:1 physicists:11 way:9 forward:1 conceivable:1 was:3 function:7 complete:7 form:21 attempted:1 omniscient:1 jul:1 idealized:2 basil:1 posterior:3 delta:2 trying:1 true:3 proposal:1 zanghi:2 he:4 made:3 applying:1 au:1 whether:4 wish:1 erice:1 attached:4 emphasize:1 us:2 theoretical:1 international:2 considered:3 frequency:1 limit:2 problem:3 attaches:1 similar:4 agree:2 detailed:3 associated:1 ad:4 defined:3 certain:6 abstract:1 describe:3 am:5 general:7 single:8 exist:3 periods:1 physical:10 traditional:1 functions:2 compared:1 no:10 objection:2 na:2 wavefunction:28 when:9 detail:2 field:9 valid:1 better:1 department:2 mathematics:3 really:2 nice:1 stat:1 hereby:1 generates:1 respects:1 problems:3 includes:1 augmentation:3 massachusetts:1 sqm:48 included:1 t6g:1 singapore:2 ago:2 assume:2 normally:1 proposed:3 required:1 holes:1 rule:2 parallelism:7 time:44 everywhere:1 once:2 having:5 unspeakable:1 augmented:3
|
quant-ph9507007.txt |@word consider:6 results:3 commute:1 go:3 γn:2 γm:2 indicating:2 case:9 amplitudes:3 very:7 rise:1 geometrical:2 fall:1 matrices:1 condition:2 rigourous:1 level:4 evaluation:1 t2:2 solution:8 t0:10 large:7 vector:1 small:5 unexpected:1 direct:3 sign:1 approximation:20 quite:1 even:1 trick:1 appear:1 giving:2 section:2 agrees:1 xvii:1 above:8 new:4 method:4 full:1 never:1 here:3 favourable:1 identifications:1 ansatz:1 address:1 strong:12 equations:2 appears:2 change:2 knowledge:1 obtained:2 involved:2 study:1 experience:1 accomplished:1 makes:1 via:1 useful:1 apply:1 use:1 asymptotic:2 prove:2 next:2 ψi:4 taken:2 more:6 becomes:1 odinger:3 equation:12 following:4 example:3 give:1 states:1 arise:3 sought:1 exclude:1 rescaling:3 discussion:1 till:1 λvn:1 instead:1 parameter:4 derived:2 tries:1 wave:2 changes:1 natural:1 yielding:1 so:7 operate:1 order:11 typical:2 wigner:7 indeed:1 pointed:1 insight:1 soc:1 indistinguishable:1 paper:2 statistical:6 itv:1 derive:1 interesting:3 actually:1 systems:5 mail:1 main:4 h0:5 overcome:1 good:1 landau:1 oxford:1 now:1 easily:2 term:1 presented:1 found:1 higher:3 em:1 en:3 ei:1 fairly:1 series:8 energy:1 t3:1 used:1 quantum:20 our:7 happen:1 beyond:1 eq:9 out:1 shown:1 space:1 nuovo:1 rev:3 chaos:1 re:1 acting:1 ref:4 shows:2 eiαn:1 theory:5 given:2 standard:2 difficulty:3 approaches:1 york:1 put:2 interaction:4 retained:1 derivation:3 could:7 times:1 consequence:1 retain:1 neglect:1 first:2 already:2 probability:3 lond:1 will:6 enlarged:1 directly:1 little:1 perturbation:28 rewritten:1 introduction:1 leading:7 lenght:1 structured:1 system:11 least:2 their:1 perturbations:3 final:1 gives:2 cope:2 stress:1 part:4 than:1 kind:1 holland:1 showed:1 approximations:1 cimento:1 depends:1 aims:1 dtd:1 determined:1 usefulness:1 seen:1 seem:1 recover:1 clearly:1 depending:1 able:3 potential:1 take:1 hightemperature:1 unless:1 any:1 vni:3 boltzmann:1 jul:1 phase:7 iterate:1 future:1 segment:1 class:1 kb:2 cause:1 considered:6 clear:1 stronger:2 face:4 physics:1 fact:5 dover:1 show:2 relation:1 solutions:1 find:2 proposed:3 parameters:2 should:2 explicitly:1 mechanics:11 hope:1 do:1 goes:1 invoke:1 get:2 dependent:6 dt:17 du:3 approach:6 arxiv:1 expansions:1 view:3 requirement:1 set:3 computed:1 undergoes:2 see:8 sec:3 result:9 analog:2 acquires:1 away:1 written:5 difficulties:4 correctly:1 between:1 drawn:1 conditions:1 αn:1 terms:1 2m:1 however:2 hypothesis:1 originates:1 both:1 taking:1 conclusions:1 σz:3 σy:2 σx:3 berry:7 messiah:1 originating:1 ch:1 cn:5 cm:2 point:3 simple:3 simply:1 applicability:1 polynomial:1 respect:1 due:3 been:1 slowly:1 treat:1 ph:1 differently:1 arises:2 coincides:1 spin:1 present:1 applied:4 cyclicity:2 exponential:1 aim:1 while:2 situation:3 vol:1 refs:1 iu:1 vn:4 ii:1 il:1 frasca:4 different:1 make:3 cross:1 same:6 orders:3 beside:3 quant:1 pauli:1 gets:2 difficult:1 development:2 independent:4 literature:1 infinity:1 ni:2 effect:3 moment:1 levels:1 moving:1 cycle:2 schr:3 onedimensional:1 ωnm:3 solve:1 greatest:1 roma:1 model:4 λv:3 just:4 λt:2 being:8 obtain:2 109b:1 λh:1 eigenstates:2 λl:1 application:5 conclude:2 except:1 concerns:1 easy:1 theorem:4 solvable:1 eigenstate:1 identical:1 rescaled:1 iλ:4 marco:1 evaluate:1 showing:3 press:1 using:3 particle:2 adiabatic:18 indication:2 integrals:2 mathematical:1 because:1 methods:1 some:6 back:2 scale:1 does:3 yields:1 proc:1 refer:2 limitations:1 run:1 power:1 oscillating:1 expansion:4 substitution:2 limitation:4 discussed:1 dependence:1 perturbed:5 computational:5 pergamon:1 into:2 integral:3 down:1 operator:1 amsterdam:1 initial:2 approximate:1 long:1 italia:1 way:2 function:2 north:1 form:3 but:3 trying:1 made:1 applying:2 us:2 limit:3 problem:2 similar:1 strongly:6 constant:3 computing:1 recognize:1 abstract:1 meaningless:1 general:2 inm:1 exist:1 hamiltonian:7 physical:1 again:1 no:3 when:2 field:7 papers:1 test:1 conclusion:1 picture:4 superposition:1 problems:1 variation:1 6m:1 kirkwood:7 important:1 variable:2 lifschitz:1 dτ:1 4m:1 mass:1 time:20 having:1
|
quant-ph9507008.txt |@word sci:1 consider:5 helstrom:2 magnetic:1 alternatives:1 results:5 consists:2 follow:1 decisions:4 whose:2 calculate:1 lindley:1 concerned:1 tr:4 tp:1 tail:1 monotonically:1 th:5 under:1 meister:2 analogous:1 characterised:1 case:12 conjecture:2 risk:1 orthogonal:1 choice:1 orientations:1 decide:3 difference:2 entire:4 turns:2 solution:4 correct:1 magnet:1 vector:1 eigenvalues:6 anal:1 mn:4 past:1 second:1 cost:36 design:1 even:2 nonlinear:1 sub:2 advantageous:1 sum:2 selected:1 foregoing:1 sequential:13 bernhard:1 above:9 scientists:1 replaced:1 consisting:1 notions:1 never:2 here:5 experimentalist:1 cos2:2 address:2 cos2n:3 consideration:2 observing:1 appears:1 2bz:1 obtained:7 degroot:1 institute:1 study:3 vectors:3 reason:1 experience:1 prior:14 procedure:3 usually:1 therein:1 malley:2 involves:2 york:3 useful:1 projection:1 requiring:1 outcomes:1 stern:1 apply:1 total:3 select:1 use:1 would:1 massar:2 probabilities:1 coins:6 negative:3 permitted:1 definiteness:1 explicitly:1 popescu:2 therefore:5 scope:1 analysing:2 more:1 knows:2 composite:2 becomes:1 operators:4 isac:1 known:2 cases:2 must:12 springer:1 valued:1 science:1 ρk:1 ρj:1 values:2 strategies:6 trans:2 example:3 process:1 states:3 effectively:1 minimum:2 numbers:1 tan:1 axis:2 information:4 verify:1 pure:1 optimal:21 verlag:1 parameter:1 ensemble:9 simplicity:1 product:2 algebra:1 may:5 after:8 plane:1 lax:1 data:1 branches:5 clarkson:1 ordinarily:1 hypotheses:1 inform:2 ones:1 so:1 asserts:1 decreasing:1 increase:1 order:2 our:3 considerations:2 indeed:1 london:2 statistical:2 differs:1 still:1 ieee:2 before:5 observational:6 le:1 acknowledge:1 chosen:4 interesting:1 choose:4 might:1 non:4 combination:1 similar:1 introduce:1 identically:1 now:9 easily:3 february:1 always:1 brody:3 sin:3 each:6 found:1 entirely:1 difficult:2 constraints:1 adjointness:1 weight:1 proliferating:1 frequency:1 obtains:1 measurement:16 quantum:14 laboratory:1 beyond:1 shannon:1 out:2 matrix:5 space:1 posteriors:1 since:8 kensington:1 holevo:1 denotes:2 particles:13 hill:1 performs:1 conjectured:1 formula:1 induction:1 ri:3 rj:3 statist:1 wiley:1 turning:1 theory:4 quite:1 approaches:1 whereupon:1 bayes:24 estimate:1 times:1 turn:1 including:1 δij:1 hence:8 assign:1 south:1 first:9 probability:8 number:4 rank:2 another:1 impossible:1 electronic:2 angular:1 γc2:1 passes:1 given:18 similarly:3 πj:7 unknown:1 adjoint:2 πi:2 system:9 their:3 intermediate:1 observations:4 calculations:2 wootters:3 final:1 recovered:1 inner:2 authors:1 constituent:1 than:2 specify:1 relative:2 determines:1 accordance:1 tree:5 zero:1 submitted:1 were:1 outcome:5 treated:2 entail:1 generality:1 topics:1 manner:1 seek:1 any:12 angle:7 efficient:1 self:3 davies:1 note:3 costs:6 take:1 forces:1 finding:1 negligible:1 detector:2 trace:1 who:1 systems:1 but:2 letter:3 device:3 coin:2 observation:4 considered:2 average:3 posterior:11 physica:1 principle:2 mechanical:2 treats:1 typically:2 calculates:1 incorporate:1 show:2 detection:1 random:1 purely:1 gerlach:1 find:2 finally:1 based:1 ensembles:3 only:5 experiment:3 updating:2 developed:1 partially:3 do:3 cannot:2 new:3 procedures:3 approach:8 arxiv:1 fixes:1 yield:1 method:1 predicted:1 through:2 ignored:2 set:3 observes:2 tossing:2 testing:1 maximum:1 observed:3 mentioned:3 see:2 individual:3 college:2 result:11 eliminating:1 discussions:1 contains:1 theoretic:2 satisfying:1 definite:2 state:10 un:3 closed:2 between:4 neither:1 conditions:1 available:3 terms:3 nature:3 physicist:12 however:10 hypothesis:5 key:1 problem:9 c22:2 cos:4 c21:1 last:2 2n:5 avoid:1 many:1 hornstein:1 equal:1 against:3 etc:2 connection:1 blackett:1 argue:1 finds:1 experimental:1 otherwise:1 among:4 noninformative:1 cn:3 cm:2 conclude:3 reasons:1 others:1 corresponds:2 sampling:1 pom:6 associated:4 throughout:1 pr:2 basis:1 equations:1 three:1 been:3 strategy:12 combined:15 expected:5 ph:2 define:1 θk:3 direction:5 corresponding:1 eigenvector:2 sufficient:1 optimality:1 angles:2 bayesian:7 c2:5 c1:7 spin:15 present:4 applied:2 unlike:1 pacs:1 value:2 will:3 associates:1 suppose:3 situation:2 sw7:1 changed:1 orientation:3 thus:2 vm:1 vn:3 according:2 bias:4 claimed:1 ic:2 binary:4 different:9 verified:1 φopt:5 trial:3 perform:2 lett:2 same:7 quant:1 filtered:1 proved:1 higher:3 independent:1 used:1 upon:2 effect:1 hand:3 changing:1 expand:1 lower:1 task:1 nevertheless:1 nonetheless:1 well:1 analysis:8 academic:1 without:3 recombine:4 λw:2 just:4 less:1 being:2 when:8 newton:1 obtain:6 immediately:1 inference:1 previous:2 preprint:1 density:3 minimises:3 except:1 simple:2 priori:1 treatment:1 theorem:2 c12:3 c11:2 rev:2 eigenvalue:1 possible:1 press:1 using:4 loss:2 necessary:1 particle:6 kennedy:1 follows:3 performing:4 steps:1 either:7 arbitrary:1 mcgraw:1 spins:1 making:2 mathematical:1 classical:8 sequence:1 conditional:2 some:2 proliferate:1 deduce:1 b1:7 choosing:2 specified:1 berger:1 provided:1 demonstrates:1 decision:22 measurements:13 samplings:1 does:1 unit:1 assuming:1 gratitude:1 bk:3 although:1 yuen:1 hilbert:1 bz:1 stage:2 comparison:1 ρˆj:1 ρˆk:3 freedom:1 o:1 practical:1 important:2 act:1 road:1 specifies:1 cambridge:1 into:2 h1:1 ηi:3 down:3 hermitian:1 weighted:2 determine:1 operator:6 next:4 utility:1 there:1 imperial:2 accordingly:1 incurred:1 was:1 knowledge:2 function:4 head:1 form:2 sequel:1 analyse:1 jul:1 hj:2 hk:2 repeated:1 hi:1 hm:1 true:2 he:1 whether:1 cij:4 up:6 below:1 owing:1 maximises:1 uk:2 distribution:7 optimisation:2 clear:1 polarised:5 instead:1 ac:2 constant:1 b2:4 defined:2 certain:1 measure:1 linearity:1 proven:1 general:4 peres:3 single:2 proves:1 field:2 formalism:1 distributions:3 worse:1 incorrect:1 again:1 mutual:1 compared:1 polarisation:2 generally:2 virtual:1 application:1 other:9 details:1 branch:2 concerning:2 briefly:2 estimation:1 calculating:2 separate:3 prepared:1 cb3:1 ξj:4 ξk:1 variable:1 structure:1 implies:1 assume:1 rule:1 having:2 weights:3 minimax:1
|
quant-ph9507009.txt |@word consider:1 results:1 disc:1 go:1 expressions:1 zinn:3 whose:2 certainly:1 const:1 calculate:1 b262:1 critical:5 th:3 anharmonic:8 include:1 divergent:4 p2:1 scienti:2 worse:1 g1:4 g0:4 rise:1 figs:4 exact:5 treating:1 entire:1 did:1 positions:1 laying:1 large:12 small:3 eigenvalues:1 noted:1 smaller:1 arnimallee:1 cosh:1 approximation:27 second:1 section:1 new:11 contributes:1 method:8 3e:2 ek0:6 condensed:1 full:1 led:1 here:1 desired:1 stancu:1 guida:2 path:2 along:1 extrema:1 stresses:1 rigorously:1 larger:3 b123:1 resulting:3 buckley:1 makes:1 via:1 useful:2 polymer:1 explained:2 replace:1 visible:1 b227:1 plot:3 use:3 uniformity:1 prove:2 remains:1 positive:3 negative:7 few:1 bender:2 type:2 until:2 knows:1 berlin:7 particular:1 known:5 must:1 c44:1 c45:1 oscillator:8 reproduce:1 following:1 making:1 example:3 expanding:1 high:1 indicates:3 numbers:1 g3:5 information:2 advantage:2 rather:2 holds:1 how:1 a173:1 ensure:1 parameter:1 fu:2 yamazaki:1 after:1 derived:2 long:1 wrong:1 plane:2 physik:3 fn:2 short:5 accelerates:1 lines:1 so:1 d22:1 order:16 typical:1 help:1 developed:2 course:1 paper:1 london:1 looks:2 statistical:2 b300:1 derive:1 d36:1 interesting:1 d35:1 d32:1 d30:1 better:3 fig:12 constitutes:1 maximal:1 them:1 scaling:1 subtraction:2 they:1 oxford:1 now:8 possess:2 term:1 university:1 hepth:1 d49:1 d43:1 found:2 genoa:1 d47:2 2i:1 en:5 ek:5 series:6 energy:12 hard:1 related:1 w10:2 tip:1 extended:1 combining:1 quantum:4 our:1 approximated:2 eq:2 special:1 out:2 shown:5 missed:1 factors:1 genova:1 symanzik:1 since:1 rev:9 denoted:1 constants:1 ref:4 correct:4 math:2 shows:5 turning:1 theory:9 singularities:1 discontinuity:2 completely:1 hep:3 incorporates:1 starts:3 could:1 exponentially:3 arccos:1 locating:1 first:2 there:3 xn:1 render:1 theoretische:1 cients:12 done:1 defects:1 another:1 quality:1 illustrate:1 given:2 perturbation:10 leading:3 system:1 their:2 1d:2 calculations:1 variational:12 exponents:2 gives:1 a34:1 required:1 part:20 rst:3 than:4 double:1 approximations:1 iteration:1 matter:1 w3:5 powers:1 perturbative:1 lowest:1 correction:3 seen:3 orders:1 latter:1 converges:3 note:2 instance:1 potential:1 take:1 forming:2 thoma:1 resumming:1 shall:1 subtracted:1 url:1 typeset:1 feynman:2 points:1 typically:1 quantity:1 parker:1 chapters:1 converge:1 implying:1 relation:3 mitter:1 ground:3 ratio:3 knowledge:6 duncan:3 explain:1 should:2 only:3 going:1 factor:3 constant:5 do:1 di:1 de:4 gef:1 erent:1 fields:1 expansions:8 across:1 qn:1 set:1 pade:1 resummed:1 see:8 college:1 truncating:1 w1:2 vol:2 state:3 smallest:1 correctly:1 between:1 email:1 recently:2 reproduced:1 missing:2 wn:4 ritschel:1 weak:4 however:3 wu:1 jg:1 improve:1 both:1 cos:1 improved:1 treated:1 vanishing:1 etc:1 improves:1 coe:13 contribution:1 extracting:2 expression:2 grounds:1 among:1 semiclassical:6 universitat:1 respect:4 ensures:1 strong:7 described:1 due:1 been:2 cient:2 pk:1 ph:2 summable:1 systems:1 obtained:3 arises:1 72k:1 quantities:1 systematic:1 present:2 case:1 fur:1 solid:5 resummation:6 value:4 will:2 fub:1 behavior:14 error:2 situation:1 tunneling:5 couplings:4 procedure:5 real:1 cents:1 thus:2 non:1 ii:1 reads:2 im:6 result:2 develop:1 barnes:1 same:3 any:2 freie:1 complex:2 quant:3 figures:1 dimensionless:2 regime:1 interpolation:1 independent:1 used:2 http:1 singapore:2 upon:1 hand:2 moment:1 kleinert:15 well:1 roughly:2 does:1 left:2 proposed:1 being:2 nd:2 accurate:1 obtain:3 world:2 previous:2 cut:5 preprint:6 eld:2 lattice:1 add:2 lett:10 identical:1 evaluate:3 possible:2 possibly:1 press:1 using:2 eex:4 necessary:1 like:4 qualitative:3 vortex:1 yields:1 integrals:3 stevenson:4 gauge:1 www:1 because:1 old:4 methods:1 some:2 proper:3 proofs:1 jgj:6 behave:1 replaced:2 janke:3 power:2 derivatives:1 pp:2 expansion:19 clarendon:1 revtex:1 although:1 d42:1 imaginary:20 super:1 properties:1 comparison:1 about:1 justin:3 extension:1 o:1 reduced:1 plus:1 sissakian:1 ow:1 slightly:1 into:2 within:1 integral:2 references:1 einstein:1 ciency:2 statistics:1 institut:1 log:2 c51:1 initial:2 approximate:1 fast:4 imperial:1 dispersion:4 extremizing:1 borel:2 way:1 was:1 suzuki:2 function:3 considerably:1 form:1 phenomena:2 tarrach:2 jul:1 reed:1 convergence:9 true:1 made:1 whether:1 us:1 w30:3 problem:1 mechanics:2 taylor:1 associated:3 abstract:1 textbook:1 general:1 accounting:1 physical:1 again:1 b176:1 dotted:3 no:1 dashed:10 generally:1 vanishes:1 nal:1 field:1 models:1 uniformly:1 important:3 b313:1 jones:4 coupling:12 assume:1 physics:1 interval:6 curve:18 ghandour:1 konishi:2
|
quant-ph9507010.txt |@word monte:1 concept:1 consider:3 graham:1 desirable:1 results:2 osi:4 scalar:1 commute:2 compact:1 rmki:1 calculate:2 equivalence:4 tr:12 those:2 stochastic:14 straightforward:1 very:1 percival:1 wave:14 husimi:2 exact:8 condition:3 leads:2 hamiltonian:4 issue:2 solution:1 large:1 vector:1 optics:7 originally:1 attracting:1 ten:1 approximation:1 second:2 substituting:1 dynamics:7 carlo:1 invertible:1 section:2 current:1 ˆa:2 version:2 above:2 kleinert:1 ˆj:5 method:1 ˆo:1 satisfy:1 full:1 simultaneously:1 respectively:1 loose:1 here:1 atoms:1 believed:1 represented:1 standard:1 equations:4 remark:1 institute:1 products:2 suggestion:1 opinion:1 fourier:1 pearle:1 via:1 jˆa:1 apply:2 establish:1 eiωt:1 takes:2 would:1 prove:1 sake:1 negative:1 ψt:7 a50:1 call:1 ρrad:7 taken:1 means:1 simpler:1 more:1 composite:2 operators:3 emission:1 berlin:3 basically:1 known:2 foundations:1 evolves:2 account:1 quantized:2 equation:10 work:5 reproduce:3 remain:1 values:4 ρt:2 freedom:1 following:5 making:1 example:1 grained:11 give:1 relativistic:2 states:8 minimum:4 want:1 sharp:2 information:1 dalibard:1 rather:1 holds:1 ghirardi:1 write:1 how:1 worry:1 pure:3 ϕt:2 answer:1 instead:2 coarsegrained:2 simplicity:1 product:2 mat:1 may:3 after:3 derived:2 applications:1 summarize:1 stress:1 short:1 natural:3 effective:1 consequently:1 explicit:1 element:1 switch:1 so:3 fundamental:1 representation:4 order:1 typical:1 wigner:3 over:1 choose:1 years:2 course:1 thermal:1 da0:2 statistical:1 mentioned:1 existence:2 belavkin:1 still:2 its:2 dϕt:1 coordinates:1 permanent:1 degrees:1 systems:1 superoperators:1 mail:1 main:1 alter:1 correspondence:3 them:1 introduce:3 anticipated:1 framework:1 walls:1 they:1 represents:1 always:1 identified:1 mode:5 each:1 soc:1 footing:1 ed:1 commuting:1 frequency:1 combining:1 quantum:30 our:5 eq:9 special:2 out:1 respects:1 space:9 restricted:1 since:5 rev:11 bad:1 research:2 re:1 ref:2 theory:4 gardiner:1 mechanisms:1 diagonal:1 possibility:1 aˆc:4 lajos:1 ask:1 milburn:2 interaction:5 derivation:1 ato:2 could:1 times:1 counterpart:1 hence:2 first:1 probability:1 variables:7 number:2 directly:1 open:2 illustrate:1 given:1 temperature:1 similarly:1 introduction:1 eqs:1 system:7 indicate:1 too:2 calculations:1 speaking:1 commutativity:1 molmer:1 exactly:5 superoperator:2 than:1 approximations:1 shabanov:1 submitted:1 halliwell:1 charges:1 a45:2 a42:2 fˆ:17 were:1 rimini:1 pointed:1 electrodynamics:2 generalization:1 affirmative:1 rent:1 their:1 symmetrized:1 subsystems:1 efficient:1 convenient:1 concerns:1 take:1 shall:2 rhs:1 phase:5 class:1 exp:18 physics:3 ritsch:1 supported:1 notations:1 relation:1 hungary:1 find:1 just:1 should:2 failed:1 ˆc:9 pretty:1 factor:2 oct:1 equilibrium:1 do:3 establishes:1 notation:2 di:4 dependent:1 oˆ:1 kfki:2 expectation:5 da:14 conceptual:2 ones:2 dt:3 interpreted:2 carmichael:2 budapest:1 arxiv:1 motion:3 investigate:1 fair:1 plausible:1 see:2 result:2 japan:1 forthcoming:1 interacting:1 a47:1 nuclear:1 positivity:3 symmetric:1 state:17 between:3 reproducible:2 reading:1 approach:1 terms:3 reproduced:1 initially:2 weak:1 however:4 unnormalized:1 distribution:6 observable:4 many:1 density:10 equal:1 context:1 expression:1 unitarily:1 relevant:2 bell:1 hybrids:1 semiclassical:21 grants:1 pob:1 considers:1 dψt:2 described:1 dum:1 aˆ:4 simplification:1 swe:5 due:1 been:3 much:1 coarse:16 interest:2 basic:1 expected:1 ph:2 define:2 corresponding:5 both:2 photon:1 coherent:5 present:3 wiseman:1 value:3 will:5 while:4 manner:1 unitary:6 coupled:2 almost:1 thus:2 non:2 according:2 ih:1 reads:1 itself:1 ia:1 currents:1 author:1 things:1 make:1 radiation:16 complex:3 quant:2 widely:1 resulting:1 used:3 upon:1 counterparts:1 hand:1 infinite:1 identity:3 relies:1 suitable:1 modes:1 nevertheless:1 no:1 well:4 model:2 usual:1 proposed:1 being:1 rotated:1 obtain:3 λa:2 atomic:10 correspondences:1 zoller:1 readers:1 absorption:2 seems:1 interested:2 lett:5 easy:1 guarantees:1 castin:1 identical:3 aspects:1 rules:1 possible:1 know:1 vacuum:2 using:1 mod:1 particle:1 follows:4 remind:1 yields:2 arbitrary:3 jˆ:2 reduced:3 therein:2 because:1 classical:9 conditional:1 springer:3 understood:2 iˆj:2 nonzero:1 cavity:5 though:1 novelty:1 extensively:1 proc:1 noise:2 diosi:1 subtract:1 hilbert:4 noisy:1 simplest:1 central:1 tracing:1 introduces:1 dependence:1 o:9 practical:1 plus:1 recognizes:1 introduced:1 sept:1 outlook:1 markovian:4 predictions:5 remarks:1 hermitian:4 references:3 operator:10 proportional:1 statistics:2 additional:1 assumed:1 strictly:1 initial:1 question:1 long:2 accordingly:1 quadratic:1 way:1 was:4 function:12 form:6 but:1 hu:1 atom:6 attainable:1 true:1 us:8 limit:1 problem:1 called:3 gisin:2 detailed:1 ac:6 natively:1 defined:3 certain:2 abstract:1 describe:2 general:1 single:2 cure:1 dλ:4 simulations:1 distributions:1 archive:1 regime:1 200a:1 otka:1 nonetheless:1 field:20 other:2 picture:3 elements:1 intend:1 models:1 includes:1 a0:6 variable:1 ago:1 coupling:1 assume:3 graining:4 time:2 observables:5 once:1
|
quant-ph9507011.txt |@word barone:1 remarkable:1 interference:1 brownian:20 entropy:5 go:1 follow:1 remarkably:1 boltzman:1 discern:1 whose:1 certainly:1 careful:2 depend:1 alamos:2 anglin:3 environment:13 program:1 those:2 ti:6 stochastic:9 insights:2 subtleties:2 division:1 wished:1 advantage:1 orthogonal:1 very:1 frequencies:1 conditions:6 induce:1 choice:1 ja:2 wishes:1 ultraviolet:1 interpreting:1 mixing:1 affect:1 little:1 exact:3 condition:1 paz:3 entire:2 magic:1 hamiltonian:5 t6:1 applicable:2 occurs:1 large:1 integro:1 small:1 equation:26 prevent:1 lagrangian:1 force:7 renormalized:2 consistent:1 direct:1 hillery:1 sign:1 approximation:2 second:2 timescales:1 value:1 subtle:2 further:2 dynamics:9 appreciating:1 canonical:2 spectral:3 appear:1 associate:2 brief:1 expressed:3 version:1 illustrations:1 values:5 mazur:1 method:1 contrast:1 edited:2 full:1 ibid:1 punch:1 here:1 natural:1 following:1 asymmetry:1 alone:1 path:2 quite:1 equations:15 implicit:1 z2:1 obtained:1 colored:2 receive:1 involved:1 inspired:2 larger:2 approaches:2 p2:3 products:1 usually:3 fbr:2 shorthand:1 lasts:1 scales:1 merely:2 f2:1 replace:1 apply:1 planck:8 linearly:2 derivatives:2 use:7 proceed:1 would:5 remains:3 positive:7 contains:1 negative:4 calculation:1 circumstances:1 therefore:1 memory:2 taken:1 associated:1 theoretical:2 today:1 more:9 hu:3 sharing:1 becomes:2 under:2 odinger:3 berlin:1 impulse:1 particular:1 cases:2 easiest:1 must:4 evolves:1 springer:1 defines:1 integrating:2 recall:2 challenge:2 work:1 oscillator:8 cancellations:1 cat:1 mq:1 temperatures:1 concepts:3 abandon:1 example:6 history:1 grained:1 compare:1 weaker:1 solved:1 process:2 sense:1 accept:1 states:3 effectively:3 performed:2 council:1 allowed:1 sought:1 guarantee:1 information:1 united:1 end:1 straightforward:3 provide:4 verify:1 discussion:4 zhang:1 write:4 how:3 rubin:1 answer:1 instead:2 verlag:1 ensemble:4 obeys:1 express:1 constraint:2 description:1 may:5 oscillators:7 after:5 derived:1 treatments:1 demanding:1 sophistication:1 wrong:1 mh:1 data:1 engineering:1 diffusion:3 branches:1 remember:1 sectors:1 light:1 spectra:1 explicit:2 exhibited:1 rather:2 sh:3 lhs:1 ultimate:1 allow:1 correlation:6 representation:5 order:1 grabert:1 wigner:23 gω2:4 produces:1 kampen:1 indeed:3 over:8 insight:2 vary:1 interpreted:2 course:2 supra:7 statistical:1 during:1 differs:1 still:5 pointer:1 its:2 environmentally:1 before:1 technically:1 derive:2 rapidly:4 surviving:1 la:1 fiz:1 interesting:1 masses:1 solving:2 scully:1 actually:4 usp:2 production:1 suspicion:1 systems:9 persist:1 mail:2 hidden:1 encompassed:1 might:1 easier:1 non:6 good:1 affected:1 predator:1 p12:1 hamilton:1 effects:1 they:2 bogoliubov:2 genuine:1 realize:1 easily:1 term:3 always:3 university:1 drop:1 ohmic:12 applied:1 theory:1 magnitude:1 each:1 2m:1 higher:1 2k:1 differential:2 generation:1 energy:1 gaussian:5 solution:2 obtains:1 amsterdam:1 quantum:41 laboratory:1 beyond:1 special:2 out:3 canada:1 emerges:1 prefactors:1 space:5 furthermore:1 since:6 crucial:1 denotes:1 b288:1 re:1 acting:1 dominated:1 mottola:2 gov:2 ref:1 correct:2 math:2 linear:22 unwieldy:1 mω:8 given:2 standard:4 completely:2 complicated:2 intermediate:1 generate:1 incorporates:1 derivation:1 language:1 times:3 motion:19 turn:1 signature:1 consequence:1 uses:1 βn:4 generalizations:1 think:1 first:1 origin:1 does:1 intuition:5 initial:17 probability:3 reveals:1 variables:4 confuse:1 number:4 fast:2 directly:2 open:2 f1:1 spread:1 idea:1 ingold:1 differ:1 needed:1 behaves:1 system:12 unruh:1 their:6 assumption:1 master:2 eqn:4 white:2 leggett:1 kac:1 final:6 lingering:1 gives:1 reversed:1 convention:1 environmental:17 part:3 schr:3 than:4 serv:1 past:1 kind:2 bei:1 effective:4 anticipate:1 see:5 halliwell:1 preparation:2 were:1 providing:1 treated:3 garrido:1 pre:1 counter:1 generality:2 fluctuation:3 dynamically:3 connell:1 few:2 say:1 analysis:1 need:2 cumbersome:2 confirms:1 demonstration:1 any:9 elsewhere:1 paths:1 computationally:1 studying:2 responsible:1 able:3 note:1 sciences:1 high:1 generalized:4 forces:1 so:5 explanation:1 gω:3 reconciled:1 even:6 exactly:2 unless:2 opposite:1 rhs:1 object:2 simplify:2 propagate:1 but:10 letter:1 phase:5 sophisticated:1 probabilistic:1 why:1 kb:2 consequences:1 considered:1 stronger:1 physica:1 points:1 principle:2 mechanical:6 quadratic:1 typically:3 fact:4 quantity:1 sector:6 impression:1 show:2 probe:1 purely:1 relation:4 solutions:1 interpretation:2 analogue:1 trivial:1 q1:3 o:4 q2:3 ratio:1 parameters:2 heavily:1 only:11 explicitly:1 factor:1 integrate:1 local:8 achieve:1 equilibrium:1 do:5 mixture:1 notation:1 means:3 dependent:5 familiar:1 zurek:2 simplest:1 stop:1 cannot:3 nearly:1 despite:2 combinations:2 compute:1 dt:1 holland:1 pωi:6 evolution:5 densities:1 fields:1 arxiv:1 remove:1 whether:1 nauk:1 qf:7 qi:11 describes:2 explanations:1 dpi:4 kernel:1 set:1 p2ω:1 national:1 correlations:1 up:1 observed:2 habib:5 depends:1 bare:4 result:1 p22:1 discussions:1 incorporating:1 techniques:3 caldeira:2 said:1 mechanically:1 pictures:1 away:1 definite:3 functionals:3 tend:2 importance:1 state:2 identification:2 closed:1 between:5 conceptual:1 boundary:2 approach:3 available:1 publishers:1 terms:4 initially:2 complement:1 suppresses:1 however:4 gratefully:1 vanishing:1 cut:4 analyzed:1 news:1 phasespace:1 suppressed:1 problem:11 thank:1 reaction:7 essentially:3 prescription:1 many:3 uncertainty:2 according:2 acknowledged:1 etc:1 receives:1 distinction:1 contribution:1 expression:1 finds:1 nearby:1 reside:1 co:3 timescale:1 cl:1 simple:2 harmonic:1 environments:3 121a:1 moreover:2 rep:2 factors:1 ensures:1 described:3 transformations:3 addition:1 due:2 been:3 quickly:1 much:7 pf:8 damping:1 interest:1 basic:1 degrees:2 ph:1 pi:10 corresponding:3 both:3 linearity:1 subscripts:1 excite:1 cos:2 new:1 neumann:2 understand:2 specifically:1 systematic:5 efficients:3 general:6 fokker:8 present:2 case:6 p1:1 inertial:1 processes:2 contemplated:1 tanh:1 contexts:1 defining:1 bill:1 single:1 salman:1 will:12 while:2 replaced:1 dkdk:1 pessimistic:1 coupled:1 von:2 thus:3 them:1 encouragement:1 encountered:1 ik:1 seem:1 capture:1 different:1 dragging:1 perform:1 realizing:1 formulations:1 indistinguishable:1 same:4 clearly:1 shorter:1 epoch:2 parts:3 quant:1 emphasize:1 widely:1 regime:3 events:1 difficult:1 independent:6 used:2 zwanzig:2 disadvantages:1 trajectories:1 disagree:1 effect:1 moving:1 entanglement:4 frequently:1 recent:2 relies:1 prescribed:2 off:4 nevertheless:1 well:5 echoed:1 academic:1 without:2 solve:1 machinery:1 model:4 chemistry:1 usual:2 just:1 less:2 being:2 isolate:1 obtain:4 regardless:1 yet:2 rapid:1 kluwer:1 density:7 point:5 seems:1 boston:1 unambiguously:1 deliberately:1 treatment:1 easy:3 appreciate:1 dqi:3 take:1 identical:3 aspects:2 rev:3 represents:1 z1:1 increases:1 know:1 background:1 press:1 using:8 necessary:1 like:1 particle:3 identifying:1 qualitative:1 adiabatic:3 unnecessary:1 specific:1 integrals:3 james:1 lok:1 become:1 reduced:3 heisenberg:1 shed:1 because:5 methods:2 classical:36 successfully:1 some:2 back:7 identified:1 q21:1 q22:1 respect:2 oscillations:4 pω:2 contaminating:1 happens:1 scale:1 cooper:1 lead:1 avoid:1 langevin:10 integration:1 causal:1 when:3 equal:3 provides:3 propagating:1 refer:1 presented:1 noise:12 slight:1 uniformly:1 equivalent:1 although:1 found:2 simpler:1 most:3 freedom:2 anomalous:1 dependence:1 recognized:2 distinct:3 a2:1 nothing:2 greatly:2 mixed:1 constraints:1 cambridge:2 markovian:2 previously:1 into:4 integral:4 functional:1 bath:3 dissipation:3 weighted:1 references:1 determine:1 sov:1 operator:1 proportional:3 conceptually:3 classicality:1 often:1 schramm:1 van:1 classically:4 assumed:1 support:1 there:4 knowing:1 long:3 los:2 appears:3 cauchy:2 inner:1 way:2 was:2 propagator:2 assumes:1 coarse:1 function:18 north:1 complete:2 form:3 converse:1 jul:1 formalisms:1 gain:1 delta:4 true:3 considerable:2 factorized:2 applying:1 emil:1 intuitive:3 ωq:1 wish:1 ford:1 uv:1 variations:3 ωt:1 us:1 ur:1 ωi:3 liouville:4 fluctuations:1 distribution:3 piece:1 called:2 expect:1 mechanics:8 required:1 constant:3 computing:1 defined:1 abstract:1 describe:1 influence:4 denote:1 peres:1 separating:1 examine:1 research:1 our:1 formalism:3 dγ:2 physical:6 tedious:1 again:1 functions:7 nm:1 no:2 generally:4 green:1 application:1 other:3 compares:1 details:1 department:1 interpretable:1 nice:1 conclude:3 picture:5 permitting:1 separate:1 models:5 dies:1 problems:5 includes:1 meaning:1 important:8 qω:2 coupling:2 dω:4 assume:2 physics:4 lanl:2 factorizes:1 mass:2 time:15 far:1 decoherence:3 robert:1 restored:1 once:2
|
quant-ph9507012.txt |@word limited:1 focus:1 gy:1 existing:1 although:1 overlap:1 lewenstein:3 edu:1 go:1 follow:1 contributions:2 issues:1 inverse:1 show:1 groundstate:1 finally:1 does:1 under:2 dramatically:2 ingredient:1 supported:1 advantage:1 very:5 choice:1 putting:1 emphasized:1 difference:2 riemann:1 presented:1 occurs:1 large:3 small:13 enhance:1 optics:1 application:1 smaller:7 ten:1 unpolarized:1 approximation:2 imply:1 enhancement:14 further:1 dynamics:1 targets:1 theory:1 even:2 what:3 sub:1 brackets:1 sum:2 expressed:1 uniform:4 current:1 above:3 ground:5 acknowledgments:1 coefficient:1 component:1 here:2 atoms:12 ranges:1 desired:2 focused:1 cos2:2 represented:1 box:1 institute:1 involved:1 study:1 action:1 formation:1 narrow:2 changes:1 emerge:1 useful:1 divide:1 suddenly:1 requiring:1 castin:1 scaled:1 total:8 unit:1 shlyapnikov:1 calt:1 sample:1 kinematics:1 therefore:1 themselves:1 theoretical:1 more:3 separated:1 formally:1 clearly:1 initial:3 emission:1 normalized:4 particular:3 must:4 involve:2 account:2 integrating:1 science:1 averaged:1 tc:9 obvious:1 temperatures:4 burnett:1 drops:1 performed:2 figure:2 give:1 process:1 thermally:1 suggestions:1 pieces:1 states:14 numbers:2 magnitudes:1 times:2 occur:1 information:1 describes:1 discussion:2 feature:1 chemical:3 how:1 pure:1 sin:1 wave:1 de:1 description:1 singular:1 may:4 after:3 different:3 consequence:1 plane:1 coming:1 fi:1 destructive:1 meaningful:1 natural:1 third:1 light:11 author:1 explicit:1 correspond:1 negligible:1 allow:1 keeps:1 order:3 typical:1 pulsed:1 over:7 displayed:1 course:2 thermal:10 experiments:1 including:1 mentioned:1 cold:5 still:1 its:2 before:1 rapidly:1 energies:2 interesting:3 boson:1 previously:1 degrees:1 differently:1 derivative:1 er40701:1 might:2 versus:1 non:3 greater:1 numerically:1 polarizations:2 fig:1 band:1 effects:4 they:5 eµ:1 separately:1 term:4 finite:3 subtler:1 always:2 drop:1 sufficiently:1 magnitude:2 trap:7 2b:2 2c:3 entirely:1 mean:1 significantly:2 energy:6 sov:1 reduce:2 frequency:3 measure:1 multiparticle:1 wavelength:3 transitions:4 eq:1 ep:3 out:1 ultimately:1 factors:2 rev:6 particles:3 investigation:1 evaluation:2 integrated:1 doppler:1 turning:1 linear:3 interactions:1 discontinuity:1 free:2 california:2 matthews:1 estimate:1 could:3 transition:3 david:1 motion:3 produce:3 place:1 isotropic:1 hence:4 origin:1 already:2 features:1 probability:2 variables:2 number:6 hitherto:1 utilized:1 ensher:1 done:1 long:1 precisely:1 angular:4 size:6 given:6 salient:2 temperature:9 twenty:1 condensate:4 occupancy:5 needed:2 assumption:1 observations:1 eqn:1 hundred:1 final:6 grant:1 trapped:1 relative:2 continuous:3 optical:4 somewhat:1 translation:1 than:1 jump:1 quantitative:1 target:2 double:2 rate:17 determined:1 amplitude:2 were:1 treated:2 collecting:1 addressing:1 lines:2 curves:2 crossover:1 substantial:4 occupied:6 orders:1 conversion:2 strength:3 angle:8 zero:2 depending:1 convenient:2 latter:1 aside:1 polarization:1 ideal:2 potential:6 so:2 detector:2 analogs:1 exactly:1 beyond:1 though:1 most:1 involving:2 significant:2 formulae:1 analytically:1 trapping:1 kb:2 average:2 typeset:1 points:1 ntotal:10 fact:1 phenomenon:1 intensity:4 rayleigh:3 probe:1 scattered:4 merit:1 converge:1 svistunov:1 consequent:1 d3:2 occupation:4 parameters:1 situations:1 should:1 jan:1 dalibard:1 only:3 factor:4 do:2 dominant:1 means:1 simplest:2 expectation:1 beam:4 cannot:1 ossbauer:1 despite:1 densities:1 sharpness:1 fields:1 arxiv:1 remove:1 implication:1 fixed:4 thanks:1 reveals:1 hν:1 unpublished:1 maximum:1 observed:1 collectively:1 depends:1 enhanced:1 discussions:1 kinetic:1 analog:1 interacting:1 macroscopic:1 review:1 pd3:1 state:19 smallest:1 closed:1 between:4 terms:3 nature:1 initially:1 weak:2 jp:1 however:5 incident:4 bose:20 jetp:1 distribution:6 comparably:1 faced:1 both:1 cos:1 limits:1 many:2 equal:1 politzer:3 figures:1 context:1 contribution:4 comes:1 adjusted:1 relevant:2 simple:2 had:1 harmonic:1 high:2 dimensional:1 simply:1 decreases:2 libbrecht:1 mc2:2 described:1 puts:1 three:2 been:2 much:2 treat:2 interest:2 pj:1 ph:1 choose:1 concentrated:3 corresponding:3 thousand:1 coherence:1 gas:7 dramatic:2 external:2 angles:20 present:4 case:1 laser:1 pacs:1 solid:3 conserved:1 value:1 will:3 dept:1 while:2 behavior:1 cancelled:1 situation:2 almost:1 heating:4 technology:1 disappear:1 confirmed:1 propagation:1 perhaps:1 border:1 ep2:2 same:4 any:2 shifts:1 stimulated:9 quant:1 largest:2 units:5 dimensionless:2 several:3 independent:2 used:1 see:2 again:1 comprehensive:1 numerical:1 effect:4 moving:1 resonance:2 infinite:1 passing:1 recent:1 lower:4 off:4 traps:1 nevertheless:2 makes:1 roughly:1 components:1 position:1 arising:1 just:2 percent:1 vanishes:1 shape:1 underlying:2 atomic:6 immediately:1 spatially:1 momenta:1 scattering:26 yet:2 note:5 density:8 cornell:1 photons:1 guaranteed:1 add:1 caltech:1 lett:2 versa:2 excited:4 momentum:12 identical:3 evaluate:1 results:1 possible:2 increases:1 five:1 confined:1 using:3 part:1 scatterings:3 helpful:1 like:2 particle:6 identifying:1 signal:3 manifest:1 alkali:1 either:1 integrals:1 become:1 reduced:2 preskill:1 because:6 often:1 phenomena:2 back:1 born:1 evaluated:1 classes:1 happens:1 ignore:1 scale:1 cooper:2 javanainen:3 electromagnetic:1 measurements:1 per:1 critical:4 eliminate:1 2a:2 perpendicular:1 expansion:1 revtex:1 shapes:1 super:2 about:1 actual:2 discussed:1 dependence:7 o:3 essential:1 practical:3 range:1 seeing:1 presence:1 condensing:1 into:8 integral:3 due:2 appropriate:2 references:1 determine:2 einstein:3 proportional:3 bosonic:1 statistics:4 transfer:2 support:1 there:5 gases:2 width:1 anderson:1 quadratic:2 bosons:2 low:6 fraction:2 forward:1 was:1 function:2 medium:3 pd:1 form:1 some:2 but:2 volume:2 expected:1 heat:1 atom:11 line:2 october:1 qualitative:1 whether:1 wieman:1 up:1 below:8 simplifying:2 occupancies:2 fluctuations:1 problem:1 define:1 similar:1 interval:1 defined:1 abstract:1 contribute:1 fg03:1 denote:1 quantum:1 single:3 laboratory:1 work:1 physical:2 ni:5 functions:3 compared:3 no:10 dashed:2 unoccupied:1 when:1 detail:1 nf:7 field:1 pasadena:1 mass:2 you:3 really:1 photon:8 variation:2 transfers:2 vice:2 space:1 diffraction:1 weights:1 time:3 far:1 having:1 virtue:1
|
quant-ph9507013.txt |@word consider:2 similarity:1 results:1 fig1:2 localized:1 whose:1 heller:1 under:1 include:1 belonging:3 very:1 dell:1 wave:17 exact:1 condition:8 hamiltonian:2 turns:1 try:1 small:2 rate:1 substituting:1 estimated:1 cfr:1 even:1 what:1 localization:3 favour:1 ψl0:2 above:1 increasing:1 method:3 satisfy:1 full:1 degree:3 respectively:2 spacing:1 here:1 reported:2 cylindrical:1 along:7 strong:1 appears:1 obtained:4 chaotic:13 generalizing:2 study:1 studied:1 allows:1 reports:1 leaving:1 products:1 action:2 narrow:1 summation:3 linearly:1 plot:2 superpositions:1 would:1 live:2 classically:4 depicted:2 therefore:3 type:2 more:1 sort:1 particular:2 cases:2 must:1 high:1 account:2 deformed:1 values:3 thin:2 following:1 example:3 performed:2 degenerate:2 figure:3 calculation:1 expanding:2 states:3 numbers:15 want:1 sense:1 eckhardt:1 sharp:1 verlag:1 motion:6 discussion:1 di:4 regions:1 ρn0:3 circular:1 sommerfeld:1 algebra:1 replacing:1 after:2 orbits:2 ff:1 verified:1 revealed:1 constants:1 short:1 ρnl:3 light:1 correspond:1 so:1 shade:1 order:7 least:3 wigner:1 help:1 indeed:1 over:1 satisfied:1 years:1 stability:1 course:2 paper:1 through:1 argued:2 captions:1 still:1 longitudinal:1 probability:4 chosen:2 interesting:1 solving:1 tori:2 vicinity:1 actually:1 degrees:1 systems:10 derivative:1 into:2 τq:4 eventually:1 affected:1 combination:1 numerically:1 framework:1 billiard:9 they:3 now:1 level:1 establishing:1 possibilities:1 l2:1 l0:17 radial:3 2l:2 universit:1 side:1 referred:1 another:1 exhaust:1 benito:1 energy:4 related:3 used:1 quantum:16 wavelength:1 eq:8 out:1 large:6 shown:2 rev:3 chaos:1 attracted:1 formula:1 ref:5 benjamin:1 linear:4 barrier:2 written:1 fisica:2 possibility:1 assures:1 besides:1 org:2 estimate:1 r2:1 could:4 scars:11 keep:1 counterpart:1 turn:1 symmetry:1 striking:1 restrict:1 construct:3 directly:3 angular:8 given:1 checked:1 introduction:1 dipartimento:2 system:9 approximately:2 their:1 too:1 structures:3 gives:1 shell:7 ryzhik:1 centered:1 transverse:3 part:1 authors:1 than:2 png:4 distance:1 zero:1 future:1 contrary:1 ann:1 mind:1 spectrum:2 quantising:1 distorted:1 seen:1 concentration:1 any:2 viewed:1 essentially:2 billiards:1 mechanism:1 potential:1 build:3 spectral:2 most:1 jul:1 successive:1 phase:2 uncertainity:1 class:1 especially:1 considered:2 calculated:1 kn:1 physica:1 exp:4 fact:1 phenomenon:3 show:3 relation:1 subtle:1 ratio:4 state:1 only:5 factor:2 integrable:9 constant:1 local:3 means:1 de:1 cannot:1 words:1 prime:1 hits:2 arxiv:3 gutzwiller:2 rotationally:1 common:1 fixed:1 view:1 variations:1 packet:9 observed:1 namely:3 radius:1 result:3 close:2 contour:4 closes:1 satisfying:1 eigenfunctions:4 nuclear:1 sites:1 eigenstates:4 enough:1 costant:1 closed:4 between:4 invariant:3 conditions:1 available:2 notice:1 terms:3 attention:1 however:1 robnik:1 jl:2 vanishing:2 extent:1 concentrated:5 untouched:1 cos:2 last:1 2n:1 many:1 taking:2 conclusions:1 called:2 fulfilled:2 sensitive:1 connection:2 contribution:1 expression:1 otherwise:1 mechanics:2 point:1 wall:2 had:1 asymptotically:4 period:1 respect:1 li:1 considering:1 ps:2 pq:1 described:2 second:1 quantisation:2 trajectory:13 been:5 balian:1 much:4 ph:3 fig:2 wants:3 suggested:1 direction:1 corresponding:3 precision:3 fuctions:1 catania:4 presented:1 present:3 case:6 intriguing:1 appearance:3 value:4 will:2 region:2 procedure:6 almost:1 averaging:1 ii:1 reads:2 rif:1 around:6 different:1 italy:2 generic:1 suggest:1 belong:1 lett:2 same:6 clearly:1 unity:2 quant:3 gets:1 kn0:2 higher:2 independent:2 extended:1 http:2 trivially:1 hand:1 moving:1 expand:1 knl:7 task:1 minimize:1 well:3 bohr:1 academic:1 coordinate:4 just:1 being:4 when:1 actions:1 shape:2 yet:1 preprint:1 density:6 seems:1 simple:3 spread:5 treatment:1 easy:1 theorem:1 solvable:1 eigenstate:1 momentum:2 eigenfunction:2 format:2 possible:4 press:1 integer:1 semi:5 particle:3 adiabatic:1 specific:1 imposes:1 unstable:1 sezione:1 arbitrary:2 become:1 stationary:3 essential:1 right:1 classical:21 some:5 springer:1 understood:1 examples:1 table:4 vol:1 does:1 bessel:2 bf:4 integrals:1 each:1 expansion:1 step:2 contraint:1 properties:1 asymptotic:4 extension:1 freedom:1 quantal:3 mean:1 bloch:1 considerations:2 presence:4 h2:1 spreading:1 gradshteyn:1 integral:2 because:1 references:1 elementary:1 few:2 approximate:5 long:2 italia:2 series:1 bogomolny:1 function:6 survives:1 elsewhere:1 form:2 energies:1 but:1 hoped:1 repeated:1 corso:2 infn:2 made:1 embedded:1 characteristic:3 smooth:1 up:4 us:1 limit:6 suitable:1 problem:6 display:1 strongly:1 zeroes:1 associated:3 defined:1 recognize:1 abstract:1 generating:1 exist:1 formulation:1 lifetime:5 eric:1 regime:1 functions:2 nl:1 polygon:1 integrability:2 no:1 fixing:1 generally:1 other:1 mottelson:1 details:1 spatial:1 conclusion:1 star:1 superposition:3 accidental:1 tranform:1 peak:3 structure:2 building:2 implies:2 longer:3 packets:1 mass:1 time:7 n0:5 inc:2
|
quant-ph9507014.txt |@word represent:3 consider:5 both:4 alternatives:2 four:1 eds:1 commute:1 go:1 displaying:1 cases:3 forget:1 whose:4 certainly:1 depend:2 irrelevant:1 concerned:1 tp:1 finally:1 restriction:2 stochastic:3 analogous:1 applied:1 very:2 differently:1 choice:2 every:2 entire:4 hamiltonian:16 did:2 positions:1 solution:1 discrete:3 vector:17 dealing:1 healey:2 picked:1 further:1 specker:2 even:6 what:3 apparatus:12 section:3 brief:1 version:1 suspect:1 above:6 obvious:1 consisting:1 ihτ:1 full:2 never:1 here:2 understanding:1 identifications:1 iσx:1 bj:1 berkeley:2 quite:1 equations:1 appears:2 change:3 finkel:1 obtained:1 leaves:1 prior:1 suggestion:1 hospitality:1 elaborated:2 hardy:2 summation:2 apply:2 causal:2 use:4 takes:1 would:11 probabilities:1 contains:1 next:1 comparing:2 ψi:8 call:2 opposed:1 taken:2 undivided:1 type:1 tell:1 more:2 started:1 initial:6 operators:2 odinger:2 particular:2 foundations:1 unfaithful:5 iσy:1 must:3 evolves:1 certainty:1 equation:2 work:1 modified:1 theories:5 values:13 example:20 fraassen:2 give:1 calculation:1 suggestions:1 states:3 indicates:2 degenerate:1 sense:1 occur:1 guarantee:2 end:1 rather:1 discussion:2 get:2 write:2 how:4 answer:2 instead:3 product:1 description:1 may:1 max:1 after:2 collection:1 wrong:2 attempt:1 third:1 correspond:2 element:2 so:10 fundamental:1 correlation:1 putting:2 σza:1 superscript:2 determinate:1 interpretation:1 indeed:1 over:6 lahti:1 course:3 paper:3 london:1 differs:3 satisfies:1 still:2 its:2 before:7 acknowledge:1 chosen:1 scully:2 actually:3 suspicion:1 choose:1 mail:1 might:3 easier:1 non:2 obtaining:1 reflected:2 they:2 symposium:1 now:3 discuss:1 nor:1 possess:2 represents:3 term:12 englert:2 always:2 university:3 presented:2 sufficiently:1 arrow:1 each:6 found:1 side:5 formulate:1 independent:1 measure:2 quantum:5 laboratory:2 happen:2 eq:41 out:3 shown:3 matrix:2 space:2 since:9 rev:2 particles:1 denoted:1 gov:1 ref:5 correct:3 math:1 shows:1 philosophy:1 theory:12 assured:1 lawrence:2 standard:2 difficulty:1 surely:1 put:2 interaction:16 discussing:2 could:9 times:3 place:1 tempting:1 view:1 first:11 there:6 probability:1 number:1 precisely:2 given:8 necessarily:3 guest:1 requirement:1 introduction:1 eqs:7 system:17 least:1 indicate:2 nian:1 identity:2 final:5 gives:1 collapse:1 relationship:1 completed:1 exactly:1 took:1 speakable:1 july:1 representing:1 kind:4 second:10 limiting:1 supposed:1 were:5 interactive:1 san:2 spectrum:1 generalization:1 say:4 seen:3 seem:1 dynamics:14 routledge:1 thought:1 responsible:1 physique:1 note:4 ideal:1 take:7 broglie:3 unless:1 shall:1 any:10 most:2 synthese:1 but:9 acknowledgements:1 measured:15 surprising:1 considered:3 sometimes:1 sussman:2 exp:3 physics:1 specification:2 fact:5 quantity:6 show:1 sza:3 szs:14 ratio:1 spite:2 state:23 should:3 only:6 bases:1 ambiguity:1 hamiltonians:4 beable:23 notation:4 means:1 de:3 likely:1 cannot:1 during:4 dt:2 bar:9 arxiv:1 yield:5 calling:1 though:1 kochen:4 remains:1 vink:11 temporarily:1 our:2 national:2 see:11 result:4 said:1 interacting:3 away:1 definite:6 written:1 between:7 jos:2 terms:3 nature:2 initially:1 confusion:1 however:5 reproduces:2 unnormalized:1 suggested:5 observable:1 interpretations:2 prescription:2 taking:2 equal:3 agree:1 participating:1 σz:6 σy:1 σx:1 context:1 forgotten:1 argue:1 cj:2 ci:6 bell:11 simple:1 ca:1 corresponds:3 associated:1 considering:5 described:1 basis:2 been:3 ai:6 belongs:1 combined:2 ph:1 define:2 contribute:1 corresponding:2 6e:1 commutes:6 quantities:5 bohmian:1 understand:4 c2:6 c1:6 general:1 spin:2 those:3 case:6 unlike:1 harder:1 value:36 choices:1 will:28 suppose:2 situation:1 walther:2 identical:1 von:19 thus:4 them:1 middle:1 im:1 vanish:1 fermion:1 different:5 make:3 same:4 lbl:1 quant:1 pauli:1 conversations:1 several:1 difficult:1 evolve:1 used:2 singapore:1 upon:5 hand:6 necessity:1 supposing:1 expand:1 eigenvectors:2 schr:2 nevertheless:1 well:1 obviously:1 bohm:11 without:2 components:1 position:8 model:1 usual:3 proposed:1 being:1 when:6 world:1 alternative:1 hji:4 eigenstates:2 mittelstaedt:1 point:1 had:6 other:4 lett:2 theorem:1 iπ:2 iσ:1 eigenstate:5 momentum:1 real:2 easily:1 read:1 couple:1 measurement:55 possible:2 dewdney:2 hiley:1 know:1 press:2 using:4 ruled:1 like:1 particle:5 follows:2 beables:14 yields:5 alternatively:1 terminology:2 right:5 neumann:19 namely:4 some:3 somehow:1 examples:6 b2:1 duration:2 avoid:2 measurements:7 does:6 assuming:3 refer:1 measuring:1 scientific:1 dieks:2 jumps:1 bi:3 expansion:1 restrictive:1 although:2 therefore:3 hilbert:2 about:1 universe:1 completing:1 discussed:3 dependence:1 o:1 2i:4 δij:1 important:1 ensure:2 modal:5 introduced:3 cambridge:2 faithfulness:3 markovian:1 within:1 integral:1 appropriate:4 because:1 references:1 operator:4 proportional:3 van:2 placing:1 question:1 intention:1 squires:2 andy:1 exceptional:2 was:7 treat:1 complete:1 form:1 restrictions:1 jul:1 bub:2 collapses:1 made:2 whether:2 us:7 until:3 discretized:2 below:1 limit:2 called:1 b1:2 mechanics:3 required:1 constant:1 defined:3 certain:1 abstract:1 aj:1 moved:1 denote:3 single:1 exist:1 formulation:2 erie:1 meth:1 irrespective:1 47a:1 faithful:19 want:1 no:3 generally:1 occasional:1 naturforsch:1 interested:1 details:1 tij:3 department:1 tity:1 elements:2 preceding:1 helpful:1 a1:2 a0:6 a2:2 included:1 independently:1 implies:2 assume:2 interval:1 together:1 notion:1 time:12 starting:1 unspeakable:1 once:1
|
quant-ph9508001.txt |@word consider:4 caused:1 forbidden:1 activated:4 results:22 eds:2 go:1 activates:2 localized:1 relationships:1 depend:1 violate:3 aug:1 subjected:1 send:8 supported:1 those:2 random:1 consequently:1 far:5 choice:2 untenable:1 jacob:1 affect:1 condition:21 school:1 presented:2 cause:3 notes:1 applicable:1 science:1 manifestly:2 a123:1 configurations:6 rohrlich:5 tel:2 consistent:5 past:6 zero:3 enhancement:1 further:1 casual:1 even:1 established:1 what:2 appear:1 incompatible:2 section:1 axes:1 near:3 access:3 experiment:1 goes:1 steinberg:1 preserved:1 pioneering:1 respectively:5 modify:1 jointly:1 selective:4 operating:1 others:1 causality:14 along:5 nachr:1 obtained:2 study:1 allows:3 prior:1 procedure:1 permit:2 action:3 bob:25 studies:1 honor:1 criticism:1 via:1 regardless:1 projection:2 outcomes:1 analyzing:1 nonlocal:1 apply:4 causal:4 would:8 probabilities:1 give:1 predictions:4 next:1 comparing:1 jam:3 therefore:5 means:1 theoretical:1 diagrams:2 more:2 separated:8 introducing:1 israel:3 anticorrelation:1 holt:1 tested:1 carrying:1 particular:3 foundations:2 cases:1 must:9 eberhard:1 tokyo:1 recall:1 setup:2 work:1 taup:1 arrangements:1 concepts:1 following:3 example:2 claim:2 figure:1 stated:1 relativistic:14 allowed:1 accept:1 states:1 contradicts:1 lorentz:6 performed:1 arise:2 station:1 axis:5 information:4 respective:1 requirements:1 rather:2 s2:4 s1:4 holds:1 arrangement:3 how:2 answer:1 ordinary:1 ensemble:1 beyer:1 superluminal:10 may:1 after:1 derived:1 them:4 diagram:2 date:1 geometrical:1 parallel:1 shortcomings:1 induction:1 natural:1 third:1 joint:1 light:26 separations:1 s3:4 so:3 allow:3 tamper:4 hassan:2 discussion:1 horne:1 acts:2 help:1 indeed:1 satisfied:1 d19:1 held:1 paper:1 london:1 experimentally:1 mentioned:1 japan:1 satisfies:2 still:1 its:2 before:1 perfect:1 derive:1 thank:1 jim:17 aviv:3 window:2 systems:5 might:3 versus:1 non:22 affected:2 propose:1 introduce:1 framework:1 kamefuchi:1 they:5 oxford:1 now:2 discuss:2 droz:1 lies:1 tampering:2 university:1 infer:1 possibilities:1 inequality:1 each:6 found:5 entirely:1 realism:4 constraints:6 activate:2 conflicting:1 frames:2 sandu:1 used:5 obtains:2 measurement:3 loops:3 our:1 beyond:3 event:1 special:1 out:7 shown:6 space:5 nuovo:1 since:3 rev:13 projected:1 research:1 particles:6 contained:2 daniel:1 denoted:1 lecture:1 supports:1 shows:4 benjamin:1 provide:1 theory:2 possibility:5 differing:1 jammers:4 completely:2 york:2 put:1 rises:1 forbids:1 pairs:5 ministry:1 geometry:1 could:3 creates:1 turn:1 place:2 chiao:1 hence:4 speeds:1 first:4 number:3 restrict:2 done:2 least:2 another:2 impossible:1 open:1 angular:1 aharonov:3 illustrate:1 given:2 necessarily:1 checked:1 introduction:2 eqs:3 relations:2 their:6 assumption:2 too:1 scheme:4 frame:2 recovered:1 gives:1 originating:1 collapse:1 explanation:1 albert:1 part:1 than:2 distance:2 nathan:1 showed:1 penrose:1 require:1 transferred:1 a46:1 absence:3 were:3 result:2 deciding:1 generality:1 well:2 overcomes:1 measure:4 alley:1 any:13 routledge:1 lie:3 convenient:1 latter:1 able:1 mechanism:9 polarization:3 instance:1 take:1 timelike:1 transmit:1 completed:1 unless:1 opposite:1 who:2 reach:2 singlet:1 letter:6 device:6 measured:2 technion:1 average:3 gather:3 stronger:1 order:7 proceedings:1 principle:1 link:5 physics:3 shimony:2 phenomenon:2 show:1 vigier:3 probe:1 disturbs:1 determined:1 find:7 current:1 based:1 proposed:1 parameters:1 duncan:1 notice:1 situations:1 explain:1 outside:3 should:1 dalibard:1 only:9 explicitly:1 equally:1 isham:1 local:24 petroni:1 do:4 his:3 notation:1 get:1 assumed:1 preferred:1 truly:1 criticized:1 famous:1 cannot:6 reversal:1 new:3 years:1 reveal:1 a81:1 podolsky:1 arxiv:1 experiments:3 roger:2 predicted:3 vincent:1 conform:1 requirement:1 set:2 predicts:1 observer:3 imposing:1 violated:1 correlations:28 j1:14 j2:5 immigrant:1 detection:1 see:2 projections:1 discussions:1 close:4 violates:2 satisfying:1 inequalities:3 away:1 tend:1 state:5 future:18 various:1 between:5 invariant:2 prentice:1 conditions:6 available:1 ends:1 triplet:1 recently:1 nature:3 component:1 however:9 tacit:1 succeed:1 selectively:1 here:4 configuration:14 received:1 interpretations:1 discernible:1 many:1 region:2 a49:1 expression:1 experimental:9 among:1 jammer:6 relativity:1 bell:6 address:1 community:1 jammed:1 consideration:1 respect:4 forms:1 described:1 second:1 locally:1 due:1 been:2 defined:1 workshop:1 combined:2 interest:1 ph:1 abstract:1 fig:10 describe:2 corresponding:5 both:6 santos:1 sufficient:2 observers:1 denote:2 spin:14 present:1 applied:1 value:1 will:12 while:6 suppose:3 loop:2 spacelike:8 thus:2 violating:2 encountered:1 bias:1 cone:15 technology:1 binary:10 different:5 perhaps:1 inc:1 perform:1 suggest:2 make:1 lett:12 same:2 quant:1 several:1 events:9 independent:3 arrives:2 imply:1 published:1 effect:4 emanating:1 experimenter:3 unpublished:1 wholeness:1 insure:1 center:1 locality:2 epr:7 bohm:9 without:1 components:1 model:4 arising:1 popescu:5 generally:1 proximity:1 unary:10 aspect:3 using:1 paul:1 speed:1 eigenstates:1 previous:2 contradicting:1 implicate:1 conclusions:2 absorption:2 hall:1 signals:6 source:2 combine:3 questioned:1 violations:2 momentum:1 generalized:1 aspects:1 demands:2 showing:2 possible:7 hiley:1 entangled:7 press:1 immediately:1 accepted:1 necessary:2 helpful:1 particle:3 signal:5 alice:24 separately:4 imposes:1 either:4 setups:1 claredon:1 grangier:1 because:2 cones:7 sequence:4 some:2 somehow:1 b1:7 embodied:2 lead:3 measurements:15 exceeding:1 overlap:10 does:5 eliminate:1 tends:1 demonstrated:1 obey:2 june:1 communicate:2 step:1 permitted:2 about:1 carried:6 freedom:1 accepts:1 o:1 kwiat:2 range:1 rosen:2 ou:1 slightly:1 raised:2 presence:3 previously:1 communication:5 into:5 within:6 three:4 down:2 pair:3 schemes:1 references:1 determine:1 einstein:1 operator:2 physical:1 her:1 interacted:1 precludes:1 there:1 question:4 transform:1 rapisarda:1 restricts:1 conservation:1 mandel:1 way:1 was:1 disallowed:1 complete:1 form:2 tally:3 but:5 contradictory:5 ramat:1 astr:1 themselves:1 he:2 absent:1 society:1 whether:5 minkowski:4 up:2 cim:1 similar:3 agree:1 precedes:1 mechanics:18 shih:1 ai:5 certain:1 ak:1 aj:5 general:1 quantum:29 single:2 exist:1 defines:1 no:4 na:4 nb:8 when:3 other:7 test:2 jamming:49 models:1 preceding:1 problems:1 a1:7 generated:2 astronomy:1 implies:1 assume:1 clauser:1 interval:1 d24:1 together:2 experimenters:5 time:7 reached:1 signalling:3 requires:4 covariant:1
|
quant-ph9508002.txt |@word represent:1 concepts:1 consider:4 rev:2 forbidden:1 lack:1 results:1 unchanged:1 existing:1 leads:3 obstruction:1 commute:2 egles:1 causes:1 whose:4 inverse:2 const:1 aug:1 tr:2 quasi:2 those:1 under:3 hermann:1 tg:10 include:1 γg:2 straightforward:2 very:1 implicitly:2 rise:1 translations:7 springer:2 induce:1 choice:4 denoted:1 isomorphism:1 reinvestigate:1 redefinition:2 difference:1 matrices:1 fakult:1 condition:1 solves:1 level:4 positions:1 solution:3 try:1 vector:5 section:13 manifestly:1 eigenvalues:1 prevent:1 zd:1 direct:2 literature:1 translating:1 zero:4 dynamics:2 implemented:1 canonical:2 what:3 δrab:1 specification:2 brief:1 expressed:3 d3:1 version:1 localized:1 above:1 3c:2 new:4 3a:3 boost:2 3d:4 satisfy:2 respectively:1 never:1 equals:1 here:4 understanding:1 les:1 groups:3 address:1 directions:1 depend:1 along:3 quite:2 respect:1 appears:1 galilei:24 remark:2 leaves:1 vectors:1 allows:1 resulting:2 action:21 opinion:2 implement:3 fourier:2 quotient:1 via:2 followed:1 projection:1 coordinatized:1 extra:1 namely:1 texts:1 vc:1 translational:1 summation:1 total:6 use:2 superpositions:2 would:5 positive:2 contains:1 next:3 comparing:1 explicitly:1 kinematics:1 therefore:7 ψm:16 taken:1 more:4 sort:1 formally:1 integers:1 composite:2 becomes:2 operators:6 corrected:1 odinger:14 berlin:2 correspondingly:1 particular:4 known:1 projective:4 must:6 parameterize:1 none:1 valued:2 recall:1 equation:15 mi:44 london:1 mj:1 infinitesimal:3 obvious:2 learn:1 following:4 vt:2 example:3 meant:1 compare:3 reserved:1 abelian:2 relativistic:2 sense:2 lψ:3 states:14 irreducible:1 times:2 occur:1 axis:5 needs:1 rays:2 domenico:1 rather:5 verify:1 discussion:2 acts:8 write:1 how:5 actual:1 pure:6 instead:2 ordinary:4 verlag:3 parameter:2 priori:5 inputs:1 product:1 continues:1 algebra:5 may:6 db:1 derived:1 dc:1 freiburg:4 plane:2 ρmix:2 physik:1 fg:3 multiplication:3 end:1 law:11 constants:1 stress:1 dynamical:24 imply:2 spectra:1 correspond:2 su:2 element:8 provide:1 so:6 allow:2 representation:11 order:10 talk:1 restriction:1 helv:1 interpretation:4 kiefer:1 giulini:3 indeed:3 over:2 machida:1 interpreted:2 xi:41 including:2 motions:2 differs:1 existence:1 satisfies:2 its:4 boosts:3 before:1 derive:2 group:41 2zb:1 chosen:1 masses:11 coordinates:5 actually:3 forms:1 degrees:2 systems:2 mail:1 kupsch:1 alter:1 correspondence:2 non:6 motivated:1 combination:3 views:1 material:1 evolution:1 isomorphic:4 break:1 framework:3 they:1 half:1 rotation:1 now:16 discuss:1 thep:1 easily:4 term:3 stated:1 hamiltonian:5 redundancy:1 composition:1 d3n:3 l2:3 turns:2 found:3 universit:1 side:2 subset:1 ann:1 primas:2 map:1 energy:4 idea:2 bijective:2 extended:5 yield:1 measure:2 quantum:20 our:9 eigenstates:4 out:3 shown:2 matrix:2 space:24 restricted:2 since:4 crucial:1 denotes:2 particles:3 acting:1 ζi:22 herder:1 rn:3 induced:1 integrated:1 math:4 shows:1 theory:9 diagonal:1 free:1 standard:10 admits:1 difficulty:1 reason:4 york:1 besides:1 put:1 untransformed:1 beginning:1 generate:1 r4:1 definition:1 interaction:1 derivation:1 r3:1 impose:1 εabc:4 motion:2 derivations:3 δij:1 hence:6 retain:1 app:1 think:1 first:3 xj:1 already:2 symmetry:16 question:1 variables:6 xa:2 thereof:2 perform:1 restrict:3 multiplying:1 done:1 relations:1 representations:4 precisely:1 angular:3 illustrate:1 given:19 necessarily:1 their:1 introduction:1 adjoint:1 system:8 least:2 needed:1 assumption:2 statement:2 reductionism:1 gives:1 shifted:1 acquire:1 wisdom:1 part:1 translation:9 than:2 expanding:1 plausible:1 herold:1 edition:1 distinguishes:1 cimento:1 see:4 contrary:1 were:2 treated:3 distinguished:1 hz:1 r3n:4 fashion:2 symmetries:6 dynamically:1 argument:1 generalization:1 20a:1 20c:1 20b:1 20e:2 20d:1 need:4 seen:3 any:4 nouvo:1 ray:3 lie:2 constructions:1 jour:1 minimally:1 convenient:2 self:1 note:1 potential:3 take:2 continuous:4 unless:1 centre:4 price:1 measures:1 germany:1 ht:3 significant:1 formulae:1 phase:7 acknowledgements:1 had:1 enveloping:1 commutation:1 observation:1 consequences:1 considered:6 calculated:1 sometimes:3 cover:1 face:1 points:2 principle:3 exp:20 mechanical:4 velocity:1 left:1 notion:1 fact:3 laws:2 precise:1 saying:4 show:3 text:1 hm:8 namiki:1 levy:1 purely:2 spaces:6 relation:1 solutions:6 trivial:2 find:3 knowledge:1 parameters:2 implementation:3 commutators:1 explain:1 written:3 topological:1 should:13 only:6 going:1 generators:1 factor:1 integrate:1 araki:1 local:1 zeh:1 dn:3 do:8 notation:1 means:7 dependent:1 familiar:1 de:2 overall:6 expectation:1 da:3 cannot:5 valuable:1 words:1 3b:1 dt:2 2mi:6 regarding:2 arxiv:1 wightman:1 remove:2 investigate:2 redefined:1 common:1 contain:1 identify:1 raghunathan:1 fixed:3 valid:1 view:3 kernel:1 requirement:4 set:7 physically:1 manufacture:1 relative:1 argued:1 depends:1 individual:3 geometrically:1 declares:1 uller:1 discussions:1 inequivalent:1 kinetic:2 wonder:1 phases:2 invoked:1 interacting:1 label:2 symmetric:2 state:8 identification:1 between:3 invariant:7 geometric:1 measurable:1 attention:1 terms:1 extend:1 nature:1 complement:1 restricting:1 p2i:2 however:3 vanishing:1 complicate:1 δab:1 multiplier:1 configuration:6 thank:1 x2i:1 2n:1 many:3 taking:1 according:2 minus:1 stuttgart:1 admit:1 context:6 casimir:2 uni:1 expression:2 finds:2 aa:1 relevant:1 point:5 simple:2 character:1 cg:5 corresponds:2 simply:2 rpi:1 associated:2 superselection:20 separable:1 considering:1 better:1 ensures:1 described:1 transformations:3 second:1 union:1 associativity:2 due:1 been:1 much:1 treat:2 galindo:1 expected:1 ph:2 pi:5 ignorable:1 universal:2 define:6 arises:1 corresponding:8 quantities:1 r4n:2 equations:3 curves:2 remedied:1 last:1 general:3 spin:2 present:4 case:3 kuchaˇr:1 look:1 value:1 heidelberg:2 will:2 shall:2 situation:5 procedure:1 manner:1 va:2 vb:5 unitary:6 thus:3 them:1 discrepancy:1 disjoint:1 reads:1 rij:2 wave:1 vanish:1 bargmann:4 different:15 thereby:1 anymore:1 adjoin:1 pay:1 make:3 belong:2 lett:1 same:4 clearly:2 quant:2 arguments:1 largest:1 physical:11 infer:1 difficult:1 independent:2 used:1 phm:10 trivially:2 hand:4 usually:3 internal:3 invariance:10 identity:2 subgroups:1 schr:14 center:2 whole:1 no:8 well:1 obviously:3 without:1 solve:1 consistency:1 model:5 chemistry:1 latter:1 contingent:1 subgroup:4 distances:1 just:11 being:1 obtain:1 actions:1 properties:2 transforms:1 using:3 localize:1 momenta:2 yet:1 down:1 lebesgue:2 density:1 ease:1 nonrelativistic:1 seems:2 appeared:1 add:1 other:2 transformed:1 treatment:1 input:2 transformation:15 momentum:3 generalized:1 real:5 acta:1 spinless:1 represents:1 rules:7 showing:1 measurement:1 possible:2 spanned:1 possibly:1 21d:3 21e:1 21b:1 21c:1 background:1 21a:1 press:1 integer:1 accepted:1 formal:3 insert:1 leblond:1 necessary:2 like:2 particle:4 δv:2 alternatively:1 serves:1 specific:1 yields:2 translated:1 δg:4 δb:2 reduced:1 gauge:3 δa:2 mathematical:1 right:3 old:1 classical:11 some:6 understood:2 election:1 specified:1 proper:4 generates:1 lead:1 avoid:1 unavoidable:1 integration:1 comments:1 does:8 prog:1 minimal:2 refer:3 inserting:1 obey:1 equivalent:7 each:5 ruf:1 expansion:1 display:1 shifting:2 redundancies:1 2m:1 refers:1 subtract:1 hilbert:12 comparison:1 about:1 kinematical:1 central:8 extension:6 freedom:2 o:5 costs:1 arise:1 carries:1 extensions:3 act:2 slightly:2 considerations:1 equally:1 formerly:2 presence:1 h2:2 into:2 within:5 integral:2 functional:1 accommodate:1 lies:2 appropriate:1 references:1 determine:2 operator:6 proportional:1 strasse:1 conceptually:1 mere:2 existed:1 additional:2 prepare:1 strictly:1 there:8 hex:4 transform:1 conservation:2 way:1 call:2 function:6 δkb:1 form:5 piron:1 forming:2 regard:4 but:18 change:2 pascual:1 larger:1 hb:2 stating:2 true:1 made:1 applying:1 consist:1 instructive:1 wish:2 variations:1 us:5 ur:1 2πq:1 ug:18 similar:2 called:1 mechanics:11 ac:1 ab:2 constant:3 defined:1 recognize:1 abstract:1 describe:1 denote:1 teubner:1 single:1 commuting:1 check:2 defines:4 again:2 functions:2 locality:1 whereas:2 generally:3 detail:1 quantization:1 field:2 book:1 details:1 spatial:1 really:4 elements:6 superposition:2 waves:2 separate:1 symbol:1 problems:1 includes:1 generated:2 important:1 variable:7 structure:1 rxi:2 implies:3 assume:1 values:1 factors:2 packets:1 theor:1 rule:11 having:2 equivalently:2 mass:25 time:7 far:1 observables:8 decoherence:1 original:2 once:1
|
quant-ph9508003.txt |@word secondly:1 gs:23 results:2 illustrated:1 eds:1 ge:1 huge:1 go:1 follow:1 primer:1 factorizing:1 otro:1 depend:1 referring:1 containing:1 recurrence:20 estructura:1 decir:1 aut:1 th:1 include:1 presentation:1 applied:1 straightforward:2 very:1 keeping:1 espacial:1 wave:3 fronsdal:1 difference:1 special:1 level:1 nagel:7 occurs:1 deals:1 discrete:7 indices:1 optics:1 f0n:1 miller:2 paso:1 direct:2 sign:1 second:5 perspective:1 gn:4 further:2 revista:1 diferenciales:1 spectral:1 appear:1 giving:1 find:4 sus:1 above:1 new:2 method:3 satisfy:3 relationships:1 simultaneously:2 degree:5 fiz:1 respectively:5 spacing:1 here:3 free:1 represented:1 ratio:1 quite:1 equations:5 appears:1 change:1 calculate:1 box:1 instituto:2 institute:1 shift:9 study:2 studied:1 allows:1 products:1 suggestion:1 published:1 action:1 changes:2 york:2 family:1 hermite:5 merely:1 apply:1 seligman:1 derivatives:1 use:2 asymptotic:1 uso:1 stated:1 pero:1 finally:1 next:1 sitter:3 call:1 therefore:1 criteria:1 taken:1 associated:1 type:3 obtenemos:4 more:2 operators:2 kn:3 curvature:4 aware:1 particular:1 known:1 cases:1 funciones:2 hints:1 mg:1 deformed:1 recall:2 equation:5 work:3 oscillator:5 modified:1 salam:1 salas:7 del:2 following:9 making:1 mx:2 claim:1 give:1 process:1 relativistic:8 table:1 rescaling:1 dws:1 aldaya:7 soc:1 thing:1 means:2 write:3 far:1 pure:1 renaud:1 answer:1 symposium:2 parameter:9 polit:1 product:3 fs:19 mat:1 algebra:1 may:3 ladder:3 after:1 different:2 factored:1 applications:1 4th:1 fits:1 representations:1 types:1 las:2 orden:1 short:1 whenever:1 consequently:1 su:1 sh:2 so:1 allow:1 octavio:1 order:8 operations:1 wigner:2 indeed:2 romania:1 paper:3 guadalajara:1 le:1 group:4 la:3 ln:5 relativity:1 estudios:1 actually:1 lv:2 production:1 mail:3 might:3 deformation:1 them:1 yn:6 factorial:2 integral:2 amenable:1 processes:3 mention:1 effects:1 they:2 instead:1 front:1 ys:8 sixteen:1 dimensionless:1 easily:3 term:1 gets:5 2p:2 2es:2 identified:1 theory:2 found:2 2n:28 gazeau:1 el:3 domain:1 arxiv:1 weight:1 series:2 energy:1 idea:2 related:2 grav:1 entering:1 combining:1 quantum:2 our:7 eq:7 es:10 out:4 space:1 gradient:1 tales:1 since:4 rev:3 19b:2 fellowship:1 contained:1 rel:1 constants:1 rn:14 gov:1 respecto:2 math:4 torres:1 numerical:1 linear:4 8b:1 hull:2 8a:2 ısica:3 departamento:1 gravitacional:1 base:2 23b:1 onoma:1 dubna:1 e2:1 definition:1 pairs:2 r0:1 r1:1 dubbed:1 resumen:1 introduction:1 gordon:2 universidad:2 teor:1 qn:4 hadrons:1 think:2 first:10 grado:1 symmetry:1 variables:2 number:1 relations:25 another:1 impossible:1 electronic:3 ser:1 given:2 f1n:1 guanajuato:1 esas:1 leading:4 eqs:11 dfs:2 their:6 confirming:1 zeros:1 fn:1 calculations:1 scheme:8 final:1 ugto:2 para:3 ryzhik:2 continuous:1 obtained:6 part:2 relaciones:4 x2:8 x3:2 coefficients:7 showed:1 double:1 reyes:1 limiting:1 matter:1 were:1 minus:1 usefulness:1 estudio:1 ann:1 argument:2 generalization:1 needs:1 clearly:1 lie:1 relationship:1 depending:2 convenient:2 latter:3 sciences:1 take:1 indexed:1 mir:2 distrito:2 oscillators:1 exactly:2 shall:5 who:1 centro:1 algebraic:1 involving:2 gradshteyn:2 phase:1 exico:5 considered:1 inferred:1 ks:3 proceedings:1 exp:2 physics:1 fact:3 quantity:1 ambiguities:1 ametro:1 selection:1 mexico:1 show:2 supported:1 anyway:1 solutions:4 substituting:2 usando:1 polinomio:1 subtracting:1 relaci:3 parameters:1 contraction:1 should:4 only:2 going:1 factor:1 partially:1 interested:1 do:1 klein:2 get:3 df:1 dg:1 de:27 dys:1 ones:2 aforementioned:2 du:1 procedures:1 gen:1 dp:2 λc:1 qs:15 covering:1 differential:7 factorization:12 acknowledgments:1 navarro:8 common:2 contain:1 ecnico:1 view:3 coefficient:1 set:1 gegenbauer:9 reference:1 see:5 num:1 result:4 techniques:1 mexicana:1 gravitation:1 strathdee:1 federal:2 written:2 identification:1 between:1 consecutive:1 approach:1 ends:1 terms:2 wn:2 however:4 derive:1 ws:8 como:1 ωc:1 both:4 many:1 taking:1 compton:2 una:1 connection:1 hω:1 context:1 fnn:7 apdo:3 comes:1 con:2 magurele:1 cn:1 nonrelativistic:1 simple:6 por:1 harmonic:3 anti:3 polynomial:16 moreover:2 gto:1 mc2:1 most:2 asks:1 19a:2 three:1 been:3 mart:1 ed:1 logarithmic:1 ph:1 pi:2 6a:2 6b:2 6c:2 corresponding:1 6e:1 ınez:1 sufficient:2 avanzados:1 recalled:1 derivative:1 c2:3 present:2 case:4 exponential:1 pacs:1 will:3 information:1 while:1 suppose:1 situation:1 procedure:1 opt:1 fondo:1 almost:1 metric:1 thus:4 ii:1 reads:2 examined:1 par:3 d10:1 make:3 d18:1 roman:1 same:5 any:1 shifts:1 quant:1 proved:3 finite:1 used:3 trivially:1 investigaci:1 hand:1 sigue:1 dgs:3 authors:1 levels:1 dullemond:1 identity:1 noll:2 kept:1 entre:1 well:1 analysis:1 academic:2 simulated:1 firstly:2 21b:1 usual:2 just:1 newton:1 obtain:6 infeld:2 graduate:1 yet:1 preprint:1 ads:7 point:3 seems:1 nacional:1 wavevector:1 add:1 book:1 conacyt:2 lett:2 relevance:1 rosu:3 5a:2 5b:1 identical:1 secondorder:1 read:1 showing:1 possible:1 corresponds:1 five:1 background:3 21a:2 press:2 using:2 23a:1 postal:3 projects:1 mod:1 b108:1 like:1 particle:1 follows:5 discarded:1 either:1 integrals:2 fnal:1 terminology:1 bucharest:1 because:3 often:1 creation:3 some:6 supplementary:1 examples:1 respect:10 esquema:2 though:1 integration:1 dehesa:1 does:1 connecting:1 hep:1 cnn:3 wavefunctions:2 plugging:1 step:1 properties:1 proceed:2 es2:1 getting:1 obreg:2 discussed:1 factors:4 o:4 wolf:1 introduced:1 slightly:1 procesos:1 h2:1 into:2 obtaining:1 negative:1 down:4 pair:8 en:4 references:1 pares:1 there:1 u2:14 los:3 way:2 jinr:1 was:1 function:1 form:2 m2:1 but:4 true:1 coupling:1 gravitational:3 up:2 us:1 theoretical:1 metropolitana:1 un:5 limit:1 distribution:1 similar:2 2ξn:1 detailed:1 required:1 constant:8 int:1 abstract:1 am:1 general:1 dξ:23 wavelength:2 6d:4 simplest:1 physical:1 functions:24 cim:1 nx2:1 na:2 whereas:1 when:2 zernike:1 nx:3 application:4 other:4 details:1 spatial:4 nr:1 theor:1 reached:1 polynomials:10 important:1 ξn:21 variable:8 atakishiyev:2 structure:1 ago:1 factorized:1 resolution:2 tricks:1 rs:19 rule:1 time:1 4b:1 nuovo:1 4a:2
|
quant-ph9508004.txt |@word represent:1 consider:4 gp:2 brownian:9 results:2 extensively:1 leads:1 grateful:1 gn:4 expressions:2 gi:1 inverse:1 calculate:1 aug:1 tp:1 environment:14 th:1 p2:7 dowker:1 g2:9 g1:10 zhang:11 very:3 rise:1 springer:1 exact:1 condition:2 differentiated:1 hamiltonian:3 pacs:1 solution:10 hartle:1 solved:1 small:1 optics:2 work:1 literature:1 second:2 canonical:2 spectral:2 what:1 stands:1 section:2 expressed:2 above:3 mq:1 order:3 consisting:1 coefficient:1 edited:1 respectively:4 here:5 behaviour:2 asymmetry:1 operating:1 path:3 standard:1 equations:2 obtained:4 institute:1 shift:1 study:3 ignoring:1 resulting:1 complicated:1 fourier:3 involves:1 via:1 useful:2 plenum:1 total:1 planck:2 readily:1 derivatives:1 use:3 contains:2 next:2 comparing:3 linear:3 therefore:1 m2:1 type:1 theoretical:1 more:2 formally:1 dλg:1 operators:1 roland:1 particular:3 known:1 cn2:7 cases:3 iii:1 must:1 evolves:1 keeping:1 dsν:2 integrating:1 mm:1 equation:46 mn:30 oscillator:2 reads:2 ρr:13 values:8 following:4 arrive:2 example:2 numbers:1 compare:1 give:3 high:1 effectively:1 assumptions:1 performed:1 verlag:1 information:1 end:1 straightforward:1 dependency:1 provide:2 s2:23 s1:14 get:6 dekker:1 ordinary:1 sin:29 simplicity:1 may:6 oscillators:2 qqn:2 derived:3 pqn:2 fe:1 fn:4 natural:1 explicit:2 rather:1 imγ:1 so:3 paz:12 prefactor:1 wigner:16 over:2 choose:1 thermal:2 paper:2 london:1 ωn2:4 statistical:1 satisfies:2 still:1 its:2 derive:1 group:1 lc:1 solving:3 coordinates:1 forms:1 complex:1 systems:2 mail:2 carmichael:1 pursue:1 non:1 university:1 combination:2 evolution:8 they:3 now:4 yu:2 discuss:2 easily:3 term:3 2w:3 reasonably:1 2d:1 sufficiently:1 2b:1 2c:1 2m:2 d47:2 side:1 d45:1 homogeneous:4 ohmic:1 dωi:1 doing:1 gaussian:2 related:1 elementary:4 frequency:3 obtains:2 measurement:1 quantum:11 laboratory:1 eq:13 special:3 out:2 shown:2 matrix:4 factors:8 furthermore:1 since:4 rev:8 denotes:1 mγ:1 suggesting:1 ref:1 after:2 theory:1 mω:2 given:6 quite:1 completely:2 advantages:1 york:1 definition:1 interaction:4 βp:5 derivation:4 gell:1 ds1:1 motion:7 due:1 hence:2 βn:3 first:4 origin:1 there:1 features:1 variables:4 encouraging:1 directly:1 u2:18 open:2 differ:1 temperature:2 similarly:5 introduction:1 eqs:2 system:17 unruh:1 their:4 master:15 constants:2 calculations:1 leggett:1 final:1 gives:1 a32:1 tool:1 believe:1 undoubtedly:1 than:3 coefficients:19 diffusion:1 halliwell:4 determined:4 bare:1 anm:4 mind:1 need:1 seen:2 any:1 convenient:1 note:2 green:3 haake:1 heisenberg:1 towards:1 shall:4 who:1 satisfy:1 most:2 formulae:1 multiply:1 preexponential:1 acknowledgements:1 kb:1 considered:1 later:1 physica:1 typeset:1 feynman:1 proceedings:1 exp:5 physics:1 qbm:5 quantity:1 substituting:3 find:1 q1:2 q2:2 2bz:1 written:4 only:1 explicitly:2 factor:1 equilibrium:2 do:2 notation:1 means:1 dependent:7 zurek:2 expectation:4 new:1 dt:14 du:1 2mn:4 ds:12 dp:3 dq:2 prime:1 qp:10 processes:1 approach:1 arxiv:1 method:2 qi:13 through:1 qm:5 dpi:5 qn:51 kernel:1 set:1 physically:1 hγ:2 w0s:4 see:2 college:1 result:1 w0:2 uncorrelated:1 momenta:1 techniques:3 αq:5 caldeira:1 p2m:2 state:5 between:1 ωm:3 boundary:1 conditions:6 αn:3 terms:10 adding:1 initially:2 p2n:3 weak:1 omn:1 vernon:1 wt:1 both:2 cos:18 last:2 many:1 taking:1 according:1 etc:1 whole:1 mann:1 otherwise:2 cn:40 cm:2 point:1 simple:5 harmonic:2 121a:1 exhibits:1 respect:2 kernels:1 pq:10 described:3 pw:3 equivalent:1 dqdp:3 been:4 strategy:1 ting:1 combined:3 ph:1 pi:8 pn:30 pm:5 direction:1 easy:1 ωt:2 am:1 determination:2 derivative:1 fokker:2 case:5 p1:1 tanh:1 transformation:4 will:2 replaced:3 sw7:1 ip:1 thus:1 iv:1 ii:1 ik:7 limit:2 ic:2 ie:1 different:1 integrodifferential:1 perform:1 make:1 same:1 another:1 parts:1 quant:1 constructed:1 higher:1 used:1 numerical:1 hand:1 purpose:1 changing:1 expand:1 well:1 without:1 solve:1 sets:1 paradigm:1 moments:1 obtain:1 press:1 using:8 alternative:3 yet:1 heuristic:1 density:7 mathematically:1 nato:1 bnm:4 dqn:2 hat:1 dqi:6 momentum:1 identical:1 evaluate:1 confined:1 immediately:3 advanced:1 appearing:1 particle:5 follows:4 reduces:1 manifest:1 yields:1 multiplicative:1 reduced:6 right:1 qn2:3 some:6 realistic:1 mγδ:1 coth:3 integration:2 manipulations:1 provides:1 bm:1 bn:5 agreement:1 expansion:1 step:1 revtex:1 found:1 bz:1 about:1 central:1 tracing:4 discussed:1 o:3 addition:1 plus:4 introduced:1 cambridge:2 presence:1 into:4 integral:3 functional:2 bath:8 wn0:1 references:1 inverting:1 determine:1 operator:3 classical:2 few:2 initial:15 u1:21 transform:4 imperial:2 quadratic:1 regarding:1 way:2 treat:1 function:11 form:8 hu:11 heat:1 hn:3 dissipative:1 made:1 compute:1 inhomogeneous:1 ωs:6 up:2 us:3 liouville:1 ui:3 uk:2 ωn:60 demonstrate:1 problem:1 called:1 blackett:1 mechanics:1 ac:2 defined:3 abstract:1 combining:1 influence:1 general:7 our:1 physical:2 incorrect:1 functions:4 nn:1 variety:1 generally:1 es:1 picture:1 briefly:1 a16:1 models:2 june:1 deriving:2 important:1 variable:1 mω2:10 sides:2 regime:1 coupling:1 dω:1 assume:1 dτ:13 required:1 mass:2 time:10 decoherence:2 having:1 once:1
|
quant-ph9508005.txt |@word measurements:1 partial:1 consider:3 pointing:1 rev:6 leads:2 roy:3 computation:3 consists:1 sci:1 primes:9 factorizing:1 whose:4 speeded:1 deterministic:2 factoring:3 finally:1 elliptic:1 under:4 eliminate:1 p2:4 conjecture:2 supported:1 straightforward:2 evolves:1 very:2 hewlett:1 condition:1 school:1 riemann:1 immediately:1 presented:1 ref:1 solution:2 correct:2 large:6 discrete:2 optics:1 application:1 zn:2 smaller:1 deutsch:2 miller:1 go:1 likely:1 further:3 implemented:1 odd:5 machines:2 log3:1 even:5 employ:1 sub:1 fine:1 sum:1 cyclic:1 above:5 new:7 ever:1 method:9 supporting:1 evolving:1 respectively:1 never:2 equals:1 here:2 hku:1 hkl:1 address:2 alone:1 sieve:2 digits:3 great:1 unproven:3 institute:1 study:1 goldwasser:2 allows:1 completely:3 commonly:2 trial:6 amount:1 schumacher:2 implement:1 fourier:1 via:1 useful:1 secure:1 classification:1 scales:7 logical:1 replace:1 hardy:1 unitary:1 total:2 sch:3 alamitos:1 use:1 takes:6 would:1 failed:1 distinct:6 positive:2 give:1 a51:1 few:1 therefore:6 more:4 comparison:1 composite:9 outputs:1 operators:1 validity:1 appendix:5 sharply:1 particular:1 known:6 hold:1 logarithm:1 involve:1 springer:3 ma:1 ibm:1 science:1 work:2 dev:1 values:2 mp:1 following:2 fulfill:1 dec:1 example:3 performed:1 division:3 process:2 programming:1 bennett:2 states:1 assumptions:1 numbers:9 counting:1 verlag:3 information:1 gcd:5 verify:1 discussion:2 a400:1 machine:1 far:1 nontrivial:1 occasionally:1 optimal:3 massive:1 product:2 may:4 turing:1 earlier:1 variant:1 different:1 date:2 revealed:1 efficiently:1 attempt:1 varieties:2 element:1 complexity:2 18th:1 algorithms:4 dream:1 order:13 operations:16 indeed:1 over:1 equally:3 kong:2 course:2 paper:1 london:1 statistical:1 during:1 mentioned:2 satisfies:2 still:2 ieee:1 its:3 before:1 satisfied:2 group:6 chosen:6 lo:1 lh:1 better:1 choose:2 jacobi:1 mail:2 easier:2 theo:1 non:6 good:2 running:3 halt:1 propose:1 evolution:1 investigated:1 number:46 break:1 exponentially:1 half:1 oxford:1 now:6 discuss:1 easily:1 february:1 always:1 university:1 loosely:1 crypto:1 l2:2 2a:1 reasonable:1 l1:1 2l:8 found:6 soc:3 constraints:1 ed:3 reduce:1 idea:1 gifford:1 deterministically:1 used:1 combining:3 quantum:28 our:13 operation:2 summary:1 eq:10 conjectures:1 ultimately:1 lenstra:2 factors:6 res:1 since:3 interference:1 particles:1 acting:1 induction:1 occurs:1 math:4 log6:1 foundation:1 after:3 log2:2 theory:6 possibility:1 labs:1 difficulty:1 reason:1 complicated:1 york:6 besides:1 jozsa:2 additional:1 benioff:1 computers:2 messages:1 so:5 times:4 turn:1 hopeless:1 assumed:1 hence:3 βi:1 first:6 major:1 already:2 probability:8 zm:5 obtained:2 primary:1 lond:3 multiplication:3 improvements:1 done:7 another:1 art:1 size:1 wilczek:1 passes:1 given:2 their:4 introduction:2 eqs:1 system:5 least:6 πm:1 1a:1 indicate:1 scheme:3 bits:6 speaking:1 gives:1 recursively:1 proving:1 rsa:4 part:3 natural:1 than:10 outline:1 peaked:1 impractical:1 princeton:1 divisible:1 namely:1 classes:2 amplitude:1 powers:1 distinguished:1 extracting:1 boston:1 ann:1 modern:1 argument:1 curves:1 randomly:8 primality:29 say:1 need:2 weinfurter:1 any:2 relatively:3 constructions:1 built:1 efficient:11 latter:1 ideas:2 note:2 instance:1 potential:1 take:2 finding:4 negligible:3 mis:1 residue:2 ireland:1 sure:3 multiple:1 though:1 sequence:1 birkh:1 most:6 extremely:1 90er40542:1 average:1 later:1 typeset:1 feynman:2 proceedings:2 exp:3 mechanical:4 physics:1 fact:3 shor:24 set:4 show:1 text:1 random:2 terminate:1 discovered:2 keywords:1 trivial:5 find:7 based:2 implementation:1 pomerance:1 should:1 analytic:1 only:8 factor:10 ksl:1 hope:1 ciphertexts:1 abelian:2 cryptography:3 get:1 de:1 lucky:1 addison:1 truly:1 fastest:5 altogether:1 applying:1 secondary:1 prime:31 acm:2 runs:1 fields:1 arxiv:1 factorization:30 public:4 common:2 multiplying:3 modulo:4 exists:3 achieved:1 testing:2 plausible:1 see:6 computer:5 fail:1 subject:1 satisfying:1 please:1 yet:1 state:3 various:1 reading:1 conditions:4 discovery:2 notice:1 barenco:1 recently:2 comp:4 however:3 jr:1 concentrate:1 hypothesis:2 algebraic:1 huang:2 sleator:1 picking:1 come:1 2pn:1 both:3 taking:1 annual:2 space:2 bristol:1 interesting:1 com:1 key:6 simple:1 ca:1 asymptotically:4 cryptosystem:1 period:1 2nd:1 factorize:4 polynomial:4 table:2 2pk:1 tuning:1 second:4 addition:2 computing:3 been:2 springerverlag:2 secret:2 much:2 interest:1 zpn:1 pj:8 pk:1 ph:2 pi:10 pn:8 cohen:1 compositeness:3 direction:2 aj:4 formed:1 coherent:1 ours:1 general:1 spin:1 present:2 divisor:1 case:3 divisions:4 p1:4 exponential:1 pacs:1 value:1 will:5 while:1 suppose:3 situation:1 35th:1 necks:1 changed:1 almost:5 refs:3 thus:11 equal:1 greater:2 hong:2 grant:1 perform:2 acknowledgments:1 make:1 same:1 clearly:2 parts:3 quant:2 knuth:1 finite:1 development:1 evolve:1 extended:1 eds:1 effect:1 counterparts:1 hand:2 sys:1 eavesdroppers:1 purpose:1 infinite:1 frequently:1 totally:1 kept:1 analysis:2 obviously:1 without:1 greatest:1 bottle:1 olden:1 decimal:1 proposed:2 less:1 being:1 generally:1 obtain:1 identify:1 using:15 speed:5 ams:1 heuristic:1 generator:1 sciences:1 auser:1 extra:2 wright:1 operator:1 setting:1 lett:4 theorem:8 input:2 remaining:1 tests:3 checking:1 lehmer:10 measurement:2 possible:1 test:34 working:2 know:3 integer:7 bit:15 advanced:1 mod:10 generated:2 like:2 alternatively:1 reduces:2 performing:1 multiplicative:2 security:3 works:1 reasonably:1 spins:1 making:2 mathematical:1 methods:1 classical:12 people:2 tells:2 some:10 bach:2 towards:1 moreover:2 provided:2 vol:1 calculating:1 avoid:1 shall:1 kilian:2 does:1 decomposition:1 adleman:3 proc:3 refer:1 run:10 power:9 each:6 wesley:1 revtex:1 although:3 2m:1 pokfulam:1 refers:1 composites:1 bz:1 gained:1 integers:3 certificate:1 concretely:1 constraint:1 eavesdropper:1 prove:1 a3:1 o:45 practical:1 strassen:3 rosen:1 ensure:1 complimentary:1 consequently:3 road:2 massachusetts:1 primitive:2 computational:3 into:1 getting:1 lies:1 references:1 determine:1 elementary:19 factorized:3 hep:1 log:208 prepare:1 probabilistic:6 there:8 transform:1 fast:2 decode:1 los:1 pa:2 way:2 rumely:1 was:2 assumes:1 function:1 atkin:2 complete:6 form:6 hp:1 hk:1 iassns:1 repeatedly:1 encoded:1 fg02:1 true:1 collapses:1 longer:1 made:1 compute:1 packard:1 society:1 2πi:1 up:7 us:6 below:2 verification:5 problem:1 similar:1 called:1 multiplications:2 mechanics:1 constant:5 classic:1 int:1 recognize:1 abstract:1 describe:1 proven:1 evidence:1 chap:5 exist:1 promised:1 chau:2 doe:1 happen:1 again:2 nj:1 compared:1 no:4 extract:1 ekert:1 wavefunction:4 when:4 field:2 other:3 details:1 hpl:1 department:1 symposium:2 denote:2 superposition:1 accidental:1 problems:2 shown:6 variation:4 a1:2 a0:4 chance:2 a2:2 a4:1 stoke:1 koblitz:1 needed:6 cryptographic:1 lane:1 faster:2 algorithm:41 assume:2 4b:1 required:5 parallelism:1 time:23 4a:1 requires:9 4c:1 once:4
|
quant-ph9508006.txt |@word represent:2 logarithms:2 consider:11 modi:1 parametrizing:1 global:1 reversibility:1 results:1 gg:20 computation:28 consists:1 follow:1 expressions:1 issues:1 row:1 relationships:1 whose:4 simon:2 patches:1 aug:1 alamos:2 ects:1 factoring:1 b265:1 answered:2 jvi:2 critical:1 manifolds:2 th:6 under:2 norm:18 summarizes:1 p2:2 halfspaces:1 g2:3 advantage:16 orthogonal:3 far:1 implicitly:1 choice:2 corollary:7 worst:1 decide:2 formula:1 bounding:1 matrices:8 dim:1 induced:5 subsets:2 tra:1 positions:1 solution:3 juxtaposition:1 discrete:2 vector:5 bq1:1 laur:1 eigenvalues:3 selecting:2 evaluations:2 upper:8 smaller:1 neighborhood:2 gg0:1 deutsch:5 estimates:1 b22:3 approximation:13 fold:1 second:5 bg:1 implemented:1 auspices:1 even:2 established:1 what:1 approximability:3 adds:1 appear:1 invertible:1 section:4 version:1 3n:5 subspaces:1 sup:1 increasing:1 body:1 margolus:1 full:1 ning:1 lled:1 respectively:3 here:2 understanding:1 ranges:1 modular:1 operating:1 groups:1 address:4 cult:4 strong:2 observing:4 transformation:2 change:1 obtained:5 great:1 property:2 formalizing:1 shift:1 study:2 vectors:9 allows:1 bv:1 hbb:1 spheres:1 accomplished:1 resulting:1 knill:2 action:1 cardinality:3 suitable:3 bq:1 tasks:1 useful:1 projection:5 family:1 nearest:1 explained:1 logical:1 outcomes:1 boolean:1 achievable:2 apply:2 total:9 unit:7 use:6 takes:1 would:2 levine:1 remains:1 positive:1 stated:1 negative:2 sherman:1 properties:1 comparing:2 linear:2 compensate:1 therefore:5 associated:1 care:1 vj:1 more:7 formally:2 vl:20 operators:25 distribution:2 reversible:4 normalized:4 known:2 foundations:4 cases:3 hold:3 origin:1 involve:1 balls:4 frobenius:2 integrating:2 mm:1 local:2 work:6 det:1 labeled:1 assumptions:1 values:2 ms:1 following:10 im:3 example:1 proof:27 f0:1 f1:2 give:3 process:1 bennett:4 purposes:1 ecting:1 states:20 sphere:7 minimum:1 bene:1 performed:1 hyperplane:2 sense:1 every:1 counting:1 lems:1 string:1 information:3 eng:1 rather:1 means:5 revisit:1 write:8 maps:2 instead:1 those:1 verlag:1 parameter:1 sin:4 map:3 product:7 fs:7 uj:1 fv:3 singular:1 may:2 turing:1 after:1 mapping:1 ball:2 hence:2 independent:2 fc:2 improving:2 summarize:1 types:3 short:1 natural:2 outline:2 culty:1 lemmas:4 explicit:2 su:5 element:3 complexity:14 so:9 fundamental:1 ned:8 representation:5 transitivity:2 order:2 operations:16 restriction:1 acts:2 n0i:1 dx:2 22n:1 over:5 entries:3 soc:1 n0b:2 course:1 paper:3 london:1 still:2 ieee:3 its:5 machine:1 outer:1 how:1 chosen:1 interesting:4 erators:1 guesses:3 suboptimal:1 li:2 better:3 choose:6 annual:3 k2n:4 main:1 might:1 setting:1 correspondence:1 them:1 good:2 k2l:4 orthant:2 universality:1 isomorphic:1 ces:1 they:2 gate:18 trade:2 sleator:1 now:5 restrict:1 probl:4 dirac:1 always:1 orthonormal:12 did:1 inequality:7 l0:2 each:16 2l:5 found:1 2n:16 polynomially:1 2i:2 2j:4 2k:2 homogeneous:1 domain:10 square:3 inputs:4 ed:2 energy:1 hard:3 reduce:1 idea:2 related:1 elementary:1 extended:2 ex:1 measure:23 quantum:56 laboratory:1 approximated:3 0i:1 special:1 out:1 large:3 shown:2 matrix:12 space:23 restricted:1 since:3 induces:7 projected:3 denotes:2 re:1 acting:4 nite:6 max:2 denoted:5 constants:1 get:1 gov:1 induction:2 shows:2 theory:8 diagonal:4 possibility:1 standard:6 vazirani:2 small:1 reason:1 ect:1 members:5 nition:4 estimate:4 remainder:1 compositions:3 union:3 ky1:1 pairs:1 v1:3 unitarity:1 vitanyi:1 exponentially:6 circuit:24 consequence:3 qn:1 onto:7 xj:3 initial:1 jpc:1 lond:1 probability:9 xb:2 u1:1 number:15 oracles:1 u0:4 exact:4 construct:2 another:4 open:2 xw:1 size:1 1q:1 given:13 necessarily:2 introduction:1 least:4 their:2 too:1 1g:2 1i:5 restrictions:1 siam:2 bits:9 1n:2 way:2 relationship:1 ted:1 exactly:1 proving:2 jj2:16 measurable:2 sx:3 authors:1 rst:25 believe:1 representing:1 than:5 b0i:1 distance:13 eiw:1 showed:1 imply:1 submitted:2 determined:2 amplitude:4 contribution:2 gives:7 result:10 comput:2 generality:2 argument:8 therfore:1 iw1:1 need:2 null:1 any:10 viewed:1 gi:4 conversion:1 angle:1 zero:1 depending:1 general:8 studying:1 note:13 high:2 concerns:1 absorbed:1 build:1 mx:1 jxi:3 algorithms:1 k9:1 begin:1 sure:1 unless:5 though:1 simulated:1 iwk:1 metrics:5 most:22 involving:1 entry:1 phase:2 acknowledgements:1 probabilistic:5 why:1 es:3 inequalities:4 parametrize:1 richard:1 neighborhoods:1 considered:4 average:1 cover:1 counted:1 proceedings:6 points:1 exp:11 25th:2 weakest:1 notion:1 fact:2 science:3 shor:4 spaced:1 show:9 random:3 speedup:2 proba:1 x2:10 spaces:2 orthants:1 substituting:1 careful:2 trivial:2 d1:1 q1:3 x1:7 based:1 knowledge:1 parameters:1 favor:1 hf:1 2bq:1 should:2 lemma:35 only:6 going:1 41q:3 factor:7 constant:1 bernstein:2 jab:2 preliminaries:1 columns:3 dn:7 do:4 dk:1 notation:2 di:9 zurek:1 de:17 overall:2 next:3 cannot:2 words:1 report:1 erent:2 dt:1 conjunction:1 ux:1 iw:5 acm:2 qs:5 covering:2 remove:1 whether:3 investigate:1 34th:1 uw:2 view:4 2p1:1 guessing:2 requirement:1 set:16 decides:4 exists:10 national:1 erentiable:1 j1:3 j2:7 maximum:2 relative:5 depends:1 decided:3 descriptions:1 sions:1 terms:1 analog:2 un0:5 c2s:4 satisfying:3 tensor:4 pattern:2 review:1 p2m:2 state:8 smallest:2 various:1 correctly:2 between:7 subscript:1 approach:1 available:1 letting:1 barenco:5 recently:1 ability:1 extend:2 qubits:7 ju:3 jv:26 restricting:3 weak:3 however:1 ww:1 implementing:1 rapid:1 jj:5 jk:1 group:2 come:1 ug:2 jb:2 wx:3 both:3 essentially:1 last:3 reverse:1 desired:3 many:7 taking:2 la:1 according:2 contract:1 context:1 qubit:8 estimation:1 0n:1 comes:2 otherwise:4 comment:1 among:1 relevant:2 point:4 simple:1 royal:1 others:1 16b:1 2nd:1 dimensional:3 represented:4 ab:2 simply:1 exhibits:1 xi:3 sequences:3 polynomial:1 respect:1 jii:1 considering:3 pv:6 ciently:4 basis:11 addition:1 z0:1 px:5 locally:1 due:1 been:2 ja:2 pb:2 pc:8 cient:1 describes:1 interest:2 basic:1 expected:1 ph:1 universal:2 j0i:10 contribute:3 partly:1 0s:1 josza:1 subspace:4 gap:1 observe:2 understand:1 24g:4 checkable:2 evidence:1 former:1 present:1 case:7 hughes:1 p1:1 exponential:5 2pq:1 value:2 choices:2 will:8 euclidean:4 suppose:1 behavior:3 1ij:1 projecting:1 vb:4 unitary:53 n2n:3 almost:6 vi:2 metric:4 vk:2 thus:5 non:5 probabilistically:4 ik:2 ij:2 converts:1 ig:1 binary:2 lengths:1 suggest:1 make:2 s2n:4 same:6 clearly:1 member:3 complex:3 quant:1 arguments:2 see:5 accumulating:1 products:1 several:2 subalgebra:1 composition:3 ectively:1 sterling:1 fairly:1 erence:1 used:11 raymond:1 solved:5 lie:1 yao:1 structurally:2 parametrized:1 usually:1 v2:1 moving:1 changing:1 interested:1 identi:1 identity:4 recent:2 eigenvectors:1 marathe:1 lower:6 task:1 well:4 analysis:1 ugi:1 patterns:3 without:4 solve:2 does:1 i2n:1 sets:3 asymptotically:1 jbn:1 model:2 dimension:20 jbi:18 usual:2 xed:8 gates:23 manifold:2 less:2 being:2 observed:1 distribute:1 obtain:8 actions:1 via:4 previous:3 ective:2 intersection:1 preprint:1 density:8 had:1 except:2 capabilities:1 thermodynamics:1 k0:2 conjugated:1 theorem:16 input:12 remaining:1 take:2 real:4 seminorms:1 9b:3 evaluation:1 around:3 rev:1 exploiting:1 checking:3 decomposed:1 possible:2 spanned:3 formalize:1 increases:2 pages:5 background:1 press:3 using:7 bit:11 replace:1 domains:3 helpful:1 loss:2 necessary:1 like:3 semi:1 nitely:1 follows:9 separately:1 cx:1 steps:1 schwarz:2 arbitrary:5 output:10 works:1 page:1 making:1 right:1 classical:13 sequence:4 conditional:3 some:4 back:1 understood:1 repeat:1 b0:13 choosing:2 guess:2 diagonalizing:1 prasad:1 dense:1 dimensions:6 2e:1 decision:10 2g:1 decomposition:2 eliminate:1 yields:1 proc:1 prob:15 either:1 measuring:2 measures:6 2b:2 power:1 nitions:1 elucidate:1 equivalent:1 l1:2 bi:2 bu:11 step:4 simplex:1 2m:11 described:1 approximating:4 hilbert:7 submanifold:1 coordinates:3 extending:1 column:2 pu:2 discussed:3 factors:1 o:16 distinct:2 range:9 a2:2 greatly:1 act:2 warner:1 op:1 subset:2 equally:1 contains:1 angles:1 computes:2 j1i:2 into:1 within:3 integral:3 bound:13 references:1 determine:4 operator:17 reducing:1 physical:1 rows:3 computer:3 additional:2 cleve:1 assumed:1 support:1 there:24 question:3 approximate:4 u2:6 los:2 borel:1 inner:3 fraction:3 was:3 naturally:2 function:5 24n:1 complete:2 form:3 identities:1 jui:36 but:2 volume:7 construction:1 true:2 count:2 made:1 compute:4 improved:2 intuitive:2 circuits:23 inside:1 smooth:1 bounds:7 us:2 below:1 un:31 ui:9 submanifolds:1 uk:9 sum:3 instantiating:1 problem:10 similar:3 eigenvector:1 ub:8 detailed:1 lanl:2 ub0:1 certain:1 abstract:1 measurement:4 covers:1 denote:5 single:2 guessed:5 satis:3 our:2 corresponding:4 distributions:3 operation:8 constructed:1 again:2 functions:11 compared:2 nx1:1 nm:1 nn:1 no:4 ekert:2 discus:1 ne:3 ng:3 tight:1 other:6 details:1 outputs:1 department:1 ns:2 arithmetic:1 conclusion:1 symposium:5 perpendicular:2 elements:6 divincenzo:5 problems:17 representable:2 variation:7 includes:1 a1:1 oracle:3 generated:2 important:2 bounded:3 log:49 included:1 structure:1 independently:1 implies:8 assume:6 required:2 4q:10 4n:2 appendix:4 volumes:1 time:2 n0:10 lives:1 n2:5 n3:1 requires:9 avoid:1
|
quant-ph9508007.txt |@word replacing:3 represent:1 consider:10 rev:1 jr0:6 results:7 monthly:1 integration:1 gg:4 computation:7 consists:1 follow:2 issues:1 relationships:1 whose:1 dimensionality:1 aug:1 knill:3 ects:1 b265:1 tail:1 compensate:1 tj:1 tk:9 excluded:1 under:3 norm:4 applied:3 amplitudes:1 straightforward:1 outside:1 far:1 implicitly:1 ously:1 corollary:6 worst:1 entries:1 bounding:1 convexity:3 orthant:1 qni:1 gov:2 jhe:1 subsets:1 t0:1 large:13 discrete:1 vector:4 universal:1 section:1 small:9 c01:1 c02:1 rk:7 inspection:1 application:1 speci:2 direct:1 approximation:14 fold:1 second:4 estimated:1 auspices:1 even:3 what:1 rate:1 giving:1 hypercube:2 ned:7 uniform:9 version:1 above:4 sup:1 new:1 learned:1 increasing:1 consisting:1 satisfy:2 margolus:1 pose:1 notions:1 respectively:2 never:1 here:3 ranges:1 desired:3 simon:1 ements:1 address:1 cult:1 ignore:1 8e:1 z1:3 change:1 obtained:9 remark:1 tx:1 technical:1 involved:2 study:1 vectors:3 allows:1 alamos:4 action:1 proof:26 boundedness:1 projection:1 claim:2 highly:2 scaled:1 inequality:8 limn:5 summation:1 apply:2 total:6 derivatives:1 use:10 takes:1 would:2 prove:2 distinct:1 positive:4 negative:3 properties:3 comparing:1 linear:1 noting:1 therefore:2 means:1 jd0:1 more:3 formally:2 th:4 operators:6 robbins:1 problem:2 2w1:1 appendix:1 particular:1 foundations:2 cases:2 hold:1 must:3 states:8 balls:1 recall:1 work:1 mk:4 excessively:1 values:3 ms:1 concepts:1 already:1 making:1 factorials:1 endow:1 example:1 def:1 performed:1 nearest:1 give:2 bennett:1 cation:1 minimum:2 numbers:1 sense:1 information:3 goal:2 eng:1 acts:1 write:5 get:1 gate:5 parameter:1 polytopes:1 map:1 product:2 fs:1 fu:3 fx:3 fy:3 fz:1 derived:1 minimized:1 applications:1 fi:1 constants:10 vance:1 natural:2 outline:1 culty:1 lemmas:4 explicit:1 summing:1 su:4 element:3 complexity:4 interior:1 so:10 sn:3 fundamental:1 decreasing:2 every:2 integrand:1 sg:1 order:1 operations:2 origin:1 holds:1 tk0:3 over:2 paper:5 falling:2 y1:4 y0:2 ieee:2 its:8 group:2 symmetry:3 ln:92 interesting:1 fix:1 expectations:1 suboptimal:1 li:4 better:1 concavity:4 choose:4 erences:1 covered:1 main:1 might:1 into:1 yi:4 non:7 good:2 factorial:1 scaling:1 ces:2 they:1 identically:2 multidimensional:1 now:3 2t:2 term:4 fully:1 concave:4 2z:1 2d:1 2e:1 2g:2 reasonable:2 l1:1 2m:17 side:2 mean:1 subset:2 domain:8 en:1 transforming:1 weight:1 inputs:2 ed:1 energy:1 hard:3 elementary:1 ball:1 gates:12 measurement:2 quantum:20 laboratory:3 operation:1 event:2 es:2 out:1 w2:4 bxi:1 shown:4 matrix:1 space:5 rounding:1 restricted:1 since:7 induces:2 denotes:1 re:1 acting:1 nite:6 maximized:3 denoted:1 formula:1 rn:8 induced:4 induction:2 occurs:1 math:1 shows:1 theory:2 b3:5 monotone:1 diagonal:1 standard:2 versus:1 laur:1 base:2 w1k:1 w1j:1 members:2 estimate:6 remainder:2 compositions:1 r0:2 language:1 geometry:1 similarly:1 turn:1 american:1 exponentially:3 circuit:11 hence:6 onto:1 support:1 first:4 xj:1 xk:4 xi:27 xn:1 probability:7 upper:1 variables:2 number:10 approximate:4 clear:1 another:2 open:1 given:8 e1:2 asymptotic:1 strict:4 introduction:1 1x:3 adjusted:1 least:2 yij:1 belongs:1 assumption:1 1g:2 1i:2 1j:9 bits:1 gives:8 statement:3 relationship:1 tuple:4 addition:1 exactly:2 jj2:4 part:2 rst:9 july:1 x1:1 than:2 distance:15 last:4 require:2 imply:4 submitted:1 normalizing:1 project:1 determined:1 y0j:2 nding:1 result:7 fashion:1 behavior:1 generality:2 well:2 correction:2 argument:1 say:1 close:1 disjoint:1 any:5 hessian:3 computationally:1 zero:3 lim:3 note:12 decomposing:1 absorbed:1 combining:1 jxi:6 performance:1 jxj:4 begin:2 continuous:1 unless:1 most:10 involving:1 acknowledgements:1 probabilistic:1 pages:2 inequalities:3 jx1:2 jx0:2 deviations:1 observation:2 ke:11 considered:1 average:9 cover:1 face:1 proceedings:3 exp:3 notion:2 fact:3 quantity:2 slope:1 shor:1 show:7 random:3 12n:2 attempts:1 participate:1 corner:1 rough:1 trivial:6 eliminated:1 d0:7 help:1 based:3 knowledge:1 distributed:3 written:2 negligible:1 should:1 lemma:40 only:5 factor:1 probabilities:1 continuity:1 do:3 cube:2 di:12 dg:1 de:16 expectation:1 da:2 enthusiastic:1 nearly:1 closely:1 report:2 2mk:5 dt:7 boundary:1 following:2 resolve:1 textbooks:1 stirling:6 twice:1 34th:1 xmax:1 set:6 exists:5 achieved:2 lnt:1 national:3 erentiable:5 j1:10 j2:2 maximum:5 relative:2 reinforce:1 computer:2 w3:4 descriptions:1 w1:11 discussions:2 jx:19 dtd:1 techniques:1 permuted:1 satisfying:2 tensor:1 ways:3 review:1 label:1 symmetric:1 jt:2 state:7 between:3 subscript:1 c2m:1 publishers:1 barenco:1 recently:1 extend:2 qubits:10 ju:1 complement:1 weak:2 however:1 science:2 js:12 jl:3 jn:7 densely:1 jj:1 jk:7 jd:1 monotonicity:2 ug:3 motivations:1 both:2 polytope:3 reverse:2 taking:1 annual:2 according:2 contract:1 chosen:1 0g:1 embedding:1 0j:2 divincenzo:2 qubit:2 expression:2 comes:1 otherwise:3 strongly:1 ci:7 relevant:2 abbreviate:1 point:1 16e:8 asymptotically:4 dimensional:1 coordinates:11 je:2 polynomial:1 respect:1 restriction:1 considering:1 ciently:2 basis:3 equivalent:1 due:2 been:1 implicit:2 yao:1 describes:1 interest:4 expected:2 applying:2 ph:1 pi:5 pn:1 formalized:1 j0i:4 concentrated:4 determinant:1 corresponding:2 observe:2 24g:3 derivative:4 c3:9 c2:12 c1:11 general:2 those:6 c4:1 case:4 exponential:1 nd:5 jln:5 value:3 choices:2 will:5 zeitouni:1 near:1 suppose:1 evaluating:2 applies:1 situation:1 property:2 dembo:1 optimize:1 exponent:2 unitary:11 almost:7 vi:1 metric:2 7p:1 thus:4 them:2 need:1 yj:6 ready:1 jz:9 binary:1 righthand:2 16e2:1 make:2 same:1 member:1 complex:1 quant:1 arguments:2 several:2 composition:3 higher:1 independent:2 used:3 http:1 see:4 absorb:1 structurally:1 hand:1 domains:2 purpose:1 unimodular:1 bartlett:1 contribution:3 identity:2 slicing:2 lower:1 suitable:1 maximizing:1 0n:12 i2s:1 x0:6 without:2 deferring:1 components:1 coordinate:5 jbn:1 model:1 jbi:4 left:1 xed:4 satis:3 being:1 composing:2 obtain:7 thanks:2 integer:2 68q:1 ams:1 letting:2 lit:1 lebesgue:4 density:4 except:1 tuples:4 location:1 theorem:32 relevance:1 input:8 remaining:1 real:1 cramer:3 exploiting:1 evaluate:1 showing:1 decomposed:1 sums:1 possible:1 additivity:1 finding:1 press:2 using:8 bit:3 unique:2 loss:2 necessary:1 like:2 success:1 identifying:1 follows:11 faber:1 translates:1 separately:1 always:1 output:3 mathematical:1 sleator:1 www:1 because:1 classical:1 some:6 b0:1 b1:5 b2:10 convex:5 tvd:20 proofs:5 provided:3 avoid:1 2c1:2 2c3:6 does:1 summand:1 prob:2 measuring:1 replaced:1 2b:5 power:1 nitions:1 uniformly:2 bn:1 each:6 bi:3 expansion:1 miscellaneous:1 step:2 references:1 found:2 approximating:2 bx:1 hilbert:1 proceed:2 gained:1 simplify:1 theorems:3 factors:2 o:11 union:2 range:1 a2:2 extensions:1 act:1 2k:3 primitive:1 j1i:1 h0:4 within:9 integral:4 bound:3 copies:1 appropriate:1 accounts:1 operator:4 next:3 yj1:14 assumed:1 strictly:8 there:19 transform:1 los:4 ehe:4 inner:1 fraction:3 series:1 translate:1 was:3 function:10 jones:1 form:3 enough:7 lint:2 volume:2 hn:9 true:1 hg:4 he:14 compute:1 consist:1 circuits:6 supt:1 bounds:9 us:1 below:1 projecting:1 ui:1 sum:2 continuously:2 distribution:19 similar:1 called:1 detailed:1 taylor:1 constant:5 choosing:2 ai:2 certain:1 abstract:1 measure:8 nnc:2 denote:3 proves:1 exist:8 our:3 distributions:8 approximated:1 physical:1 ni:1 functions:5 nk:4 nm:1 no:4 nc:9 when:1 ne:13 nal:1 ng:1 tight:3 other:2 special:2 department:1 nt:5 cleve:1 deviation:4 symposium:2 elements:10 may:1 expressible:1 problems:1 representable:1 variation:4 a1:1 a0:1 generated:1 important:1 bounded:2 included:1 nn0:2 sinh:1 independently:2 implies:9 partitioned:1 assume:7 requires:3 lanl:3 cally:1 together:1 smooth:3 n0:4 n1:4 n2:3 laws:1 4b:3 nxk:2
|
quant-ph9508008.txt |@word protocol:5 they:3 proposed:1 depends:1 directions:1 random:1 satisfied:1 notations:1 course:1 paper:2 pulses:1 computation:1 innovative:1 consists:1 japan:1 suffer:1 data:3 its:1 before:1 polarization:1 kanagawa:1 based:4 probability:1 aug:1 computers:1 susceptible:1 photons:13 cryptology:1 either:1 failed:1 only:4 version:1 ardehali:1 fig:3 interprets:2 transit:1 sent:4 happened:1 sagamihara:1 his:6 cryptography:2 loss:2 very:1 beams:4 zurek:1 measurement:1 nonorthogonal:1 choice:6 beam:14 october:1 listening:1 half:1 front:7 bit:1 now:1 minute:1 splits:1 splitter:11 particle:1 level:1 did:1 always:1 signal:1 arxiv:1 mirror:1 alice:10 remove:1 silvered:1 whether:4 theory:3 steps:1 2a:9 2b:9 each:2 crossing:2 through:1 went:1 podolsky:1 wrote:1 mathematical:2 inserts:2 randomly:3 set:1 decides:2 another:2 sequence:4 sends:2 conditions:1 idea:2 pulse:1 see:3 fiber:1 concludes:1 quantum:9 ieee:2 out:2 proceeding:2 announces:1 eavesdropping:1 interference:1 nec:1 research:1 may:1 experiment:7 tests:1 above:2 new:5 india:1 encounters:1 contrast:1 she:4 edited:2 who:1 recently:1 scientific:1 orleans:1 processing:1 confidence:1 here:1 constructive:1 reported:1 them:1 york:2 key:5 put:1 news:1 along:8 come:1 generate:1 both:4 about:1 last:1 her:3 attacks:1 route:10 uncertainty:1 equal:2 against:1 keep:1 american:1 published:1 routes:2 discard:1 bob:10 finds:1 experimental:2 first:2 splitters:3 already:1 secure:1 unnoticed:1 point:2 press:1 into:2 pp:1 coding:3 reflected:1 highly:1 brought:2 instances:5 schemes:1 done:1 approximately:4 primarily:1 einstein:1 constructively:1 univ:1 bangalore:1 conference:2 use:2 transmission:3 proceed:1 second:1 their:2 adversary:1 there:1 detected:3 been:1 comes:1 reprinted:1 low:2 realization:1 tells:1 ph:1 scheme:3 was:4 until:1 systems:1 introducing:1 life:1 bennett:7 sigact:1 knows:1 triggered:6 mind:1 explanation:1 wheeler:9 photon:11 delayed:6 but:1 back:1 checking:1 foundations:2 removed:2 those:1 he:2 count:1 states:2 polarized:4 unfortunately:1 publicly:1 princeton:2 wiesner:3 work:1 intensity:3 us:1 theoretical:1 while:1 were:1 following:3 distribution:4 example:1 rev:4 detailed:1 references:1 losses:1 mirrors:1 detectors:7 abstract:1 describe:4 thus:9 direction:1 general:1 1980s:1 single:1 distributions:1 any:3 axis:3 binary:2 different:3 advantage:1 mermin:1 no:1 perhaps:1 corporation:1 travel:1 rosen:1 when:2 lett:3 same:1 arrangement:4 note:1 instance:2 high:1 other:1 quant:1 take:1 branch:1 according:2 detector:5 interfered:1 smolin:1 brassard:5 independent:1 briefly:1 used:1 shall:1 models:1 quote:1 after:1 nj:1 informs:1 uses:1 prepares:1 acquired:1 else:1 inserted:6 cryptographic:2 especially:1 salvail:1 light:2 register:1 epr:1 microelectronics:1 marlow:1 academic:1 proceedings:1 so:1 principle:1 consistency:1 international:1 model:2 laboratories:1 physics:1 ekert:2 came:5
|
quant-ph9508009.txt |@word consider:4 interference:2 magnetic:1 results:1 four:3 eds:3 violate:7 aug:1 deterministic:1 nonlocal:26 tween:1 asking:1 conjecture:1 lations:1 very:1 rise:1 electron:5 laser:1 condition:3 school:1 presented:1 button:3 vector:2 phase:1 a120:1 equation:1 tel:2 consistent:4 measurable:1 past:1 likely:1 even:2 what:4 appear:1 incompatible:1 deeply:1 sum:7 axes:4 summers:1 ˆb:6 version:1 above:1 fractional:1 new:2 ever:1 3e:1 satisfy:1 here:2 modular:3 free:1 superconductivity:1 indeterminism:1 directions:1 path:1 along:2 equations:8 deduced:1 box:2 sending:1 jams:2 vectors:1 action:3 bob:6 honor:1 equivalence:1 see:1 logical:4 outcomes:2 claredon:1 apply:1 causal:1 unit:1 would:2 probabilities:4 positive:2 chooses:1 monotonically:1 call:1 tell:1 today:1 more:2 separated:1 israel:3 becomes:1 holt:1 particular:2 foundations:4 iii:1 must:2 khalfin:1 tokyo:2 science:1 inertial:1 rohrlich:4 theories:2 reproduce:1 concepts:1 petersen:1 example:2 point:1 give:1 relativistic:19 preserving:3 states:1 numbers:1 sense:3 absolute:2 information:1 rather:2 technology:1 holds:2 located:1 anyon:1 influences:1 answer:1 instead:1 influenced:1 may:2 after:1 plane:1 summarize:1 realized:1 third:1 beam:1 light:8 separations:1 so:3 fundamental:3 correlation:3 order:2 talk:1 horne:2 acts:1 years:1 including:1 japan:1 satisfies:2 still:1 its:4 derive:1 relativity:4 decreases:1 aviv:3 systems:5 hidden:1 might:2 maximal:3 them:1 combination:1 landau:1 kamefuchi:1 they:3 symposium:1 oxford:1 now:2 nor:2 university:1 settings:1 relativisitic:2 possibilities:1 inequality:10 crossing:1 found:3 entirely:1 notes:1 ed:1 principles:1 society:1 sandu:1 measurement:1 quantum:45 our:2 eq:2 event:1 special:2 space:1 since:1 induces:1 research:1 looking:1 daniel:1 lecture:2 math:2 theory:18 given:1 possibility:1 completely:1 besides:1 imagine:1 ask:3 axioms:6 forbids:1 definition:1 ministry:1 could:4 messages:1 keep:1 motion:9 relativistically:1 consequence:2 already:1 probability:1 variables:2 carry:1 rastall:1 aharonov:11 wilczek:1 guess:1 observer:2 similarly:1 introduction:1 least:1 passed:1 exactly:1 immediate:1 than:7 distance:1 nathan:1 showed:1 penrose:1 measured:1 imply:5 preparation:2 were:1 modern:1 say:1 need:1 seen:1 any:5 paths:2 angle:1 isolated:2 violates:1 entirety:1 potential:2 take:1 transmit:1 allow:2 measures:1 singlet:1 most:2 letter:1 successive:1 pair:2 inserted:1 class:1 constancy:1 technion:1 considered:1 tsirelson:2 sometimes:1 stronger:1 electrons:1 physics:3 section:2 lying:1 quantity:2 son:1 show:1 violation:5 supported:1 gauge:1 find:3 causality:22 proposed:2 explain:1 only:6 jam:1 black:2 isham:1 local:4 axiom:7 do:4 his:2 joint:1 cannot:1 lahti:1 podolsky:3 conditions:1 arxiv:1 yield:2 summary:1 through:1 available:1 set:1 reference:1 unpublished:1 correlations:26 immigrant:1 relative:2 depends:1 result:2 corre:1 nonlocality:23 pattern:2 shimony:4 state:1 between:8 invariant:1 neither:1 approach:1 preserve:1 nature:1 combining:1 however:4 come:1 suggested:1 restrictions:1 last:1 limits:1 many:2 region:1 passing:1 otherwise:1 mechanics:18 jammer:1 jim:3 nonrelativistic:1 alone:1 werner:1 moreover:1 considers:1 krenn:1 pendleton:1 invert:2 locally:2 int:2 much:1 ph:2 direction:1 describe:1 indeterminacy:1 both:3 quantities:1 photon:1 fund:1 angles:1 maximally:1 spin:1 spirit:1 presses:1 uncertain:2 value:4 while:2 pressed:1 irrespective:1 taking:1 theo:1 spacelike:3 thus:4 ii:2 pressing:1 cone:3 march:1 interacts:1 binary:1 different:1 thereby:1 perhaps:1 make:3 shifts:1 quant:2 events:2 conflict:1 independent:3 arrives:1 singapore:2 lie:1 effect:6 experimenter:3 center:1 acknowledgement:1 well:1 bohm:7 displacing:1 without:1 sets:3 model:4 left:1 popescu:4 when:1 reviewed:1 unary:2 aspect:4 speed:1 yet:1 preprint:1 absorption:2 photons:1 bell:3 seems:1 signals:1 slits:3 lett:3 momentum:4 aspects:3 showing:1 possible:2 increases:1 press:1 world:2 particle:2 signal:1 alice:6 flux:3 imposes:1 either:1 because:1 cones:1 classical:1 smoothly:1 deduce:1 ourselves:1 affects:2 measurements:9 overlap:1 cirel:1 does:4 proc:1 minimal:1 scientific:2 equivalent:1 symp:1 svozil:1 about:1 constraint:1 coexist:1 discussed:1 remains:1 range:1 obeys:2 seeing:1 equally:1 rev:3 within:2 bound:1 negative:2 lies:1 references:1 determine:1 einstein:3 frames:1 statistics:1 her:1 interacted:1 assumed:1 initial:1 question:3 why:3 restricts:2 workshop:1 physicists:2 forward:3 was:1 function:3 arise:3 form:3 offer:1 unsettled:1 regard:2 but:4 ramat:1 true:1 whether:2 bounds:1 us:6 limit:1 strongly:1 defined:3 certain:2 abstract:1 measure:1 influence:1 general:1 clauser:2 arises:2 physical:5 no:3 rosen:2 vanishes:1 field:4 other:5 jamming:6 observable:1 briefly:1 denote:1 separate:3 time:1 important:1 variable:2 astronomy:1 structure:2 implies:4 faster:2 assume:1 requires:1 required:1 together:5 reprinted:1 experimenters:1 electromagnetic:2 backward:1 chsh:13
|
quant-ph9508010.txt |@word represent:1 unavoidable:1 sci:1 forget:1 pointing:1 caused:2 magnetic:2 both:2 results:19 chiao:4 fig2:1 controversial:1 fig1:3 consists:1 follow:1 expressions:1 faster:1 gk:1 objections:1 whose:2 depend:3 clarification:1 aug:1 collisions:1 equivalence:1 presents:1 answered:1 quasi:6 tj:1 those:6 th:3 under:1 pay:1 analogous:1 vladislav:1 worth:1 sent:1 case:7 comparatively:1 advantage:2 returning:7 very:5 nonselfadjoint:1 differently:1 wigner:1 wave:42 electron:2 putting:1 figs:7 dispersions:2 overcomes:1 experimentally:1 difference:4 petroff:1 condition:1 discovered:1 obvious:1 quantitatively:1 presented:5 transmission:10 ref:35 pacs:1 solution:2 t0:3 correct:1 large:2 detected:1 small:6 smith:1 commented:1 work:2 parigi:1 b27:1 consistent:1 prediction:1 sign:2 approximation:1 imply:1 plenum:1 equal:1 incidentally:2 further:3 dynamics:1 belief:1 even:12 aim:1 what:3 settlement:1 sub:2 clock:2 contributions:1 brief:1 expressed:5 find:1 rohrer:1 looking:1 above:1 lifshitz:1 new:13 increasing:2 consisting:1 contrast:1 quenched:1 evanescent:3 respectively:17 a28:1 here:6 behaviour:5 believed:1 slow:2 them:3 berkeley:2 directions:1 causality:1 along:2 principle:1 equations:4 appears:1 growing:1 calculate:1 ukraine:3 incoming:7 noticeable:1 suitably:1 institute:3 study:1 larger:7 reason:1 reports:2 c18:1 resulting:1 adv:1 usually:1 symmetrical:1 adopting:3 suitable:3 der:1 criticism:3 useful:1 rodrigues:1 merely:1 explained:4 integrations:2 replace:1 vac:1 addressed:1 decrease:1 dumont:1 apply:1 total:3 florence:2 causal:4 unit:1 frustrated:1 plot:4 conventional:8 microscopy:1 would:1 commun:4 probabilities:2 positive:10 continuous:1 negative:11 few:3 therefore:6 marchand:1 type:2 theoretical:4 more:11 introducing:2 entrance:2 stingl:1 furthermore:3 acceptable:2 carriers:1 corrected:1 emission:1 validity:1 normalized:2 particular:7 known:3 rare:1 cases:5 hold:1 iii:5 ocs:1 account:1 eberhard:1 anything:1 leavens:12 recall:6 equation:2 averaged:1 remain:1 values:15 reshaping:3 following:3 making:1 averages:3 example:3 stimulating:1 claim:2 modulation:1 figure:5 chosen:1 process:5 relativistic:4 aleksandr:1 near:7 collision:2 assumptions:1 performed:3 want:1 unphysical:1 standard:1 mccumber:1 evidently:1 axis:3 oliveira:1 requirements:1 hoc:1 kwiat:3 rather:4 verify:1 holds:1 feature:2 regions:2 located:3 hot:1 actual:1 pure:1 extinguished:1 acta:2 ordinary:3 guarantee:1 parameter:1 priori:2 ψin:3 de:1 electronics:1 description:1 superluminal:4 may:3 use:1 derived:1 containing:1 lab:1 barriers:2 coming:1 hauge:1 evaluations:4 choice:1 meaningful:2 grow:1 curve:16 stress:4 giardina:1 attempt:1 dynamical:1 succeeded:1 negligibly:1 light:1 cutler:1 murst:1 correspond:3 like:2 provide:1 cannot:3 negligible:1 sect:7 fundamental:1 decreasing:2 definitions:11 subsequently:1 increase:3 order:4 least:1 interpretation:2 closely:1 devote:1 indeed:1 over:10 garrison:1 vary:1 years:1 stability:1 whilst:2 paper:5 through:13 preliminary:2 during:10 mentioned:1 existence:5 kinetic:2 ieee:1 its:8 refs:7 facolt:1 tending:1 delgado:3 rapidly:3 thank:2 directional:1 jin:5 interesting:3 temporal:1 relativity:1 complex:1 decreases:1 actually:6 absence:2 distinguishing:1 degrees:4 fig:12 ours:1 τt:10 main:2 defining:4 correspondence:1 eventually:2 non:8 good:1 return:7 propose:1 processes:9 introduce:2 anticipated:2 jaworski:2 mention:2 transmissions:1 precession:1 penetration:19 they:3 half:1 oxford:1 landau:1 now:4 transparent:1 nor:1 possess:1 easily:1 term:2 finite:1 dirac:1 always:7 university:1 fluctuate:1 prosperi:1 did:3 wong:1 transmitted:2 mode:1 reasonable:1 noticeably:1 crossing:1 found:4 universit:2 higher:1 mean:17 proposing:1 weight:4 meets:1 2e:1 ed:2 energy:5 reduce:1 gaussian:3 related:2 group:2 constitute:2 elementary:1 milan:1 literature:1 travelling:4 obtains:1 entering:1 measure:1 quantum:14 our:57 ev:27 eq:5 regge:1 after:2 out:3 shown:2 fluxes:1 kiev:5 3rd:1 space:6 rep:1 since:3 interference:6 ret:9 research:4 particles:7 re:3 investigation:1 technol:1 reader:1 formula:1 get:1 receiving:1 forth:4 integrated:1 performing:1 anwar:1 theory:4 barrier:39 fisica:1 quite:3 approaches:7 york:2 besides:1 put:3 org:4 wall:2 publication:1 definition:7 integrating:2 retained:1 marchioro:1 applications:2 explanations:1 could:2 days:1 times:18 motion:4 appearing:1 american:1 enders:2 gordon:1 enough:2 hence:1 distinguish:1 speeds:2 first:2 oper:1 xi:34 features:2 probability:5 tachyon:2 waves:9 xf:27 reflected:5 clear:1 approximately:1 another:1 clarity:1 causing:1 spread:1 passes:5 differ:1 discussed:1 needed:1 introduction:2 leading:3 eqs:8 goldberger:1 relations:1 fm:1 their:3 appl:3 listed:1 calculations:9 dwell:6 postulate:1 final:5 speaking:2 low:1 a37:1 abovementioned:1 baldo:1 centered:3 academy:3 exactly:1 direct:3 part:8 frascati:1 authors:1 eliminated:1 than:7 png:8 reflection:10 connections:1 nanostructures:1 bergamo:1 spielmann:1 accordance:2 gotten:1 namely:1 aims:3 whenever:2 a45:1 contrary:2 amplitude:1 ingegneria:1 extinguish:1 anomalous:2 a48:3 a49:1 rewrite:1 footnote:2 boston:1 ann:1 mind:1 ρdx:1 already:2 say:1 himself:1 manner:1 distorted:1 need:1 seen:1 seem:4 apparently:3 any:8 elsewhere:1 paths:1 generalizes:1 issue:2 academic:1 convenient:1 self:1 answering:1 physique:3 gravity:1 thorough:1 erage:1 sciences:3 potential:7 take:3 analogy:2 so:7 reproducing:1 switching:1 play:2 towards:1 shall:2 collaboration:1 object:4 depths:1 semiconductor:1 connected:3 formulae:5 phase:4 austr:1 uttiker:1 probabilistic:2 appear:5 workshop:1 ka:1 quotations:1 wiley:1 considered:5 sala:1 average:6 later:1 milano:1 physica:1 feynman:4 proceedings:1 points:3 electrons:1 reflections:1 exp:3 mechanical:2 velocity:1 physics:2 fact:10 quantity:5 b47:1 phenomenon:3 show:5 supported:1 angstroms:6 anyway:2 analogously:2 notations:1 purely:1 reference:1 helv:1 relation:2 fletcher:2 carefully:1 02a:4 x0:1 paradoxes:1 clarifications:1 postulates:1 finally:3 based:6 just:2 parameters:4 situations:1 explain:1 heavily:1 distributed:1 iet:1 should:5 moments:2 only:11 going:2 habilitation:1 muga:5 factor:1 integrate:1 adequate:2 pointed:1 continuity:2 do:3 his:2 dk:2 notation:1 di:6 dependent:1 mainly:1 express:1 beltrametti:1 bear:1 watson:1 ones:4 b175:1 dx:4 pucci:1 report:1 dw:6 dt:36 interpreted:1 klein:1 geometric:1 portion:1 evolution:2 contributes:1 densities:2 course:4 conditions:6 arxiv:5 preliminarily:1 yield:3 method:1 garcia:1 investigate:1 clocks:2 predicted:1 discussing:1 valid:3 view:2 monochromatic:6 scanning:1 set:1 motions:1 observer:2 edited:2 physically:2 frame:3 impossibility:1 ends:1 packet:23 cologne:2 opposite:2 see:11 result:5 eliminating:1 captions:1 discussions:1 terms:1 brazil:2 instance:5 matter:1 nuclear:3 review:2 missing:1 definite:5 consequence:2 artificial:1 yet:1 boundaries:1 state:6 smallest:1 various:7 tendency:1 cooperation:1 between:14 probably:1 boundary:2 before:4 approach:12 checks:1 wide:1 available:5 variability:1 notice:3 attention:1 recently:3 statistically:1 betwen:1 initially:1 edge:5 ikx:1 however:7 tolman:1 incident:1 agresti:1 huang:1 nimtz:4 analyzed:1 article:2 distribution:4 improve:1 received:1 essentially:2 commenting:1 last:10 brown:1 met:1 qft:1 jauch:1 region:12 conclusions:2 according:1 against:1 agree:2 fulfilled:1 propagation:1 connection:2 objects:3 figures:2 lo:1 uni:1 contribution:4 expression:3 photons:2 experimental:3 strongly:1 relevant:1 afterwards:2 point:6 reasons:1 seems:5 others:1 cf:4 whatever:1 height:1 represented:2 anti:3 path:2 moreover:9 worthwhile:1 april:1 uncorrected:1 pp:1 described:1 basis:1 overlook:1 three:1 been:9 quickly:2 citations:1 change:1 expected:3 entered:1 define:1 wants:1 obtained:2 direction:6 adopted:3 corresponding:5 observable:1 quantities:3 concerning:1 modelling:1 krausz:1 observe:6 recalled:1 curves:3 systematic:1 catania:4 instant:2 careful:1 expounded:1 present:7 applied:2 k2:1 potentials:1 developing:1 solid:4 variances:8 e48:2 appearance:1 value:10 rectangular:7 will:4 dept:1 while:4 abrupt:1 editorial:1 error:1 taking:1 procedure:2 mistake:2 landauer:4 merwe:1 unitary:2 almost:5 averaging:1 overlooked:1 formulation:2 thus:3 retarding:1 discrepancy:2 iv:2 ii:5 mugnai:1 vaz:1 itself:2 confining:1 claimed:1 affected:1 mod:2 different:10 italy:6 l55:1 author:1 perhaps:1 media:2 thesis:1 intrinsic:1 lett:8 same:7 parts:1 quant:5 emphasize:1 uncertainty:1 shah:1 several:2 infer:1 exponential:1 independent:1 used:2 http:4 again:2 tachyons:1 numerical:9 upon:1 effect:10 campinas:2 v0:2 devoid:1 moving:2 internal:1 supposing:1 infinite:4 heitmann:1 opportunity:2 passing:4 normalization:2 recent:4 mentioning:1 center:1 framework:2 nevertheless:2 acknowledge:1 no:5 well:5 monaco:2 analysis:5 bohm:1 objection:1 without:1 components:6 studying:1 firstly:2 position:6 dimension:1 justify:2 proposed:4 less:1 being:5 generally:2 observed:2 shilov:1 obtain:1 valuable:1 press:3 intervals:1 sufficiently:1 photonic:1 alternative:2 speed:2 underline:1 sullivan:1 previous:5 letting:1 rapid:3 preprint:1 kluwer:1 density:5 absorption:2 regarded:4 nonrelativistic:1 had:3 except:1 improvement:1 appeared:3 add:3 interested:1 treatment:1 misprint:1 constant:3 nos:1 totally:3 remaining:1 ought:3 real:1 saturation:4 contrarily:3 rev:18 format:4 disagreement:2 possible:4 confines:1 tunnelling:48 possibly:1 increases:4 were:2 distortion:1 using:4 jauho:1 scientist:1 formal:1 modifications:1 necessary:1 semi:1 particle:11 follows:3 reduces:1 velocities:3 flux:5 yields:1 sezione:2 arbitrary:3 become:1 steinberg:3 stationary:1 page:5 therein:8 because:1 often:1 classical:3 some:10 back:2 04a:1 experiments:1 suppl:1 respect:4 duration:8 indirect:2 ourselves:2 happens:1 provided:1 cnr:1 lead:1 confirm:5 electromagnetic:2 ukrainian:3 integration:6 comments:4 recami:7 flow:1 pen:18 does:16 centroid:4 tends:2 steps:2 refer:1 vitale:1 varying:1 bg:1 scientific:3 ps:4 seconds:5 equivalent:2 martin:4 oscillating:2 agreement:2 disappeared:2 jahan:1 step:2 verifications:2 2m:1 plots:8 analyses:1 refers:1 bz:1 analysing:2 comparison:1 about:6 central:2 extension:2 dtj:2 freedom:4 ranges:1 dependence:1 o:6 essential:1 sake:1 range:1 larmor:1 mende:1 introduced:2 sept:1 chu:1 own:1 effectively:1 presence:3 pergamon:1 into:1 within:6 integral:3 due:6 down:1 remarks:1 references:1 determine:1 operator:1 nuovo:2 mass:1 theoretically:1 methods:1 behaving:1 criticisms:1 acknowledgements:1 van:1 additional:3 buttiker:1 comparing:1 assumed:2 support:1 initial:18 question:1 doctorate:1 long:1 dispersion:1 width:7 much:1 quanta:1 editor:1 way:2 forward:2 hartman:11 analyze:2 was:7 vienna:2 function:7 fabio:1 medium:1 complete:2 energies:2 phenomena:3 analyse:1 but:7 sophisticated:1 might:2 rivista:1 cnpq:1 ph:6 partially:1 infn:2 persisting:1 made:4 applying:1 intuitive:1 characteristic:1 inside:14 up:2 us:34 dordrecht:1 below:2 limit:2 problem:5 piece:1 similar:4 called:5 expect:2 mechanics:10 penetrating:3 ab:1 associated:1 ad:1 computing:1 defined:3 certain:3 abstract:1 paragraphs:1 general:4 ch:1 single:1 predictions:1 av:1 formalism:2 distributions:3 check:1 physical:3 variance:2 functions:7 paradox:1 cim:2 olkhovsky:7 computations:1 dashed:1 when:14 vanishes:1 reality:1 field:3 other:5 role:2 papers:2 mathematics:1 proposal:1 sufficient:1 realize:1 conclusion:1 integrand:1 explaining:1 briefly:2 repeat:1 kinds:1 superposition:3 separate:1 initio:1 durations:11 welcome:1 problems:2 prepared:1 a1:1 meaning:2 important:2 bounded:2 studied:1 variable:1 a8:1 gets:1 line:2 a47:1 implies:2 longer:1 practically:2 assume:2 interval:7 packets:17 rule:1 having:1 depth:4 implied:2 weights:2 presenting:2 unquenched:1 time:50 backward:1 starting:2 receive:1 once:2
|
quant-ph9508011.txt |@word homomorphism:1 four:2 localized:6 sch:3 whose:9 aug:1 auf:1 γu:6 presents:1 under:15 hermann:1 γg:15 rise:1 iτ2:3 iτ3:1 iτ1:2 encounter:1 solution:2 admissible:4 vector:20 indices:2 10b:2 consistent:1 10a:1 direct:4 second:6 even:5 ˆu:1 selected:1 nez:1 establishes:1 new:7 ˆm:1 27a:2 27b:1 27c:1 simultaneously:2 27e:1 abstractly:1 here:13 atoms:1 fairly:1 represented:5 path:1 plex:1 interpret:1 obtained:1 akt:1 schur:1 projection:21 classification:1 9a:3 9b:4 highly:1 stern:1 total:2 propagators:5 unit:3 derivatives:1 would:9 bundles:10 call:11 therefore:15 von:11 decomposable:1 separated:2 composite:1 odinger:1 hold:4 must:10 mg:3 word:2 work:8 mi:1 rλ:19 enµ:2 concepts:4 example:20 indicated:2 give:2 relativistic:1 friedr:1 want:2 times:7 end:3 hoc:2 logunov:1 feature:1 how:3 answer:1 ordinary:2 description:2 earlier:1 diagram:1 wrong:1 law:2 parallel:3 summing:2 greek:1 order:7 operations:2 restriction:5 interpretation:1 deck:1 over:8 satisfied:3 london:3 satisfies:7 before:2 highlights:1 fix:2 writing:1 distinguishing:1 persist:1 quant:3 connectedness:2 maximal:4 eventually:2 them:5 combination:2 break:1 they:13 thep:2 represents:2 classified:1 each:37 side:5 lifted:1 24a:1 24b:1 principles:3 abuse:1 used:6 rs:4 restricted:3 dewitt:1 content:1 re:2 rg:28 multiply:3 adapt:1 dowker:2 rm:26 rn:1 rh:7 ri:1 independence:1 rk:2 foundation:1 linear:17 normalized:3 associate:1 standard:17 proportionality:1 publ:1 r1:3 r2:10 r3:8 δil:6 maximality:1 δij:4 onto:8 already:7 features:4 conjugacy:5 rank:4 restrict:6 anwendung:1 relations:6 illustrate:1 toy:3 rewritten:1 similarly:1 too:2 postulate:1 ashtekar:1 17b:1 17a:1 finitely:1 princeton:2 conforms:1 project:3 classes:3 tion:2 fashion:5 sees:1 modern:1 seen:10 seem:1 tells:1 ray:6 genuine:1 convenient:4 latter:3 vgc:8 do2:1 do1:2 residue:1 though:1 simplify:1 regular:8 germany:1 phase:3 acknowledgements:1 flow:1 inferred:1 accounted:1 principle:4 sum:6 saying:1 labels:5 gauge:25 d8:10 d4:9 d2:1 d3:1 d0:3 d1:4 ba2:3 ellipsoid:1 ba1:2 implementation:3 explain:1 specify:1 constant:4 dn:1 do:12 above:10 di:2 de:3 reversal:7 dq:1 runs:1 covering:4 fields:1 nλ:1 nν:4 implication:1 automatic:1 reference:2 phenomenologically:2 generally:16 δjk:2 depends:1 projections:3 discussions:1 27d:1 dµ:45 incorporating:1 said:9 tensor:3 symmetric:2 petr:1 terms:9 extend:1 wo:3 however:17 wi:2 residual:1 picking:1 topology:5 essentially:2 und:2 faces:1 uni:1 adapted:2 16a:2 16b:2 speak:2 commutative:4 basis:15 union:1 three:6 been:6 µji:2 interest:1 basic:3 algebras:5 θk:3 θn:2 relaxing:1 cotangent:3 quantities:2 concerning:1 relevance:2 coherent:1 lift:9 applied:2 hat:1 employ:4 equivariance:5 suppose:2 viii:3 property:4 procedure:4 redefinitions:1 iq:16 ir:3 ii:7 characterize:2 ik:3 ij:6 im:1 id:2 hong:1 make:6 vieweg:1 complex:15 potentially:1 split:3 unfortunate:1 independent:3 i1:2 i3:1 i2:2 hand:5 characters:3 normalization:1 mentioning:1 academic:2 left:52 just:19 identify:3 transporting:2 facts:1 previous:5 unique:7 had:1 tuples:1 easy:3 5a:2 5b:4 explained:4 dihedral:1 possible:1 spanned:1 possibly:2 background:1 replace:1 performing:1 unnecessary:1 specific:4 arbitrary:1 componentwise:1 claredon:1 right:63 old:1 deal:2 truncated:3 truncates:1 linearly:5 dense:2 xv:1 normal:2 comments:1 everything:2 bra:1 properties:4 proceed:2 chapter:4 o:94 plus:1 eight:1 slightly:2 primitive:1 statements:1 publishing:1 rotations:3 down:2 lies:7 often:4 existed:1 support:6 why:1 accordingly:2 way:12 was:8 form:17 converse:3 δkj:1 failure:1 true:7 portions:1 versions:1 tiµ:3 inside:1 preimage:1 coverings:2 ψe:6 jauch:9 nµ:47 adopt:2 abstract:5 proven:1 braunschweig:1 dν:1 reenter:1 dλ:1 exist:3 commuting:4 check:3 physical:2 nm:1 no:10 whereas:4 when:1 setting:2 mottelson:1 nu:1 picture:2 superposition:2 truncate:3 models:1 15a:3 15b:3 assume:3 together:1 dkj:1 exponentiate:1 time:9 antilinear:3 nuclei:6 stick:1 concept:1 focus:2 adjective:1 foundations:1 displaying:1 certainly:1 inverse:1 eˆ:9 editors:2 finally:7 analogous:5 circumstances:1 sorkin:1 string:1 orthogonal:7 springer:1 seemingly:1 choice:6 orientations:1 exact:1 dim:1 dii:3 dij:7 dik:2 did:2 irreducible:19 leave:1 discrete:8 irreducibly:4 symmetrization:1 science:2 der:3 prevent:1 mn:5 says:1 dealing:1 sign:1 htr:23 appear:2 axes:2 satisfy:7 transportation:2 tangent:1 groups:14 along:6 appears:2 galilei:1 gaction:1 studied:1 simultaneous:1 usually:1 hospitality:1 conveniently:3 useful:1 diffeomorphisms:1 prefer:1 f2:2 interprets:1 logically:1 projector:3 prove:4 positive:2 wissenschaftliche:1 nonsymmetric:1 introducing:1 molecules:1 parallelly:2 appendix:13 virtue:1 cases:6 valued:10 deformed:2 labeled:1 printing:2 values:5 following:14 arrive:1 ihre:1 hears:1 expanding:1 arise:1 confused:1 dropped:1 conversely:3 verlag:1 normalize:1 redundancy:3 requirements:2 discussion:6 orthogonality:2 write:3 criterion:1 pure:20 parameter:1 map:6 product:12 quantenmechanik:2 may:14 sacrifice:1 straightforwardly:1 applications:1 representations:16 lifting:2 iθk:3 stress:2 natural:7 dynamical:4 sectors:17 whenever:1 explicit:3 su:6 st:2 so:34 representation:41 sg:5 talk:1 indeed:8 pointed:2 kong:1 exponentiates:1 course:6 differs:1 still:8 derive:1 group:54 thank:1 maps:11 interesting:2 τe:5 forms:2 dji:3 mail:1 djj:1 τq:8 correspondence:2 non:33 thereby:1 introduce:5 identically:2 eµ:1 now:30 discuss:1 equality:1 january:1 possibilities:1 realistic:1 entirely:3 domain:5 square:3 ei:5 ej:2 conventions:1 entering:1 happen:1 avoided:1 space:53 looking:1 contained:6 rational:1 formula:11 squares:1 shows:4 reformulation:1 theory:14 possibility:1 quite:3 e1:4 language:4 transition:1 vjk:1 turn:3 vji:1 think:1 first:12 xk:7 xi:1 parastatistics:2 symmetry:5 omitted:1 variables:1 directly:1 carry:3 open:1 given:44 necessarily:4 unitarity:2 indicate:1 convention:5 speaking:1 gives:2 continuous:5 eliminated:1 representing:6 than:6 coefficients:4 greenberg:1 require:3 transferred:1 were:8 nouvo:1 san:1 topics:1 argument:1 generalization:2 say:7 any:28 ideas:2 note:12 ideal:3 take:4 bogolubov:1 interior:1 coincide:1 modulus:1 δkm:1 opposite:2 price:1 algebraic:3 formulae:2 pair:3 inserted:1 surprising:1 considered:5 later:1 feynman:1 sohn:1 show:3 notations:2 spaces:12 inconsistent:1 fibre:4 state:17 only:23 explicitly:7 ges:1 viewpoint:1 get:3 oˆ:4 expectation:1 truly:1 cannot:6 boundary:3 mapped:1 physically:1 violated:1 com2:1 j2:1 relative:4 namely:1 inequivalent:7 αq:4 satisfying:5 commutation:3 ways:1 review:2 definite:1 marmo:3 label:1 αa:1 vkj:1 morales:1 between:3 geometric:3 reading:2 multiplied:1 comp:1 jm:3 ji:1 jk:1 ja:1 many:3 nomenclature:1 dkl:1 expression:1 σu:2 anti:3 moreover:5 considering:1 configuration:12 wien:1 locally:5 wants:1 direction:2 oψ:1 rephrased:1 former:2 those:10 u1i:1 cancelled:1 situation:3 metric:3 according:2 binary:1 different:15 verified:1 formulations:1 same:11 verifies:2 status:1 oik:2 singapore:1 trivially:1 invariance:5 modes:3 pennsylvania:1 onedimensional:1 hamermesh:1 without:4 components:6 coordinate:1 model:6 grounds:1 dimension:3 isometry:1 manifold:2 being:4 captures:1 actions:3 torus:4 seems:1 unambiguously:1 treatment:1 contractible:2 oµ:1 structural:3 momentum:1 real:3 aspects:3 decomposability:1 rules:12 involutions:1 repetitions:1 early:1 using:19 decomposes:2 mod:6 particle:2 reduces:4 serves:3 automorphisms:2 either:3 integrals:1 always:5 reduced:4 specified:1 images:1 nonzero:1 superselection:12 dimensions:2 decomposition:6 provides:2 refer:2 scientific:1 equivalent:8 2m:1 refers:2 2n:6 comparison:1 trivialization:1 central:1 discussed:2 generated:9 mutually:6 act:12 mixed:1 image:1 references:1 pathintegral:1 determine:2 bijective:2 assumed:3 there:27 complete:5 regard:3 elimination:2 applying:2 multiplicity:2 define:15 agree:1 multiplications:19 obtains:1 aa:2 taylor:1 ad:6 ai:11 certain:2 uij:1 general:24 tˆ:11 formulation:4 incorrect:1 again:6 completeness:2 field:8 valid:3 briefly:1 separate:1 symbol:2 thirring:1 a1:8 important:1 bounded:2 massachusetts:2 observables:28 relativity:1 curve:4 impossibility:1 mass:2 once:1 starting:2 original:1 represent:7 consider:10 discards:1 splitting:1 scalar:1 commute:8 generalize:1 follow:2 expressions:5 research:1 particles:2 equivalence:6 tr:12 tq:12 th:7 ti:1 tg:1 presentation:2 case:29 very:3 translations:1 induce:1 δgh:2 deformations:1 condition:6 leads:2 hamiltonian:7 juxtaposition:1 small:2 employing:1 zero:1 alent:1 displays:1 further:2 canonical:5 subscripts:1 what:6 nonlinear:2 ıˇcek:1 section:32 subspaces:17 method:1 contrast:1 full:2 component:3 galilean:1 equations:1 commutant:11 tµ:3 allows:2 amount:1 pick:1 action:40 specialize:1 uniquely:11 via:9 followed:1 family:2 vij:9 vik:2 lagos:1 equivariant:10 establish:1 select:1 takes:2 contains:6 ψh:2 taken:2 ψf:1 more:17 flat:2 operators:24 corrected:1 basically:1 particular:16 known:5 projective:1 none:2 recall:3 equation:1 paragraph:2 f1:2 compare:9 stated:2 states:20 pushed:1 numbers:2 sense:10 rather:8 acts:13 unitaries:1 occasionally:2 reject:1 acta:2 explains:1 algebra:40 derived:1 orbits:1 tˆµ:6 plane:2 coming:2 horizontal:3 geometrical:2 short:1 spectra:1 misra:1 fundamental:21 helv:2 giulini:3 cross:1 paper:4 through:8 filters:1 existence:1 kinetic:2 its:27 tˆg:1 conjugation:6 actually:2 absence:1 systems:4 might:4 finer:1 incompleteness:1 pauli:1 framework:2 thereof:3 oxford:2 easily:16 homomorphisms:1 fully:1 presented:1 evade:1 iff:21 die:2 found:1 universit:1 darmstadt:1 harm:1 weight:2 energy:2 reduce:3 idea:1 connect:1 quantum:30 operation:6 really:2 hartle:1 nuovo:1 since:34 induces:1 projected:3 denotes:5 acting:3 denoted:8 induced:2 issue:1 occurs:3 benjamin:1 reformulated:1 localization:2 reason:1 base:3 put:1 generate:2 definition:8 freiburg:5 major:2 number:1 done:3 least:4 differ:1 introduction:1 construct:5 expand:1 statement:3 scheme:1 part:2 translation:1 believe:1 18b:4 kind:1 18a:1 determines:1 cyclic:1 double:2 aims:1 determined:7 pairwise:1 fˆ:1 7b:2 7a:2 defect:1 conjugate:3 elsevier:2 idempotents:5 paths:2 constructions:1 jour:2 built:2 depending:1 self:9 k2:1 internal:3 build:1 analogy:3 play:1 added:1 most:3 plan:1 nothing:3 kj:1 clear:5 sometimes:1 cover:6 km:2 exp:6 physics:3 attacking:1 sector:8 eˆµ:15 multiplicities:2 relation:2 find:3 completion:1 e11:1 generators:1 factor:5 integrable:3 circle:3 columns:1 abelian:45 notation:6 dependent:2 express:3 methods:1 famous:1 rest:1 arxiv:1 wightman:10 investigate:1 annalen:1 set:22 achieved:1 see:16 individual:1 descriptions:1 theoretic:1 various:1 conditions:1 missing:1 initially:1 complement:1 attention:2 eˆm:2 inertia:1 both:3 prescription:3 quantization:8 connection:3 symplectic:1 context:2 whole:2 finds:1 experimental:1 arbitrarily:1 point:13 simple:8 corresponds:7 dimensional:24 simply:10 fibres:1 throughout:1 kernels:3 ensures:1 described:1 transformations:7 pu:4 due:10 intricacies:1 pk:4 ph:3 addison:1 usage:1 representative:2 assigning:1 unnecessarily:1 look:1 solid:1 mations:1 replaced:2 loop:6 unitary:11 vol:3 overlooked:1 reads:2 itself:1 rid:1 vanish:1 null:1 anymore:1 grant:1 read:2 emphasize:3 deletion:1 resulting:1 relatively:1 subalgebra:6 composition:2 higher:3 literature:1 lie:3 moment:2 dimv:1 recent:1 eigenvectors:1 lower:1 task:1 analysis:1 obviously:3 todorov:1 entry:1 comprise:1 questions:1 world:1 kluwer:1 rˆole:1 deliberately:1 theorem:3 rgh:1 transformation:4 generalized:7 hgh:1 isomorphisms:5 big:2 showing:1 integer:1 systematically:1 follows:12 manifest:1 separately:1 yields:5 translated:2 pointwise:4 essential:3 terminology:1 mathematical:2 neumann:11 absolutely:2 some:27 back:2 understood:4 examples:1 eˆij:1 delivered:1 shall:7 nonsimply:1 connecting:1 minimal:7 run:1 bm:12 ruf:1 bi:1 bj:3 step:2 redundancies:1 hilbert:19 tracing:1 range:1 extensions:4 into:16 within:10 integral:5 isomorphic:7 suppl:1 appropriate:1 primarily:1 proportional:2 iπn:2 rows:1 span:11 classical:10 hypothetically:1 analyze:2 sections:8 propagator:3 steenrod:1 properly:2 reed:1 reeh:1 line:3 characteristic:1 up:3 us:11 ur:1 uk:3 ug:2 similar:2 called:18 associated:4 defined:29 coincides:1 globally:3 formalism:1 defines:13 amounts:1 application:4 points:5 elements:10 sided:1 problems:2 meaning:3 allowing:1 vectors:7 sides:2 structure:5 independently:1 implies:15 required:2 orbit:1 notion:2 equivalently:5 basepoint:2 weights:1 far:3 wi2:2 ambiguities:6 results:4 gg:8 gc:5 go:1 gl:1 centers:1 gi:2 gh:8 compact:1 simon:1 disposal:1 concerned:1 uniqueness:2 include:2 indicating:1 economical:1 implicitly:1 wave:3 rotational:4 redefinition:2 zµ:1 matrices:10 notes:1 pullback:2 manifestly:1 eigenvalues:2 configurations:1 zn:1 fold:1 concludes:2 odd:9 index:3 11b:1 analogously:1 expressed:5 implementable:1 body:1 led:1 chose:1 respectively:11 identifications:4 z2:6 remark:3 wesley:1 technical:2 involved:1 larger:2 suggests:1 products:2 implement:2 makes:3 formulated:2 danger:1 equals:1 summation:1 apply:4 ninth:1 use:16 remains:1 next:2 few:1 themselves:1 hermitean:4 labelled:3 wi1:2 discreteness:2 iii:7 isomorphism:7 obvious:12 meet:1 proof:5 weaker:1 effectively:1 overbar:2 holds:2 regions:1 reducible:5 instead:2 sin:2 collection:1 rays:17 physik:2 multiplication:21 domenico:1 ambiguous:1 homomorphically:1 introduced:2 correspond:5 redundant:2 element:11 diffeomorphism:2 allow:2 furnish:1 wigner:4 produces:1 interpreted:1 looping:1 mentioned:3 aj:1 ld:5 chosen:1 lm:1 degrees:1 ls:1 13c:1 13b:1 13a:1 fourth:2 operator:10 rotation:1 transparent:1 dirac:4 university:3 identified:4 l2:6 identifies:1 homogeneous:2 weyl:2 doing:1 related:1 elementary:2 measure:7 supersymmetries:2 our:16 special:4 out:5 matrix:16 rev:3 woodhouse:1 gˆ:22 herder:1 suffices:1 math:3 8b:2 8a:3 completely:3 york:2 subalgebras:7 skagerstam:1 cured:1 geometry:4 could:10 keep:2 quaternions:1 lµ:8 hence:12 tivity:1 austin:1 bijection:1 precisely:8 aharonov:1 adjoint:9 system:12 adopted:2 their:7 perfectly:1 final:1 commutativity:3 explanation:1 exactly:2 outline:1 holland:2 isolation:1 cimento:2 richer:1 inversely:1 distinguished:2 result:5 symmetries:6 elementwise:1 need:4 clearly:6 rotor:3 angle:1 holonomies:1 mid:1 best:1 lectures:1 hq:3 unless:3 centre:13 connected:10 but:28 definitions:1 intrinsic:1 class:10 32b:1 χu:4 32a:1 repeated:1 mechanical:10 fact:11 ho:2 12a:4 12b:2 supported:1 visualized:1 ki:4 trivial:5 agrees:1 principal:7 based:3 should:7 lemma:4 bases:3 ambiguity:1 inherited:3 employed:2 local:6 interested:4 cube:1 means:7 familiar:2 overall:1 ones:4 legitimate:1 words:1 expansions:1 qg:4 contain:5 qh:1 fixed:5 view:2 conform:2 requirement:13 exists:1 hν:1 frame:1 edition:1 truncating:1 quantizing:2 phases:2 attempting:1 nuclear:2 written:6 identification:2 closed:1 invariant:23 neither:1 publishers:3 ends:1 hypothesis:2 key:1 ket:1 restrictions:1 equal:6 attributed:1 homotopy:2 etc:2 admit:1 jersey:2 otherwise:3 unitarily:2 relevant:3 co:1 cm:1 conclude:1 leipzig:1 quantizations:2 respect:6 cp:1 addition:1 copies:1 galindo:1 choose:1 filippo:2 describe:3 corresponding:4 commutes:4 sufficient:2 subspace:17 vµ:2 angles:2 last:4 denote:7 present:4 main:1 subsets:3 balachandran:2 value:2 choices:2 will:19 indecomposable:1 happened:1 inherits:1 wkj:1 vg:90 vi:17 vj:2 vk:2 thus:19 surprisingly:1 bargmann:1 35b:2 35a:1 indistinguishable:2 member:1 diagonalize:1 largest:1 units:1 finite:24 infer:2 difficult:2 guises:1 urich:1 infinite:5 identity:3 schr:1 center:2 well:3 bohr:1 bohm:1 barut:1 sets:3 arising:1 subgroup:4 26b:1 26a:1 moments:1 obtain:5 underlying:3 momenta:1 conjugates:1 preprint:1 gmn:4 density:4 combine:1 skm:1 identical:2 messiah:1 know:3 press:4 immediately:3 intersection:2 loss:1 necessary:5 like:6 lost:2 28a:1 alternatively:3 28c:1 28b:1 δm:8 displaces:1 become:1 works:2 replacement:1 because:3 centralizers:3 ideals:2 choosing:2 asserted:1 proper:2 transport:1 literally:2 avoid:1 does:11 summand:1 assuming:2 esm:1 11a:1 slight:1 selecting:1 expansion:2 clarendon:1 although:6 simpler:1 about:3 actual:2 carried:1 extension:5 freedom:2 dependence:1 a2:8 transitive:1 loops:1 projectors:5 subset:6 own:1 letters:1 functional:2 holonomy:2 strasse:1 additional:5 vˆ:35 restricts:2 inner:9 naturally:1 function:16 north:2 collective:4 sequel:1 ht:3 hu:1 volume:1 hk:1 neutral:1 construction:3 contradictory:1 gain:1 ha:5 hf:1 hg:4 made:3 whether:2 wish:4 smooth:1 below:1 projecting:2 rµ:5 demonstrate:1 problem:2 mechanics:14 universal:7 hµ:21 abhay:1 inc:2 functions:31 136b:1 variety:3 detail:4 disjoint:4 other:7 details:4 theor:1 conclusion:1 francisco:1 bundle:15 factors:2 rule:3
|
quant-ph9508012.txt |@word limited:1 four:5 consists:8 localized:1 whose:8 violate:1 aug:1 rise:1 figs:3 affect:2 solution:95 indefinitely:1 vector:4 enhance:1 10k:1 force:1 deutsch:3 consistent:5 estimates:3 direct:4 likely:9 qualitatively:3 nogoods:59 implemented:2 machines:3 even:13 errors:7 selected:7 above:10 designing:1 new:9 net:1 contributes:1 consisting:2 simultaneously:4 behavior:50 never:2 equals:1 here:26 atoms:1 reported:3 represented:4 path:3 obtained:7 items:22 leaves:2 changed:1 approaches:2 ignoring:2 characterizing:1 suitable:4 changes:4 cancellation:5 landauer:2 offs:1 highly:4 achievable:1 total:3 univ:2 linearly:4 plot:2 would:14 motivate:1 negative:1 25th:1 type:1 until:10 separated:1 reversible:3 excellent:1 serially:2 must:12 md:1 work:10 example:19 indicated:1 give:19 bennett:1 organized:1 involve:4 indicates:1 walsh:1 scheduling:3 feasible:8 npcomplete:1 guarantee:3 rareness:1 end:2 provide:3 verify:1 feature:2 machine:1 how:12 nontrivial:2 answer:2 symposium:2 brassard:1 wolfram:1 description:2 transforming:1 turing:2 after:3 minimized:1 modest:2 law:1 parallel:3 attempt:1 effective:7 summing:2 complexity:4 maintain:1 algorithms:18 menlo:3 decreasing:1 operate:2 order:4 operations:8 restriction:2 interpretation:1 over:16 london:1 satisfies:2 before:1 fit:1 highlights:2 fix:1 exhibits:1 better:9 distinguishing:3 fig:26 persist:1 potentially:4 easier:4 eugene:1 eventually:4 them:7 combination:2 they:15 goldwasser:1 represents:3 reasonable:2 each:47 mean:1 fairly:2 series:6 principles:1 taught:1 substantially:1 clauses:3 restricted:2 ajr:1 combinatorial:14 conjectured:1 rl:1 xu:1 ri:4 rk:2 numerical:2 linear:5 standard:9 vazirani:2 ian:1 estimate:5 muller:1 incorporates:1 starts:1 moving:6 already:2 coding:1 encouraging:1 implicates:2 restrict:5 another:10 illustrate:2 similarly:1 eqs:2 needed:1 confirming:1 too:3 hypothetical:1 gilbert:2 john:6 ranging:2 somewhat:4 wasted:1 distance:1 showed:1 princeton:1 bits:5 second:6 matter:3 classes:7 10th:2 enhancement:2 mind:1 seen:8 seem:4 relatively:12 latter:2 though:6 accurately:1 simplify:1 involving:5 phase:60 don:3 observation:3 definitely:1 principle:3 sum:7 incomplete:4 heuristics:2 random:46 soluble:10 attempts:1 solutions:47 subtle:1 layout:1 proposed:1 implementation:3 situations:3 specify:1 dn:1 do:15 klein:1 negated:1 report:2 increasing:1 acknowledgments:1 bad:3 precluding:1 sensitivity:2 testing:7 observed:4 depends:2 result:8 discussions:2 best:1 techniques:2 said:1 away:2 artificial:16 conceptual:1 drawn:1 approach:2 terms:5 extend:1 nature:3 restricting:1 however:13 extent:6 picking:1 suggested:2 cos:4 gsat:1 0x:1 uncertainty:1 against:4 logic:2 variance:2 contribution:6 0i:2 com:2 behaviors:6 recursive:1 2nd:2 wider:1 broadening:1 basis:4 equations:3 three:2 been:4 quickly:4 much:10 interest:8 basic:2 expected:9 j0i:14 coherent:3 applied:2 transformation:1 near:11 suppose:7 applies:1 property:1 35th:1 study:1 procedure:3 exceptionally:1 ij:1 conf:3 nonunitary:2 containing:1 perform:3 suggest:5 make:6 complex:4 quant:1 mixtures:1 avoids:1 grows:7 independent:7 inadvertently:1 pick:2 hand:4 supposing:1 a2k:1 opportunity:3 normalization:3 academic:1 greatest:1 simulated:2 left:5 unified:1 stringent:1 just:12 assigned:5 identify:1 previous:3 adding:1 mix:1 spread:1 easy:10 possible:33 possibly:2 unique:4 appearing:1 permuting:1 performing:2 specific:8 steps:5 arbitrary:2 nonintegrability:1 right:4 deal:3 golub:1 separately:1 bottom:2 comments:1 contributing:1 unit:1 algorithmic:1 illustration:2 constructive:3 manufacturing:2 limitation:2 o:3 probabilities:5 slightly:3 soc:2 j1i:8 obtaining:4 factorising:1 pair:1 raises:1 reducing:2 often:2 rely:1 initial:7 approximate:3 why:3 stuck:1 joseph:1 editor:1 way:4 was:4 synthesis:1 form:7 offer:1 epsilon:1 becoming:1 differences:1 removes:1 idealized:3 removed:1 true:5 devices:2 reiter:1 palo:2 computing:6 abstract:1 exist:1 simulations:1 distributions:1 check:5 regime:2 ni:3 nj:1 nk:2 nl:4 mceuen:1 no:24 nb:3 generally:6 ny:3 interested:1 rolf:2 np:13 superposition:19 models:1 uniformly:1 variable:18 faster:1 together:2 time:27 n2:1 neighbors:1 logarithms:1 focus:2 computation:24 foundations:2 row:1 certainly:1 depend:4 graph:5 technique:1 editors:3 environment:1 finally:8 compensate:1 analogous:3 division:2 advantage:1 orthogonal:9 keeping:1 choice:16 drexel:1 entries:6 exact:1 prespecified:8 presented:5 skewed:1 leave:2 discrete:2 prevent:1 sign:1 colin:4 cost:17 appear:13 goes:1 international:1 satisfy:4 abrupt:3 address:1 along:4 appears:5 change:3 alto:2 sending:1 studied:7 trial:5 ineffective:1 usually:3 bob:1 studies:6 plotted:2 useful:11 ions:1 f2:2 logical:2 prove:3 k0x:1 tightly:1 going:1 memory:1 associated:4 nanosystems:1 theoretical:7 today:1 introducing:3 suggestions:1 apparent:1 cases:16 effort:1 constraint:28 hardest:4 values:35 making:4 december:2 sense:1 aaai:3 allowed:2 conversely:1 requirements:15 fortunately:3 s1:2 chemical:1 optimal:2 allowable:1 parameter:2 inputs:1 may:9 auton:1 applications:1 produce:2 improving:1 destructive:3 revealed:1 grow:4 times:7 natural:1 johnson:1 explicit:1 annealing:2 so:21 sn:2 sm:3 representation:3 typical:4 indeed:1 course:1 experiments:7 statistical:1 differs:3 cold:1 still:2 ieee:2 group:1 thank:4 wallace:1 interesting:4 decreases:2 policy:1 main:2 correspondence:1 halt:1 regularities:1 introduce:3 scaling:28 now:2 discuss:1 maintaining:2 inversion:9 name:1 james:2 possibilities:3 realistic:2 weighted:1 ei:4 significantly:1 happen:2 avoided:1 eq:8 shown:15 space:8 furthermore:6 interference:7 increase:2 rational:1 suggesting:3 formula:5 correct:3 shows:5 wiley:2 theory:10 variant:1 possibility:6 quite:5 complicated:2 advance:1 kaufmann:1 benioff:1 transition:32 wrong:1 inverts:1 turn:2 atomically:1 place:1 first:15 intuition:1 benefited:1 shapiro:1 pn1:1 clause:3 variables:13 xa:1 symbolic:1 nested:1 simplified:1 specifically:11 directly:4 crit:2 open:7 size:39 given:32 necessarily:1 checked:1 unitarity:1 unruh:1 indicate:5 1g:2 structures:3 williams:4 gives:18 exploring:1 inefficient:3 mostly:2 kirkpatrick:1 eliminates:1 representing:2 than:29 coefficients:2 wide:5 nanostructures:1 unfortunately:4 require:7 future:1 were:5 outcome:1 san:2 generality:1 correction:1 argument:6 mateo:1 say:6 weinfurter:1 any:15 sat:5 efficient:2 ideas:1 note:10 ideal:14 potential:6 harald:1 take:6 performance:4 strengths:1 begin:1 multiple:7 importantly:1 multiply:1 pages:8 especially:3 surprising:1 considered:7 average:28 managing:1 refining:1 typically:1 quantity:1 precise:2 shor:3 drastically:1 show:6 inconsistent:4 slot:1 feng:1 slow:2 ratio:4 proportion:2 karlin:1 only:30 explicitly:5 black:4 get:8 samuel:1 cannot:8 nearly:1 conjunction:2 prime:1 resource:1 summary:3 umesh:2 predicted:1 mapped:1 scott:1 vision:1 physically:3 violated:1 relative:7 namely:5 ignores:2 insoluble:4 violates:1 concern:1 fails:1 ways:5 review:4 definite:3 enough:6 between:7 jf2:3 jf1:9 checks:1 jobs:1 august:1 aii:1 jr:4 concentrate:1 jf:2 concentrated:8 realizable:5 many:30 region:12 according:1 expression:1 among:18 overview:1 poly:2 satisfaction:19 exploit:5 cancel:4 moreover:7 considering:6 configuration:1 capable:1 invert:1 mark:2 workshop:2 combined:2 crawford:2 andrew:3 observe:1 external:1 those:13 case:33 vecchi:1 policies:4 promising:1 situation:2 couples:1 canceled:1 technology:1 pruning:1 binary:7 different:25 formulations:1 same:25 html:1 constructed:1 investigated:1 closest:2 trivially:1 running:1 changing:1 minimize:1 severe:2 costs:1 solve:6 components:2 otherwise:2 ekert:2 polynomial:6 gates:2 being:1 when:24 toby:1 rest:1 aspect:1 heuristic:4 zoller:1 grouped:2 photons:1 except:2 improvement:10 priori:1 versa:1 real:2 aspects:3 around:3 repetitions:1 sums:1 test:8 using:28 execution:2 mod:1 patrick:1 either:6 diffusing:1 fv2:1 fv1:5 conditional:1 garey:1 specified:14 reasons:1 nonzero:2 provided:3 recorded:1 critical:1 decomposition:3 provides:4 unoptimized:1 measuring:1 power:1 seconds:1 manufactured:1 equivalent:3 symp:1 ratios:2 inherent:1 repeating:3 comparison:6 package:1 howard:1 acm:1 practical:2 greatly:2 johnston:1 processor:1 road:1 numerically:1 references:1 inverting:3 determine:6 artur:2 elementary:1 conceptually:3 log:15 prepare:1 removing:3 there:45 start:1 low:3 lot:1 complete:25 regard:1 sophisticated:1 october:1 applying:1 quantitatively:1 adriano:1 nogood:34 detailed:5 laird:1 taylor:2 ai:1 ak:6 aj:1 deep:1 general:19 examine:4 arises:1 ay:3 again:3 completeness:1 ideally:2 mathematica:2 storage:1 valid:1 mathematics:1 deviation:2 briefly:1 separate:1 includes:1 a0:1 important:10 peak:6 included:1 procrustes:1 curve:5 parallelism:2 dyer:1 decoherence:2 starting:5 original:3 represent:5 consider:13 pointing:1 lack:1 generalize:1 expressions:3 decisions:1 caveats:2 referring:1 program:2 stochastic:1 nodes:3 norm:2 amplitudes:6 worse:1 straightforward:2 very:13 sons:1 worst:11 decide:1 condition:3 steve:1 hamiltonian:1 issue:1 applicable:1 large:19 adjust:3 small:25 rate:3 design:2 displays:1 further:4 what:7 richard:5 sun:1 section:3 brief:1 version:3 method:33 contrast:1 full:3 component:1 ranges:1 operating:2 directions:1 november:1 observing:1 search:117 increments:1 allows:5 prior:2 amount:1 permutation:1 hogg:7 requiring:3 send:1 detecting:1 select:3 readily:4 takes:4 distinct:8 comparing:1 monotonically:1 taken:1 more:39 operators:2 tested:1 particular:12 known:1 coyote:1 producing:1 none:1 vladimir:1 science:4 remain:2 examined:2 indicating:3 morgan:1 strategies:1 f0:3 f1:7 compare:4 f3:1 share:1 states:34 unbiased:1 minimum:1 numbers:2 arise:1 information:3 processors:2 rather:11 clarke:1 zhang:2 unlucky:1 maps:5 occasionally:1 schultz:1 algebra:1 weaknesses:1 derived:2 mapping:44 tries:2 fi:1 evaluations:1 concentrating:1 rationalize:1 register:2 help:1 ith:1 september:1 major:2 trade:8 paper:3 through:6 its:24 roots:2 destructively:2 rapidly:2 solving:2 fruitful:1 systems:1 stephen:1 travelling:1 might:5 good:18 motivated:4 universality:1 framework:1 motivates:1 oxford:1 yu:2 easily:2 always:3 level:72 2e:3 2g:5 2b:1 found:9 2n:5 polynomially:6 2i:1 underconstrained:8 defects:3 energy:2 hard:21 idea:1 slowdown:1 expect:2 measurement:12 quantum:90 operation:6 beyond:3 really:1 ftp:1 item:3 robert:1 since:10 research:2 dominated:1 hill:1 evaluation:6 occurs:1 pub:1 difficulty:5 teach:1 generate:6 computers:17 positioning:1 exponentially:16 circuit:1 consequence:1 assign:1 singleton:2 probability:31 number:55 instances:10 done:4 construct:3 differ:1 introduction:2 leading:4 least:10 assumption:1 expand:1 calculations:1 molecular:1 parc:2 trapped:1 park:3 immediate:2 part:2 focusing:1 determines:3 double:2 recording:1 determined:6 motivation:1 seth:1 canceling:2 randomly:11 substantial:3 js1:1 concentration:9 paths:10 zero:6 depending:2 empirically:4 build:1 analogy:1 finding:3 added:2 jsn:1 reach:1 jsi:7 most:12 significant:1 probabilistic:2 clear:2 sometimes:1 physics:3 thomas:1 particularly:16 phenomenon:2 persists:1 minimizing:1 find:30 backtracking:4 dividing:2 bernstein:2 columns:6 intractable:1 notation:2 zurek:1 preparing:1 closely:1 combinations:2 critically:2 svozil:1 exhibiting:1 common:9 locating:1 scanning:1 bars:4 set:54 bart:2 backtrack:11 intelligence:16 see:11 individual:3 sec:1 close:12 11th:1 mechanically:1 currently:2 rejecting:1 won:1 various:8 conditions:1 available:1 recently:1 attention:5 rapid:2 distinguish:4 both:8 last:1 context:2 experimental:1 arbitrarily:1 point:14 simple:30 loan:1 corresponds:4 whatever:1 dimensional:3 simply:6 church:1 described:19 create:2 due:5 strategy:2 reduction:1 describes:3 extends:1 ph:1 empty:3 addison:1 generating:1 partly:2 samples:8 precision:3 else:1 understand:2 systematic:1 despite:1 p1:5 exponential:11 solid:8 straight:2 empirical:2 evaluated:6 b01:1 technical:2 while:15 optimization:4 evaluating:8 error:8 cheeseman:2 guide:2 computed:1 unitary:13 costly:1 hoping:1 laflamme:1 encountered:2 itself:3 bernardo:2 lengthy:1 sight:2 widely:1 higher:2 development:1 calculation:1 used:11 assignment:5 viewing:1 levels:7 uses:1 purpose:3 recent:4 lower:2 analysis:2 person:1 edge:1 machinery:1 consistency:4 2gi:4 competitive:1 questions:2 world:2 alternative:2 cut:1 conclusions:1 alternate:1 guaranteed:2 location:7 input:2 remaining:5 march:1 satisfiability:6 huberman:2 evaluate:5 tunnelling:1 matters:1 bit:6 like:3 imposed:2 follows:2 interestingly:1 ignore:1 continue:2 indication:4 exploiting:7 methods:36 some:29 back:1 understood:3 b0:1 examples:4 b2:3 gradually:1 scale:3 affects:1 decision:3 per:5 behave:2 eliminate:1 proc:10 bn:1 processing:1 bk:1 step:3 plots:3 propositional:6 superpositions:7 goods:14 anything:1 extending:1 simulation:4 range:13 extensions:3 consequently:1 repair:3 computational:9 into:13 within:2 integral:1 conjugates:1 appropriate:3 steven:1 proportional:1 clustering:1 classically:2 extremely:1 placing:1 question:11 lond:1 long:4 translate:1 vienna:1 larry:1 line:1 considerable:1 intuitive:1 up:8 ur:1 exploration:1 boldface:1 similar:6 called:2 constant:1 worthwhile:1 defined:2 doesn:7 single:17 defines:1 dashed:11 occasional:1 application:1 points:5 elements:1 korf:1 problems:147 polynomials:1 william:1 generated:3 allowing:3 vectors:10 structure:30 algorithm:51 vice:1 svd:3 required:13 implied:1 far:1 requires:6 having:3 evenly:1 code:1 partial:15 illustrates:1 results:13 existing:1 illustrated:1 proposition:1 go:1 adjustment:2 contributions:3 issues:3 concerned:2 factoring:5 excluded:1 include:2 resources:3 overlaps:1 unstructured:1 mixing:2 matrices:7 arrange:4 vavasis:2 severely:2 michael:1 colors:2 fewer:1 assignments:16 barbara:2 smaller:9 dynamics:3 giving:9 networks:1 3b:1 3g:2 focuses:1 lee:1 degree:1 respectively:8 gilles:1 desired:3 explore:1 others:1 levesque:2 consideration:7 extreme:1 great:2 parameters:2 receive:3 involved:3 gent:1 larger:13 suggests:8 resulting:12 implement:1 makes:6 involves:2 examining:4 scales:6 scaled:1 decrease:4 apply:4 use:19 asymptotic:4 remains:4 next:10 few:15 duplicate:1 becomes:1 occurred:1 normalized:2 informally:1 rare:5 high:5 frobenius:1 averaged:1 averages:1 control:1 prohibiting:1 process:4 purposes:1 tad:6 effectively:1 assumptions:1 intuitions:1 feynman:2 destroying:1 holds:2 instead:10 intelligent:1 sin:2 supersets:21 singular:2 collection:2 multiplication:1 minton:1 efficiently:3 realized:1 physical:15 computations:5 light:3 lines:4 correspond:5 element:4 encyclopedia:1 discussion:3 selman:2 produces:4 move:7 p1n:1 produced:2 including:1 mentioned:1 ln:9 choose:1 mitchell:2 pending:1 freeman:1 violating:2 wolfgang:1 practice:1 chronological:1 rotation:1 february:1 dirac:1 university:1 identified:1 sufficiently:2 magnitude:4 francisco:1 constraints:39 subset:5 map:24 doing:1 inverted:2 operator:2 fraction:1 computable:3 measure:1 our:3 transitions:18 salesman:1 special:4 out:7 fundamentally:1 rev:1 microscope:1 performs:1 approached:1 interactions:1 diagonal:3 hopkins:1 completely:3 conflicts:1 philip:1 jozsa:2 determining:3 could:17 keep:2 4th:1 hence:24 powerful:2 reaches:1 improvements:1 reached:3 ordering:2 behaves:2 system:6 their:13 intermediate:3 final:10 explanation:1 exactly:3 environmental:3 schweizer:1 simulate:1 prune:3 limiting:2 amplitude:47 exhibit:5 false:2 unchanged:1 curves:9 unlikely:2 need:11 constrained:5 linked:2 viewed:6 mappings:4 able:5 si:4 instance:6 device:5 intrinsic:1 class:18 kimber:2 url:1 proceedings:1 mechanical:2 fact:13 selection:11 charles:1 planning:1 chuang:1 lloyd:1 rough:1 coloring:3 based:7 knowledge:2 should:9 hector:2 smallest:1 ethan:2 employed:1 local:1 hope:1 means:6 overall:5 ones:4 exchanges:1 areas:1 gray:14 processes:3 optimally:1 contain:2 prosser:1 fixed:5 view:4 enhances:1 requirement:11 constructing:3 exists:1 edition:3 computer:18 closer:1 phases:31 exploited:2 attempting:1 pattern:1 tend:3 state:17 difficulties:1 closed:1 crude:1 neither:1 barenco:1 ability:2 importance:1 transpose:1 interfere:2 implementing:1 key:3 sleator:1 ket:2 problem:80 david:4 restrictions:1 limits:1 taking:1 equal:7 etc:1 figures:2 grounds:1 eigler:1 adjusted:1 relevant:1 unnormalized:1 conclude:1 ca:4 cirac:1 respect:7 addition:6 discrimination:1 copies:1 yao:1 proposal:1 define:1 describe:2 corresponding:11 scalars:1 sufficient:1 coherence:6 subspace:1 essentially:2 tycho:1 backtracks:1 subsets:15 harder:2 value:16 choices:22 will:47 examines:1 almost:2 thus:35 hardware:5 vs:3 perhaps:4 cross:1 eric:1 matches:1 strange:1 cerny:1 gets:1 difficult:10 infinity:1 solved:1 effect:4 v1:5 v2:9 identity:1 off:7 center:1 nevertheless:1 well:14 baltimore:1 sets:87 usual:1 less:10 obtain:7 underlying:1 predicts:1 paul:1 overconstrained:6 web:1 superset:2 preprint:3 smith:2 capabilities:3 lattice:46 add:3 combine:1 natl:3 increased:1 increases:2 press:8 immediately:2 variants:2 necessary:9 helpful:1 sizes:6 alternatively:2 3sat:6 martin:1 become:2 page:1 factorially:1 poor:2 shed:1 because:17 qed:1 classical:37 njk:1 phenomena:1 constructively:1 growth:2 peter:4 orthonormal:5 lead:6 avoid:3 overlap:5 does:7 assuming:1 noise:4 reaching:1 selecting:7 wesley:1 although:5 analyses:4 simpler:1 about:6 actual:1 extension:1 getting:1 column:4 freedom:1 recognized:3 simplification:1 introduced:4 equally:2 letters:3 previously:2 h1:2 van:1 additional:10 restricts:1 quadratic:1 inner:1 function:6 philips:1 xerox:4 but:32 hu:1 repeated:2 construction:3 contradictory:1 goals:1 made:6 compute:5 evident:1 society:1 whether:12 below:11 converted:1 limit:5 distribution:1 mechanics:5 recognize:1 universal:4 contribute:2 denote:3 periods:1 proceeds:1 functions:1 compared:5 variety:6 trials:4 other:24 details:1 stat:1 repeat:1 ultimately:1 variation:4 chance:3 disjunction:1 matrix:22 searches:2 coupling:1 baker:1 rule:1 gelatt:1 4g:4
|
quant-ph9508013.txt |@word gw:2 alm:2 sci:1 consider:21 εq:1 eaires:1 global:1 results:14 leads:2 sαj:3 scalar:8 proposition:22 generalize:1 computation:2 kato:1 consists:5 gk:1 c2m:2 gh:1 devoted:1 whose:3 terms:3 aug:1 m2m:2 paris:3 subjected:2 technique:1 tr:70 ajj:1 tp:3 preprint:1 accordingly:2 finally:10 does:1 present:1 th:4 under:6 tr1:3 analogous:1 un:1 tb:1 norm:1 encircle:1 labels:1 deforming:1 verbeure:1 advantage:1 orthogonal:1 very:3 eσ0:3 springer:2 seemingly:1 choice:5 corollary:5 crosses:1 every:1 microlocal:1 eφ:1 little:1 matrices:2 condition:10 four:1 trj:3 specify:1 schwarz:3 level:30 altering:1 suffices:1 ramond:1 list:1 solution:15 d2:1 t1:9 large:2 mm:2 convenience:1 multiplicities:1 math:6 succession:1 small:32 eigenvalues:45 anal:1 noted:1 degeneracy:6 upper:3 too:1 work:3 neighborhood:4 decompositions:1 dealing:1 requirements:1 estimates:12 direct:7 approximation:1 located:3 second:7 displays:2 go:1 pass:1 rigorous:3 further:10 estimated:2 columns:1 linear:6 even:1 index:9 what:2 appear:1 invertible:3 incompatible:1 diag:3 section:17 foregoing:2 uniform:2 looking:1 version:1 above:40 sup:18 new:3 construction:6 tunnel:1 method:5 contrast:1 satisfy:18 compact:1 notions:1 respectively:7 never:1 component:1 proc:1 here:3 erentiel:1 les:1 elser:1 making:2 directions:1 path:29 along:24 equations:6 2kj:1 deduced:4 obtained:15 great:1 hamiltonian:1 suitably:1 technical:1 oman:2 study:13 vectors:2 allows:3 h2:8 zener:4 sjj:4 sjk:10 accomplished:1 simultaneous:1 resulting:2 explicited:1 lifted:1 permutation:9 eigenprojectors:5 hospitality:1 ikα:1 suitable:3 makes:1 uniquely:1 boundedness:1 being:3 followed:2 homotopic:1 bounds:1 requiring:1 plenum:1 limt:1 replace:2 r2m:1 finiteness:1 univ:1 planck:1 linearly:1 readily:3 collisions:1 use:7 asymptotic:25 working:1 prove:8 distinct:13 positive:4 give:4 uniformly:10 negative:2 eσ:4 next:4 ψj:5 calculation:2 going:4 call:1 therefore:1 m3:2 m2:1 taken:1 until:2 more:8 introducing:3 zh:1 ir:7 degeneracies:9 successful:1 initial:5 operators:1 factor:2 odinger:11 bold:1 appendix:2 controlling:1 observations:1 particular:7 known:4 cases:6 hold:1 iii:10 circumstances:1 logarithm:1 couples:2 keeping:1 valued:7 defines:2 deformed:1 recall:1 equation:31 mn:14 dokl:1 pour:2 ρn:2 perturb:1 ch1:2 ch2:2 minimum:1 values:3 inferior:1 following:6 fulfill:1 closing:2 trans:1 root:1 example:4 proof:15 f1:6 f2:4 impose:1 renormalization:4 figure:20 stated:2 process:2 permutations:1 carroll:2 purposes:1 eσj:8 states:2 successively:1 assumptions:2 performed:3 degenerate:5 sense:3 amplitudes:1 axis:43 normalize:1 information:3 end:2 goal:1 thing:1 rather:2 verify:2 discussion:1 get:40 edts:1 write:3 how:4 continued:6 cst:1 ordinary:2 νj:2 parameter:3 h5:9 fr:3 comparison:1 blocks:3 singular:6 may:15 max:7 ζj:10 earlier:3 derived:4 containing:1 consequence:10 ζr:7 plane:13 meso:1 compacts:1 ff:3 vertically:1 fits:1 twofold:1 wave:3 transmission:2 constants:2 iθj:9 iθk:2 drop:1 branches:1 imply:2 computations:1 lines:6 correspond:1 parameterized:2 element:9 hypotheses:4 sj:3 spectral:1 ones:1 so:28 expression:1 rellich:1 decreasing:3 taking:1 representation:2 increase:1 solov:1 order:2 ec:1 xj:5 iεk:1 holds:2 interpretation:1 deform:2 proceedings:1 considerations:1 indeed:5 insight:1 encounter:1 satisfied:7 iγ2:4 course:1 paper:10 london:1 banach:1 mentioned:1 existence:8 satisfies:14 pj1:5 its:7 pj2:1 gamkrelidze:1 superior:1 derive:1 group:1 thank:1 fit:1 la:1 energies:1 interesting:1 sα:83 lm:1 vicinity:1 exhibits:1 actually:3 resorting:1 continuations:13 absence:1 parts:1 systems:21 h3:8 mail:1 main:11 defining:2 h0:2 emphasize:1 correspondence:1 non:12 return:1 contributions:1 s12:10 regarding:3 introduce:6 landau:4 mention:1 leuven:1 h4:6 they:7 instead:2 sσ:5 now:15 pjq:5 ζk:15 possess:7 eigenvalue:13 term:1 finite:5 hereafter:1 always:5 reasonably:1 presented:4 loosely:1 asymptotique:1 sufficiently:4 mastered:1 2b:6 each:11 crossing:13 found:4 universit:3 usp:1 reproducing:1 subset:1 el:6 domain:13 differential:6 ei:11 determine:2 ek:73 ej:125 t2:5 energy:1 sov:2 product:8 related:2 society:1 literature:1 computable:1 histories:1 reached:1 quantum:6 relates:1 avoided:21 martinez:1 er:1 shown:5 matrix:60 rs:3 types:1 since:19 rev:1 denotes:10 content:1 re:44 contained:1 ajk:6 hwang:1 denoted:3 formula:13 postpone:2 induction:1 integrated:1 rj:6 shows:3 provide:1 theory:10 barrier:1 state:1 singularities:4 diagonal:7 free:1 standard:1 difficulty:1 approaches:1 necessarily:2 york:3 besides:1 edouard:1 consequences:2 estimate:14 e1:11 e3:3 e2:9 definition:8 perform:4 kept:1 r1:6 applications:4 kunz:1 similarly:7 keep:2 turn:7 american:1 levels:5 place:7 exponentially:10 barriers:2 uses:1 adjoint:6 βj:3 first:14 origin:8 xk:5 major:1 already:1 designed:1 meas:1 symmetry:7 xm:1 describes:5 variables:1 powerful:1 number:2 reaches:1 exact:2 jp1:2 relations:1 another:3 indices:18 precisely:3 open:2 ser:1 given:21 perturbation:8 checked:2 rewritten:1 gpj:1 their:4 introduction:1 unknown:1 crossings:24 system:3 least:3 γjk:3 intermediate:1 encyclopaedia:1 expand:2 convention:2 dt2:1 bound:2 john:1 behaved:1 final:2 speaking:1 denominators:1 numbered:1 moscou:1 continuous:5 s31:3 took:1 s33:2 s32:1 sciences:1 assumption:7 part:13 favorable:1 space:1 off:7 dissipativity:2 than:1 coefficients:10 wide:4 third:1 require:1 demkov:1 see:32 limiting:1 lim:19 determined:1 kth:1 macro:1 thumb:1 tackled:1 negatively:9 rate:1 perturbative:1 behaviors:1 lowest:1 symmetries:6 generality:1 rewrite:2 explicit:4 landauzener:1 mind:1 spectrum:14 generalization:4 lin:1 multivalued:15 fannes:1 need:2 any:25 paths:7 gϕ:1 strength:1 insures:1 zero:2 min:19 studying:1 latter:1 able:2 isolated:5 note:12 k2:1 k1:4 potential:2 take:6 εe:2 green:1 coincide:1 concern:2 channel:1 εb:1 cl:3 formulas:10 experienced:1 multiple:1 γj:3 centre:1 δkj:2 liouville:1 accurately:1 extending:1 attempt:1 experiences:2 pleasure:1 reducible:1 analytically:6 class:5 branching:2 constructed:5 takes:2 neighborhoods:1 considered:2 kj:13 clear:1 later:2 coincides:1 km:6 mrs:1 kr:2 kq:6 points:20 verlag:2 principle:3 exp:1 left:1 physics:3 χj:3 fact:9 quantity:3 precise:1 saying:1 incoming:1 show:6 charles:1 ending:1 notations:5 xl:3 spaces:2 relation:7 solutions:2 βk:1 substituting:1 tend:4 trivial:2 enjoyed:1 principal:1 multichannel:5 symmetric:3 fine:1 based:10 situations:1 explain:1 enough:22 should:7 analytic:65 only:10 explicitly:1 generators:8 positively:3 developed:1 integrable:2 constant:6 local:1 resp:5 achieve:1 probabilities:2 continuity:2 do:3 loss:1 dj:35 goes:1 notation:5 means:12 dependent:6 de:9 joint:2 cannot:2 dz:25 ϕk:10 ϕj:62 applying:1 dt:17 du:13 ds:3 ostrand:1 holland:1 prime:2 evolution:3 exhibiting:1 arxiv:1 expansions:1 yield:1 acknowledgments:1 instance:1 e1j:3 hioe:2 fixed:6 krein:1 approximations:1 superadiabatic:1 preserve:1 corrections:1 set:26 computed:8 exists:17 achieved:1 gψ:1 δjk:9 δjl:1 transition:6 maximum:1 relative:4 depends:3 lausanne:1 result:13 discussions:1 close:6 probability:1 techniques:3 closes:1 phases:1 satisfying:3 inequalities:2 enlightening:1 nondegenerate:2 pattern:6 review:1 siam:1 justifies:2 diverge:1 kj2:1 behind:1 difficulties:1 various:1 nonadiabatic:1 jwkb:1 between:9 ele:1 luminy:1 before:1 conditions:14 joye:8 choose:5 gives:1 recently:3 olver:1 vertical:2 effet:1 garde:1 jw:3 however:12 jr:22 strictly:1 beyond:1 hypothesis:5 jointly:1 key:1 jk:60 analyzed:1 monotonicity:1 come:5 improve:2 suggested:1 both:4 essentially:3 stationnary:1 last:3 reverse:1 limits:5 0z:2 many:1 region:2 decay:5 hence:17 acknowledged:1 called:7 fulfilled:1 chosen:2 connection:1 iv:3 berry:1 context:5 forgotten:1 σr:3 summarizing:1 adapted:1 ll:1 ck:12 cj:29 relevant:3 cn:8 cm:6 point:22 simple:2 continuation:22 aspect:2 asymptotically:8 height:1 dimensional:3 assertions:1 right:2 away:1 moreover:9 cq:1 fruitful:1 diff:1 iβj:1 traveling:1 considering:1 applies:1 described:9 basis:4 equivalent:6 z0:16 claiming:1 due:8 cauchy:2 asymptotics:2 interest:3 basic:2 pj:37 pk:2 ph:2 ann:1 dk:1 define:14 θj:3 θk:1 controlled:1 σj:5 quantities:4 sufficient:5 remark:6 argument:4 maps:1 vue:1 determination:2 curves:2 derivative:4 c2:2 c1:2 denote:8 irrelevant:1 spirit:3 those:4 case:14 encircles:7 look:1 exponential:7 checking:1 choices:1 will:3 cast:1 philos:1 replaced:3 monodromy:1 behavior:8 error:3 wiley:1 situation:4 property:6 couplings:1 loop:20 inherits:1 identical:1 unitary:2 find:1 geometric:1 vol:2 metric:2 wkb:7 thus:16 them:2 repeating:1 encountered:2 ii:8 intertwining:1 im:36 experience:1 nenciu:2 asymptotiques:1 different:3 moves:1 verified:5 generic:2 identities:1 make:2 cross:1 same:15 dγ:1 4b:2 iα:1 complex:21 quant:1 arguments:1 invariant:1 products:1 proved:1 several:4 composition:1 difficult:7 smallest:2 independent:2 used:7 infinity:3 sjl:1 sequel:1 akl:8 jkp:4 nj:4 hand:2 pechukas:1 domains:22 compared:1 want:1 potentials:3 infinite:1 jp2:5 cr:12 adopting:1 identity:11 recent:2 eigenvectors:19 lower:1 task:1 schr:10 proceed:2 framework:3 k22:1 whole:1 substantially:1 depending:1 well:9 roughly:1 analysis:8 s22:9 patterns:1 without:3 machinery:1 components:1 sets:3 exponentials:1 model:2 self:5 usual:2 ordinaires:1 construct:1 just:4 formulation:1 physique:2 accurate:1 half:3 rest:1 atomic:1 unifies:1 integer:1 useful:3 alternative:1 scattering:11 previous:2 oriented:10 conjugates:2 νr:5 generator:14 omit:1 yu:1 conclude:1 toulon:1 improvement:2 enjoys:1 other:6 treatment:1 easy:1 theorem:5 unitarity:2 heidelberg:2 skj:1 real:60 iθ:1 inelastic:1 around:10 easily:4 dissipative:50 pσ0:2 iε:6 possible:11 threelevel:1 eorique:2 ethodes:1 know:1 using:14 edt:1 unique:1 mod:1 meaning:1 semiclassical:8 mir:1 necessary:2 like:1 semi:4 follows:18 adiabatic:18 specific:4 yields:10 either:1 martin:1 recalls:1 starred:1 unperturbed:2 stationary:3 depend:2 mathematical:3 formulae:1 because:4 often:3 classical:5 discrete:1 successfully:2 some:24 back:7 understood:3 deduce:8 repeat:1 acad:1 examples:2 rise:1 respect:8 proper:1 proofs:1 happens:2 provided:10 indefinite:5 erentielles:1 lead:3 micro:1 resonances:1 shall:1 integration:6 per:2 providence:1 ese:1 behave:1 select:1 expressing:1 assuming:1 straightforward:1 demonstrated:1 gjk:4 inserting:2 conference:1 ba:2 s13:4 june:1 s11:8 2c:2 agreement:1 step:2 2m:4 epfl:1 imaginary:1 possesses:1 properties:22 projector:1 stokes:3 actual:1 uniformity:1 most:1 column:4 commun:2 discussed:2 factors:3 o:70 assertion:2 remains:5 extensions:1 soc:2 nord:2 introduced:1 consequently:5 projectors:3 block:3 therein:1 perturbed:4 contains:1 previously:1 reflexion:3 into:5 h1:8 integral:4 ηj:18 encircling:3 three:8 down:1 remarks:4 en:5 references:3 eqj:3 lemma:39 strip:3 proportional:1 prefactors:1 mere:1 riemann:1 k12:1 rows:1 institut:1 deal:4 remain:3 assumed:7 justifying:1 there:25 lond:1 noticed:2 start:3 quote:1 s23:5 structure:3 way:3 var:1 exceptional:4 was:4 naturally:2 function:7 north:1 complete:2 form:2 hp:5 hq:2 alain:1 but:9 hj:6 cedex:2 properly:1 link:1 eigenprojections:1 line:1 ρj:7 true:8 borders:1 made:3 compute:4 improved:3 pσ:2 whether:1 irα:16 inside:1 up:8 us:13 s21:7 below:20 convince:2 limit:12 verification:1 uj:8 locally:1 problem:8 marseille:3 similar:7 display:3 eigenvector:1 separately:1 jj:1 definitions:1 associated:21 links:4 defined:17 certain:6 abstract:1 describe:1 linearity:1 verifies:1 proven:4 general:9 globally:1 loops:5 single:7 invertibility:1 exist:12 rule:1 our:10 orders:1 corresponding:15 inf:13 kl:4 pfister:6 check:5 physical:1 again:1 functions:12 transitions:8 analyticity:8 differentiable:3 integrability:1 no:8 whereas:5 when:29 vanishes:1 reality:1 application:8 valid:3 concerning:1 ev:1 briefly:2 elements:17 snn:1 oneself:2 remainders:2 extra:1 symbol:1 remarked:1 problems:1 chem:1 occurred:1 ξj:2 important:3 individual:3 allowing:1 establish:1 variable:1 generalized:1 gap:1 cσ0:1 implies:2 coupling:1 assume:8 starting:2 required:2 berlin:2 together:6 roy:2 time:6 far:1 cpt:2 4c:1 once:2
|
quant-ph9508014.txt |@word represent:2 since:2 consider:4 similarity:1 results:11 leads:2 concept:1 overlap:1 go:2 certainly:1 violate:1 aug:1 irrelevant:1 behave:2 device:2 tk:2 under:1 analogous:2 circumstances:1 p2:1 straightforward:1 far:1 choice:1 englert:2 electron:7 difference:3 condition:6 immediately:1 presented:1 positions:17 t2:2 solution:4 occurs:2 large:3 discrete:1 vector:2 phase:1 dealt:1 small:6 speculation:1 noted:3 solutions:1 strongly:2 force:4 ten:1 consistent:2 d3:2 prediction:2 second:5 cost:1 value:3 further:1 theories:5 substitute:1 even:4 what:3 sub:1 giving:3 section:2 agrees:2 current:1 experiment:8 3n:1 above:1 new:3 ever:1 method:1 satisfy:2 evolving:1 degree:1 respectively:1 modify:1 here:8 agreement:1 behaviour:1 objects:1 possibility:2 separation:1 indeterminism:1 equations:4 implicit:1 derivable:1 great:1 receive:1 study:2 studied:1 allows:1 mx:2 suggests:2 simultaneous:1 walther:1 poisson:1 opinion:1 changes:2 numerical:1 genuinely:1 via:1 projection:1 logical:1 outcomes:2 hardy:7 durham:2 stern:1 select:1 use:6 would:12 ψr:7 positive:5 predictions:9 next:2 comparing:1 squires:18 ψl:11 typical:2 taken:1 3le:1 type:1 more:2 sort:1 introducing:1 formally:1 becomes:6 ti:3 odinger:2 particular:5 foundations:4 cases:1 ouput:1 must:5 none:1 rotational:1 integrating:1 recall:2 equation:16 work:1 mi:8 mj:1 reviews:1 remain:1 obvious:2 ρx:2 my:1 example:11 something:2 compare:2 cosmological:1 give:11 calculation:1 relativistic:5 arise:1 neglected:2 accept:1 states:1 trieste:1 lorentz:6 dxj:1 sense:3 unphysical:1 times:4 hydrogen:1 absolute:1 information:1 end:1 rather:3 discussion:2 write:1 very:1 opposite:1 significance:1 explains:1 2v:5 simplicity:1 description:1 may:2 after:3 derived:2 φr:2 consequence:1 wrong:5 designed:1 records:2 law:5 curing:1 yψ:2 complimentary:1 natural:2 effective:1 light:2 appreciate:1 correspond:1 cosmology:3 their:1 dispositions:1 so:11 allow:2 order:3 travel:2 integrated:1 interpretation:1 ith:1 indeed:1 over:1 move:3 satisfied:1 produced:1 course:9 xi:2 looks:1 statistical:3 responsive:1 pointer:1 its:5 before:2 derive:1 xl:9 how:7 interesting:2 scully:1 actually:2 better:1 detected:2 microscopic:1 hidden:6 might:2 variables:2 fool:1 non:14 good:1 affected:1 greater:1 orthodox:3 press:1 evolution:1 break:1 avoids:1 effects:1 they:6 half:1 own:1 now:4 discuss:1 2t:7 easily:1 term:2 electrostatic:1 respectable:1 goldstein:2 always:2 university:1 hamiltonian:1 annals:1 2y:2 d3n:2 realistic:7 magnitude:1 reasonable:1 2l:1 2m:1 went:1 2j:2 domain:1 differential:1 england:1 there:16 energy:2 idea:1 related:1 books:1 expect:1 measurement:4 quantum:46 relates:1 t1:2 eq:17 special:2 out:2 space:4 dewitt:2 cancels:1 particles:10 acting:1 m2j:1 formula:1 issue:1 correct:5 shows:2 realisation:1 working:1 theory:30 given:7 free:3 standard:4 difficulty:1 completely:2 york:1 imagine:1 put:2 inevitable:1 definition:1 interaction:1 derivation:1 reparameterisation:1 could:2 david:1 motion:3 assumed:1 hence:5 neglect:2 first:4 origin:2 xk:1 valentini:2 features:2 probability:4 ignored:1 wave:7 number:1 simplified:1 directly:3 xr:4 sounds:1 precisely:1 size:1 city:1 little:1 grangier:2 similarly:1 leading:2 ci:5 system:1 least:1 encourages:1 observations:3 calculations:1 final:1 gives:6 cope:1 academy:1 explanation:1 exactly:4 part:2 x2:2 x1:2 than:3 detection:1 level:1 penrose:1 require:2 zero:12 submitted:1 future:2 outcome:4 function:2 sees:1 explicit:2 correction:1 modern:1 few:1 peculiar:1 say:2 unlikely:1 greenberger:1 need:4 seen:1 seem:1 confirms:1 apparently:1 clearly:9 newtonian:3 efficient:1 pa:1 latter:1 able:2 gravity:3 note:7 sciences:2 potential:12 absorbed:1 take:4 forces:2 neither:3 lhs:1 detector:24 unremarkable:1 differences:2 fundamental:2 shall:3 rhs:2 most:1 detect:1 significant:3 remarks:1 analytically:1 measured:1 why:2 probes:1 deviations:1 especially:1 clear:6 later:1 detectors:9 optical:1 sciama:1 principle:1 urr:2 velocity:8 left:5 physics:14 fact:9 1982b:1 called:1 emerging:1 show:1 violation:1 text:1 gerlach:1 carefully:1 analogue:2 trivial:1 find:4 ground:1 completion:1 knowledge:1 distributed:1 written:1 should:4 values:4 dalibard:1 only:6 version:1 adequate:1 isham:1 local:5 equilibrium:1 continuity:1 do:4 goes:1 notation:1 means:4 dependent:1 between:5 preferred:1 xdt:1 words:1 2mj:1 dye:2 dt:5 boundary:2 reveal:1 processes:1 podolsky:1 arxiv:1 experiments:5 roger:3 contain:2 approximations:1 approaching:1 reveals:3 vink:2 predicts:2 exists:2 imposing:1 frame:3 correlations:1 packet:1 observed:2 see:12 individual:1 merits:1 result:5 discussions:1 theoretic:1 acquires:1 fails:1 said:1 inequalities:2 b369:1 nuclear:1 review:4 state:5 determined:2 simplest:2 invariant:5 justified:1 conditions:3 timevarying:1 available:1 terms:1 debroglie:1 nature:2 initially:2 emitted:2 however:9 p2j:1 extent:1 configuration:2 come:1 problem:6 suggested:1 both:4 essentially:1 x2i:1 many:1 uncertainty:1 equal:4 laplace:1 hψ:2 present:1 context:1 retarded:8 expression:3 photons:2 experimental:4 grounds:1 generalisation:1 presumably:1 1982a:2 bell:8 simple:6 aspect:5 others:1 dimensional:1 simply:1 boson:1 occuring:1 late:1 ensures:1 pt:1 addition:3 trajectory:1 been:4 much:2 treat:2 interest:1 expected:4 ph:1 pi:6 pl:2 define:2 direction:2 quantities:1 wheeler:2 photon:23 requires:2 zeilinger:1 bohmian:5 tentative:1 last:1 general:2 spin:3 travelling:1 those:3 pilot:1 case:6 explicitly:1 underdetermined:1 unlike:2 defining:1 evaluated:1 fapp:1 will:19 suppose:4 evaluating:1 situation:2 procedure:2 nonrelativistic:1 detailed:1 vectors:2 almost:1 thus:6 surface:1 according:4 itself:3 cone:1 fermion:1 different:1 doctor:1 perhaps:1 suggest:2 thesis:1 problems:1 same:2 any:9 complex:1 quant:1 arguments:1 largest:1 modification:1 φl:3 events:2 conflict:1 independent:4 emphasise:1 used:2 infinity:2 solved:1 trivially:1 trajectories:6 upon:1 hand:3 v0:17 moment:1 moving:3 purpose:1 invariance:4 schr:2 whereby:1 framework:1 nevertheless:2 locality:5 well:3 analysis:3 bohm:30 without:2 solve:2 comes:1 position:7 model:35 otherwise:1 dimension:1 dh1:1 justify:1 just:1 less:1 being:3 rosen:1 newton:3 obtain:4 sources:2 underlying:2 atomic:1 contextuality:2 world:2 macroscopic:1 previous:1 adding:1 unique:1 preprint:1 density:2 regarded:1 point:2 reasons:1 spread:1 treatment:1 innocent:1 theorem:2 guarantees:1 eigenstate:1 momentum:5 real:3 tests:3 aspects:1 analogy:1 depends:1 2u:4 rules:1 replaced:1 disagreement:1 possible:6 test:1 dewdney:2 know:2 confined:1 using:3 replace:2 similiar:1 necessary:3 particle:8 follows:1 sissa:1 velocities:4 ignore:1 private:1 continue:1 steps:1 either:1 arbitrary:2 rearrangement:1 accelerations:1 stationary:2 essential:2 mathematical:1 because:5 wavepackets:1 classical:14 some:10 metres:2 exposes:1 born:1 deduce:1 towards:1 escape:1 proper:2 happens:1 provided:1 proceeding:2 sufficiently:2 measurements:5 comments:1 everything:1 does:2 yields:1 demonstrated:1 refer:1 inserting:1 performed:1 a168:1 journal:1 wavefunctions:1 combines:1 clarendon:1 step:1 nowhere:1 although:3 ontology:1 properties:1 refuge:1 comparison:2 about:6 actual:4 carried:1 extension:1 constraint:1 universe:7 theorems:1 discussed:2 dependence:1 o:1 plus:1 act:1 introduced:2 automatically:1 op:2 seeing:1 equally:1 localised:1 letters:10 presence:3 communication:1 into:2 within:4 clifton:2 bound:1 negative:5 eqs:4 nothing:1 appropriate:1 right:3 references:1 determine:2 einstein:1 operator:2 additions:1 unambiguous:1 additional:2 interacted:1 removing:1 strictly:1 initial:10 question:1 u0:13 long:1 recognised:1 physicists:1 way:2 ed:2 was:2 lowest:1 complete:1 form:8 phenomena:1 regard:1 gedankenexperiment:1 but:9 gaussian:1 volume:1 failure:1 atom:1 removed:1 true:3 oxford:1 observation:1 evident:2 versions:1 characteristic:1 up:2 us:1 ur:1 record:4 below:5 frequency:1 naturforschung:1 distribution:7 similar:3 agree:4 distance:1 mechanics:18 units:2 constant:6 defined:2 certain:2 denote:1 single:1 together:2 violated:1 our:2 moves:1 distributions:1 physical:4 incorrect:1 again:3 47a:1 no:5 agreeing:2 wavefunction:14 when:5 reality:1 field:2 other:13 role:1 spatial:1 department:1 conclusion:1 exp:13 separate:1 models:1 convincing:1 important:2 variable:4 describing:1 needed:1 independently:1 assume:1 normally:2 required:3 packets:5 rule:2 observe:1 mass:3 incomplete:2 time:17 backward:1 starting:1 restored:1
|
quant-ph9508015.txt |@word beckers:1 consider:6 rev:13 magnetic:2 particular:2 dynamic:1 results:4 four:4 expressions:1 4n2:1 bars:1 dimensionality:1 aug:1 combined:2 presents:1 finally:3 present:1 under:2 anharmonic:13 fermionic:4 applied:2 conjecture:1 straightforward:1 orthogonal:1 far:1 edn:6 b188:1 connects:1 wave:4 electron:10 witten:1 redefinition:1 specific:1 nieto:7 difference:1 exact:14 presented:2 ref:12 large:1 convenience:1 small:1 eigenvalues:4 noted:1 upper:1 approximation:2 zero:5 further:2 odd:2 linear:1 even:3 what:2 appear:5 brackets:1 giving:1 fine:1 section:10 ory:1 expressed:1 axial:3 experiment:2 establishes:3 new:2 change:1 method:2 filled:2 body:2 degree:1 50th:2 respectively:1 orbitals:11 atoms:14 desired:2 cylindrical:1 separation:4 equations:3 appears:5 χnl:2 obtained:4 generalizing:1 ac02:1 vbd:4 shift:4 leaves:1 studied:1 suggests:2 periodic:5 resulting:2 published:1 bob:1 suitable:7 makes:1 honor:1 jackiw:1 appropriately:1 via:1 useful:1 clark:1 extra:2 vii:1 plenum:1 modifying:1 vols:1 redefining:2 research:1 unit:3 franco:3 remains:1 contains:1 charge:1 next:4 nucl:2 pollock:1 therefore:2 taken:1 indiana:2 associated:1 type:4 more:8 separated:1 becomes:4 operators:3 stable:1 odinger:3 interaction:2 separates:1 known:1 balantekin:1 analogous:2 must:4 involve:1 valued:1 permits:2 science:1 equation:16 work:1 oscillator:30 modified:5 theories:1 mv:1 values:6 splittings:1 example:8 numbers:4 ions:3 chosen:1 process:1 introduces:1 inaccessible:1 neglected:1 purposes:1 states:5 effectively:2 attain:1 degenerate:4 hydrogen:6 evidently:1 information:2 united:1 invoke:1 rather:2 discussion:2 acts:1 eigenenergies:1 write:1 maps:5 ordinary:1 parameter:4 circular:1 map:9 samuel:1 description:3 a370:1 may:2 zimmerman:1 oscillators:10 stuart:1 space:1 dx2:1 sven:1 birthday:2 features:1 mag:1 choice:2 data:1 realized:1 discusses:1 physical:7 sectors:1 spectra:1 lines:1 yielding:1 element:1 their:1 provide:4 si:2 ones:1 so:7 specifying:1 allow:1 enter:1 representation:2 realizing:1 ege:1 breaking:6 interpretation:3 despite:1 interpreted:3 symbols:1 paper:5 including:2 looks:1 motions:2 iachello:4 differs:1 existence:2 y2:10 its:1 before:4 rapidly:2 thank:1 sodium:2 ln:9 zˆ:1 solving:1 coordinates:4 li:1 forms:1 absence:1 complex:1 systems:2 supersymmetry:34 correspondence:1 non:1 good:2 coworkers:1 thereby:1 was:2 washington:1 outlined:3 practice:1 number:4 break:1 modification:1 effects:4 they:1 half:2 multidimensional:2 now:3 discuss:1 nos:1 eigenvalue:2 term:7 2p:1 2r:7 2s:1 university:2 level:2 radiat:1 orthonormal:2 realistic:2 trap:9 reasonable:1 each:2 2l:8 found:4 2n:6 quarter:1 2i:3 referred:1 homogeneous:1 en:5 successively:1 another:1 kleppner:1 simplicity:5 short:1 series:1 energy:13 related:2 eb:1 celebrating:1 frequency:7 connect:2 measure:1 quantum:33 differ:1 eq:11 special:1 out:3 adduced:1 shown:1 unbound:1 matrix:2 factors:3 restricted:1 robert:1 since:3 induces:1 detailed:1 denotes:1 particles:5 contained:2 characteristic:1 denoted:2 formula:2 rn:3 issue:2 reformulation:3 theory:10 interactions:5 given:18 mapping:6 admits:1 approaches:1 proportionality:2 york:1 md2:1 generate:1 definition:1 pairs:1 qj:3 could:1 transition:3 motion:6 turn:1 transfer:1 hence:1 first:3 there:5 parastatistics:1 symmetry:4 laguerre:4 rydberg:2 relate:1 variables:1 disregarded:3 clear:1 done:1 least:1 quadrupole:2 semiempirical:1 ibid:2 angular:7 size:1 1s:4 gpo:1 oneparameter:1 likely:1 similarly:1 introduction:1 leading:1 eqs:1 system:6 relations:2 needed:3 returns:1 calculations:2 realization:5 unbroken:1 gives:1 shifted:1 onedimensional:1 trapped:3 akad:1 alan:2 part:7 than:6 begins:2 relative:1 effective:3 prevent:1 double:1 second:2 recovered:2 represents:2 naturally:1 treated:2 symmetries:2 generality:1 occupies:1 defect:11 generalization:1 manner:1 bound:1 constrained:1 linked:2 viewed:4 elsewhere:1 generalizes:1 anharmonicity:2 latter:1 note:3 instance:1 potential:3 absorbed:1 generalized:1 analogy:1 finding:2 utrecht:1 play:1 aspen:1 electric:1 normal:1 most:1 involving:3 connected:1 pleasure:1 measured:1 trapping:1 volume:1 especially:1 considered:1 calculated:2 later:1 metal:5 physica:1 order:1 wiese:1 electrons:3 principle:5 exp:6 mechanical:3 link:1 charged:1 physics:5 notion:1 fact:1 quantity:1 sector:2 festschrift:1 show:2 eigenspectrum:3 cdn:3 supported:1 discovered:1 defects:2 solutions:4 participate:1 earth:1 superalgebra:3 d2:8 ground:7 q1:2 partners:2 based:3 parameters:1 eigenspace:1 situations:1 inserted:2 state:7 elucidated:1 should:3 only:3 explicitly:2 generators:2 parabolic:1 invokes:1 hamiltonians:7 dn:1 his:2 dominant:1 above:5 notation:1 means:3 contracts:1 simplest:2 cannot:1 dx:1 dy:5 combinations:1 du:1 him:1 thus:1 increasing:1 de:2 continuum:2 conditions:1 arxiv:1 summary:2 mapped:1 analytical:14 qk:1 fixed:5 satisfy:1 requirement:2 set:4 ser:1 electrodes:1 notational:1 physically:2 δjk:1 connections:6 see:4 electrostatic:2 cyclotron:3 paul:1 incorporating:2 subject:1 said:1 eigenfunctions:12 subsequent:1 review:1 missing:1 rod:1 written:2 identification:1 correctly:1 between:17 ωm:1 ωz:2 approach:1 across:1 notice:1 terms:8 reproduced:1 nature:1 analogues:1 however:2 untouched:1 vanishing:2 here:13 hydrogenic:3 modeling:2 configuration:1 sketch:1 ωc:2 restrictions:1 piece:1 brown:1 reinterpreted:1 many:1 according:2 agree:1 energies:1 connection:5 ramsey:1 context:1 distinction:1 contribution:1 expression:3 experimental:2 among:1 relevant:2 fields:3 simple:2 harmonic:13 wen:1 dimensional:8 table:5 vdn:8 described:1 three:3 been:5 describes:3 treat:2 interest:1 expected:1 ph:1 algebras:1 harmonics:2 generating:1 arises:1 supersymmetric:23 commutes:1 quantities:2 formed:1 spectrum:4 determination:1 2n2:1 evidence:1 spin:4 those:3 case:17 hughes:1 replaces:1 truax:4 ǫn:3 value:2 choices:1 will:2 while:1 replaced:2 behavior:2 involved:1 ensuing:1 procedure:1 vb:6 hunan:1 refs:1 iu:1 equal:1 ii:1 eigensolutions:3 turns:2 partner:4 interacts:1 orbital:1 different:1 formalism:1 combination:2 primary:1 trial:1 recursion:2 kosteleck:9 indistinguishable:1 kash:1 any:1 shifts:1 parts:2 quant:2 split:1 pauli:5 units:7 lithium:7 higher:1 independent:1 used:7 imply:1 numerical:1 upon:2 effect:1 hand:1 normalization:4 suffices:1 schr:3 center:1 largely:1 changes:2 anticommutators:1 directly:1 philos:1 solve:2 components:1 sets:1 model:14 dimension:2 usual:2 spherical:3 distances:1 construct:1 just:2 eigenenergy:1 being:1 observed:1 identify:1 atomic:19 integer:15 alternative:1 dehmelt:1 previous:4 adding:3 enters:1 preprint:2 generator:2 correcting:1 smith:1 except:2 outlines:1 gabrielse:1 reasons:1 setting:1 transformed:1 lett:3 natl:2 nicolai:1 eigenfunction:3 rnl:2 possible:4 bluhm:2 spectrosc:1 background:3 using:3 accepted:1 moreover:2 mod:2 like:1 excluding:1 follows:4 alkali:5 yields:4 arbitrary:6 become:1 valence:12 replacement:2 kdn:2 because:4 plausible:1 some:9 specified:6 exists:1 2d:2 throughout:1 describing:5 dimensions:9 electromagnetic:2 whole:1 provides:6 limitations:1 core:4 radial:24 simultaneous:1 performed:1 splitting:1 wavefunctions:3 agreement:1 notably:1 broken:5 step:2 shifting:1 although:1 alkaline:1 properties:3 asymptotic:3 about:1 central:1 carried:1 extension:1 freedom:1 discussed:3 practical:2 probabilities:3 stand:2 act:1 introduced:7 presence:1 into:7 formulae:1 integral:1 functional:1 down:1 appropriate:1 references:1 binding:2 bosonic:8 anticrossings:1 fill:2 additional:1 assumed:1 support:2 twodimensional:1 stark:3 iq2:2 quadratic:1 way:2 bloomington:2 sections:1 happy:1 function:3 complete:3 form:8 offer:2 bur:1 hs:8 but:7 idealized:3 repeated:1 construction:3 incorporation:1 atom:7 hb:4 fg02:1 magnetron:2 eigenspectra:1 made:1 wish:1 particle:9 limit:9 sonine:3 demonstrate:1 problem:9 define:2 similar:1 called:2 mechanics:6 constant:8 defined:2 mike:1 general:2 supersymmetries:4 single:1 exist:3 formulation:1 corresponding:1 hamiltonian:17 constructed:1 again:3 functions:5 ev:2 no:2 acknowledgments:1 when:5 debergh:1 field:4 other:8 role:1 details:4 department:3 littman:1 polar:2 elements:5 generates:3 provided:1 models:1 problems:3 polynomials:4 generated:1 important:2 nucleus:1 sqm:4 variable:2 n2:1 structure:1 land:1 implies:3 longer:1 coulomb:9 penning:8 required:1 together:1 implied:1 mass:1 nuclei:1 having:1
|
quant-ph9508016.txt |@word represent:1 consider:2 just:1 show:1 indeed:1 leads:1 course:3 arrive:1 suffer:1 d2:13 translation:1 d1:9 letting:1 write:2 depend:4 calculate:1 aug:1 acknowledge:1 chosen:1 photons:8 illustrates:1 written:2 send:1 should:1 only:1 does:4 lett:2 mail:1 must:1 defining:1 into:2 plate:6 hit:3 orthogonal:1 spurious:1 frequencies:2 plausibility:1 wave:4 possibly:1 cannot:3 they:5 affect:4 suggest:1 realize:1 condition:1 widom:3 well:1 term:1 hereafter:1 presented:1 did:1 positions:1 university:1 arxiv:1 identified:1 t0:10 wss:15 transmitted:1 either:2 each:1 references:1 fixed:1 heading:3 right:1 national:2 some:1 packet:1 approximation:2 imply:2 frequency:1 result:1 choosing:1 quantum:1 laboratory:2 eq:7 message:1 august:1 even:1 factors:1 speed:1 recorded:1 overlap:2 state:3 experiment:1 above:1 example:1 gov:1 ref:1 correct:3 arrival:4 jos:2 recently:1 theory:1 lawrence:2 initially:1 upon:2 learn:1 use:2 free:1 like:1 embarrassment:1 incident:1 possibility:1 berkeley:2 come:1 after:1 finkel:1 both:1 purports:1 never:1 could:2 introduces:1 according:1 essential:1 participating:1 turn:1 published:2 hospitality:1 argue:1 first:1 among:1 initial:1 point:2 ca:1 imagine:1 reflected:1 done:1 tp:1 another:1 operator:1 counts:1 given:1 guest:1 would:5 distinct:1 before:2 support:1 there:1 approximate:1 hitting:1 their:3 therefore:1 ph:1 analyze:1 really:1 fig:1 corresponding:1 thus:1 exactly:1 photon:1 but:1 reflecting:1 varying:1 cases:1 true:1 than:1 present:4 partially:1 case:1 evolves:2 srivastava:3 might:1 means:1 rate:5 value:7 will:3 future:5 evaluating:1 error:2 merely:1 toward:3 similar:1 called:2 exhibit:1 claim:2 addressing:1 later:1 san:2 calculation:4 likewise:1 abstract:1 influence:2 argument:2 dependence:2 states:1 need:2 our:3 claimed:1 seem:1 counting:5 lbl:1 different:2 varied:1 no:1 fortunately:1 things:1 make:1 get:2 mechanism:1 any:2 note:4 located:1 other:1 quant:1 take:1 department:1 detector:2 out:3 events:7 evaluated:2 conclusion:3 development:2 independent:2 briefly:1 sure:1 see:1 rhs:2 earlier:2 reach:3 detectors:1 variation:2 plane:3 experimenter:2 was:1 waves:2 changing:1 summarize:1 choice:2 times:1 implies:1 acknowledgement:1 nevertheless:1 requires:1 calculated:1 spectra:1 packets:11 rule:1 without:1 so:1 fact:2 exp:1 time:12 position:3 backward:1 physics:1 having:1 terms:1 once:1
|
quant-ph9508017.txt |@word sector:2 partial:1 consider:11 pointing:1 switched:1 caused:2 global:1 results:6 four:3 scalar:1 remarkably:1 preferable:4 contributions:2 compact:1 depend:3 aug:1 ty:2 ockeler:1 pˆj:1 intensive:1 charge:1 program:1 dressing:5 analogous:3 must:1 worth:3 degeneration:1 belonging:1 amplitudes:9 orthogonal:3 mg:2 choice:1 ultraviolet:1 ψaα:19 difference:1 exact:5 condition:5 leads:4 school:1 quantized:2 hamiltonian:31 irreducible:2 t4:1 nucl:4 t2:1 solution:8 large:3 solved:1 χ2s:1 thermo:1 small:1 relation:10 probably:1 noninvariance:1 destroys:1 renormalized:4 consistent:1 requirements:1 direct:1 sign:7 matrices:2 zero:10 sented:1 summer:1 eiβ:1 insertion:1 pass:4 further:8 dynamics:2 haag:2 canonical:5 universities:1 index:4 what:9 section:1 lead:1 expressed:3 find:6 current:11 infinitesimal:2 bαβ:4 reconstruction:4 3b:1 ˆk:1 3g:2 method:2 coefficient:1 condensed:1 mamaev:1 ibid:1 vall:3 respectively:1 realizations:2 component:3 q3:6 here:11 bi:1 canonically:1 hlrz:1 free:1 eikx:10 alone:1 const:4 equations:15 change:2 obtained:4 remark:1 tx:2 inputting:1 institute:1 study:1 studied:3 piercing:4 suggests:1 amati:1 iep:1 action:5 changes:1 anticommutators:1 numerical:1 via:9 projection:1 substitution:1 sample:1 ebert:4 brought:2 inequality:1 condensates:1 total:2 unit:2 µa:4 use:5 khan:1 takes:5 would:6 intensively:1 positive:1 contains:2 direction:1 negative:1 properties:2 anticommutation:1 linear:3 noting:1 call:1 therefore:5 renormalisation:1 qcd:1 cαβ:6 means:2 type:2 theoretical:1 reflects:1 more:6 sort:1 nauka:2 separates:1 formally:1 vacuums:1 becomes:2 operators:10 localization:1 carrying:1 particular:2 known:3 hole:1 maryland:2 fermionic:5 states:24 account:1 ma:19 λm2:1 mc:4 vaks:2 recall:2 equation:21 work:1 reads:1 theories:3 fock:4 values:2 following:9 repre:1 spontaneous:8 example:2 initial:1 transition:4 renormalization:7 calculation:2 relativistic:8 table:2 dependence:1 high:1 spi:6 taking:1 want:1 sense:1 exclude:1 serial:1 occur:1 simple:5 verlag:1 crucial:1 respective:3 end:3 provide:1 verify:1 discussion:1 breaking:7 uther:1 orthogonality:1 evidently:1 write:5 polarizabilities:1 nontrivial:1 gcr:4 pair:1 currents:1 opposite:1 answer:4 parameter:9 sin:28 classify:1 inputs:2 de:1 mat:1 algebra:1 may:2 after:8 derived:2 needs:1 demanding:2 consequence:1 representations:5 wave:3 excited:1 realized:4 physical:12 dynamical:8 imply:1 spectra:14 correspond:4 su:25 st:2 perform:1 aβ:21 green:1 allow:1 decreasing:2 representation:15 order:3 interpretation:2 numbers:2 indeed:3 over:8 vary:1 years:1 stability:1 held:1 paper:2 same:14 hypersurface:1 argued:1 existence:3 kinetic:1 still:1 excitations:21 its:12 respect:2 derive:2 group:4 tˆk:1 δg:1 chosen:1 interesting:5 masses:7 expectations:1 actually:1 forms:2 absence:1 production:1 degrees:3 systems:1 mail:1 hidden:1 defining:1 into:10 compensators:1 maximal:2 non:6 good:2 return:1 combination:1 dan:1 efimov:1 processes:1 introduce:2 functional:1 volkov:2 effects:1 they:6 identically:1 front:1 rotation:1 now:14 realize:4 klevansky:1 represents:1 term:2 finite:6 equality:1 inheriting:1 lies:3 always:7 university:4 traced:1 divides:1 sufficiently:1 2g:16 2a:4 reasonable:1 fields:6 found:2 monomials:1 2ea:1 rakow:1 2k:1 heavy:1 tensor:1 ei:5 splitting:1 formulate:1 exhaust:1 generation:1 korenblit:1 energy:28 hard:1 ea:42 idea:1 related:4 eb:6 bosonization:1 antiparticle:1 gaps:4 isospin:1 combining:1 quantum:11 our:2 mapping:1 transitions:1 out:6 singularly:1 shown:2 eguchi:1 opened:1 space:8 since:3 lagrangian:5 particles:9 investigation:1 postpone:1 occurs:1 achieving:1 shows:3 χ2v:2 commutation:1 earlier:1 theory:9 written:2 attempt:1 possibility:1 standard:1 difficulty:1 reason:3 ect:1 besides:3 indicates:2 generate:1 pairs:6 interaction:12 chiral:2 r2:1 could:6 impose:1 rather:1 isu:1 motion:1 turn:2 length:2 relativistically:1 place:6 hence:3 interact:1 first:7 exotic:1 already:1 symmetry:30 consideration:1 possessing:1 number:11 interpret:1 na:1 clear:3 done:1 construct:2 another:1 impossible:2 equating:1 differ:1 temperature:1 introduction:4 condensate:1 system:11 relations:12 iab:1 their:4 fermions:6 calculations:2 realization:3 scheme:2 iap:1 speaking:1 larkin:2 shell:1 statement:1 tˆj:2 continuous:1 serve:1 feldman:2 barbieri:1 part:9 hup:1 too:1 natural:2 translation:2 theorie:1 coefficients:1 atomizdat:2 kind:3 determines:2 holland:1 was:2 require:2 e2iϕ:1 see:3 final:2 annihilation:4 charges:7 determined:3 unbroken:7 regions:1 were:1 radius:2 enables:1 russia:2 symmetries:3 rewrite:1 fluctuation:10 modern:1 turned:1 spectrum:15 generalization:1 seen:4 element:1 any:6 relatively:1 lie:2 angle:1 dαβ:9 depending:2 self:1 mechanism:2 note:7 k2:132 k1:114 contact:1 take:3 bogolubov:2 k4:73 so:4 coincide:2 degenerated:1 moscow:1 accuracy:1 heisenberg:5 ˆp:5 added:1 ray:1 fundamental:1 normal:5 object:1 xψ:1 singlet:3 most:2 connected:3 comparing:1 phase:5 analytically:1 why:1 singled:1 χv:2 kg:1 kf:1 ke:1 characterizes:1 considered:2 calculated:2 later:2 coincides:2 dimension:6 phis:1 friedrich:2 velocity:1 shirkov:1 left:1 physics:2 fact:8 quantity:1 2m2:1 show:5 jµ:3 supported:1 notations:2 implying:1 spaces:5 gauge:1 solutions:6 saturated:1 trivial:1 d3:74 q1:45 henceforth:1 2ma:2 q2:48 based:1 parameters:2 true:2 state:39 should:3 only:5 generators:4 greenberg:2 transcendental:2 developed:1 i4:2 local:1 pointed:1 do:2 above:3 get:2 multiplet:2 express:1 expectation:1 aα:69 2mc:8 tachiki:1 ones:2 closely:1 consecutive:1 ali:1 dt:1 interpreted:2 reveal:1 evolution:3 increasing:2 qu:1 continuum:1 conditions:3 arxiv:1 alteration:1 investigate:2 eiϕ:1 though:1 contain:3 looks:1 kernel:1 set:5 fair:1 achieved:1 frame:3 j0:1 up:1 namely:2 bare:7 result:3 eliminating:1 w0:9 inequivalent:6 isovector:5 satisfies:1 wightman:1 acquires:1 interacting:1 ways:1 µv:6 µs:12 symmetric:2 enough:1 future:1 between:2 invariant:4 iǫijk:2 approach:1 reinhardt:3 gives:1 nambu:2 terms:9 nature:1 ikx:8 however:4 condensing:1 enters:1 french:1 δab:1 tˆi:3 jetp:1 suppressed:1 both:1 essentially:3 last:6 reverse:1 many:1 region:5 compton:2 equal:13 constructed:1 quantization:1 enabling:1 admit:1 contribution:1 expression:9 fix:2 con:1 strongly:1 relevant:3 co:1 point:4 reasons:2 iϕ:1 corresponds:3 dimensional:8 directions:1 bα:20 bβ:4 σab:1 cancel:1 constant:14 mc2:6 described:2 transformations:14 iψ:2 addition:2 come:1 three:2 been:1 acheived:1 pb:1 slowly:1 eigenstate:1 basic:1 microscopic:1 ph:4 define:4 2mc2:4 hepp:1 generating:1 contribute:1 corresponding:7 versa:1 restrictions:1 quantities:3 sufficient:1 cos:28 gap:12 external:1 demand:1 c2:66 c1:4 spin:3 case:9 splits:1 straight:1 expanded:1 appearance:1 conserved:1 value:18 spontaneously:11 will:20 frameworks:1 momentum:4 leaves:1 situation:1 skewsymmetric:2 salpeter:2 procedure:1 seven:1 unitary:7 iq:1 characteristics:1 thus:12 them:5 according:4 expressions:3 vv:8 ready:1 mod:1 fermion:1 disappear:1 different:8 grant:1 lengths:1 uben:1 make:5 unite:1 clearly:1 reconstructed:1 parts:1 quant:1 uncertainty:1 proved:1 several:1 difficult:1 development:1 independent:3 used:2 i1:2 i3:2 i2:2 effect:1 hand:1 average:1 moment:2 supposing:1 infinite:5 invariance:2 cr:1 off:3 nevertheless:1 whole:1 well:2 grib:2 analysis:5 peculiarities:1 without:2 solve:1 components:2 sets:2 model:20 arising:2 latter:3 usual:2 restore:2 permissible:1 just:1 less:1 generally:2 numbering:1 obtain:13 rest:2 regulates:2 cease:1 aspect:2 arrowed:1 λj:3 arctan:1 scattering:1 eigenstates:6 previous:1 k3:73 4m2:42 cut:3 preprint:5 generator:3 density:7 nonrelativistic:1 had:1 parametrization:1 iω:3 lattice:1 add:1 combine:1 lett:1 easy:3 theorem:1 input:1 5g:2 heavier:2 transformation:1 accompanied:4 iφ:1 real:4 schweber:1 desy:3 multiplets:1 iγ:3 possible:5 fys:1 increases:3 helicity:2 background:1 vacuum:45 using:3 apart:1 insert:1 theor:1 necessary:4 like:1 particle:35 follows:17 reduces:1 performing:1 communications:1 horsley:1 yields:1 arbitrary:1 δf:1 become:2 stationary:2 reduced:1 replacement:4 because:5 lectures:1 creation:4 some:2 springer:1 q21:1 q22:1 q23:1 moreover:3 χs:1 happens:1 eiγ:4 meson:2 describing:2 dimensions:2 isoscalar:6 2e:9 quarks:1 integration:1 eiφ:3 ether:1 leap:1 does:2 decomposition:2 ig:1 mesonic:1 minimal:1 inserting:2 formfactor:5 varying:1 run:1 bb:21 aαβ:4 infinitely:1 irkutsk:5 each:2 conventional:2 expansion:3 broken:14 although:2 2m:7 eiω:2 eiψ:2 possesses:2 hilbert:6 asymptotic:1 constrains:2 about:1 energetically:4 carried:1 oh:1 column:1 freedom:2 2iϕ:1 generated:2 o:2 mutually:1 restoration:1 stand:1 conceals:1 act:1 calculating:1 circumstance:1 consequently:1 dimensionless:2 homogeneous:2 equally:1 rev:3 publishing:1 presence:5 dyson:1 within:1 integral:3 bound:16 down:4 included:1 hermitian:1 right:2 references:1 sov:3 operator:3 proportional:1 next:2 variables:2 hep:3 additional:2 area:1 strictly:1 there:12 question:2 3m2:1 medd:1 width:1 accordingly:1 low:2 way:4 jinr:1 bubble:2 propagator:1 function:4 north:1 form:12 vanishing:1 forming:1 regard:1 but:5 matsumoto:1 volume:4 construction:1 hn:6 hb:1 isotopic:7 clarify:1 ha:2 hf:4 partially:1 absent:2 made:1 la:1 inside:1 variations:2 maximum:1 us:9 bethe:2 nonrenormalizability:1 below:3 owing:1 limit:4 critical:3 how:1 fαβ:10 problem:4 called:2 russian:5 aa:42 ab:1 ordered:1 af:1 defined:6 certain:2 abstract:1 describe:5 am:2 determinant:1 lasinio:3 general:1 single:4 arises:1 exist:1 commuting:1 check:3 nonrenormalizable:2 chance:1 again:1 functions:4 vidensk:1 selsk:1 know:2 no:5 dressed:1 whereas:2 when:11 vanishes:2 schwinger:1 field:19 jona:2 other:2 remarks:1 department:1 really:3 appends:1 company:1 conclusion:2 picture:3 excitation:14 models:1 problems:1 includes:2 meaning:2 important:3 allowing:1 superconductive:2 structure:3 matrix:1 independently:1 regime:1 coupling:6 vice:1 veneziano:1 changed:3 2bα:1 4m:3 mass:25 time:4 4g:3 requires:1 restored:2 once:1
|
quant-ph9508018.txt |@word represent:1 partial:1 consider:1 pairing:2 magnetic:3 leads:1 ginzburg:1 fortiori:1 comments:1 involved:1 hole:4 improperly:1 rd:1 const:1 aug:1 concerned:1 eˆ:1 charge:5 does:1 th:1 under:5 tc:1 advice:1 returning:1 far:1 induce:1 wave:9 electron:3 every:1 school:1 mc:1 appart:1 level:1 sucher:1 solution:1 large:6 discrete:2 vector:3 enclosing:1 small:1 encloses:1 smaller:1 tel:2 periodicity:1 consistent:2 sign:1 zero:1 cost:1 tangential:1 picked:1 odd:3 theory:1 even:1 appear:1 d2:1 sum:3 uniform:2 current:1 above:4 new:1 falling:2 contributes:1 equivalent:1 coefficient:3 exchange:1 component:1 here:4 its:2 cylindrical:4 address:1 depend:1 along:3 quark:1 observing:1 appears:1 change:1 shift:4 suggests:2 periodic:3 resulting:1 unpaired:1 suggestion:1 domains:1 via:1 extra:2 substitution:1 cylinder:1 total:3 univ:1 unit:6 readily:1 use:1 quasi:1 takes:1 would:6 remains:1 positive:2 negative:1 next:1 mediate:1 therefore:2 qcd:3 type:5 theoretical:1 more:2 introducing:2 israel:1 odinger:2 varying:1 known:1 r0:2 cases:2 eα:1 derivation:2 ii:1 quantized:2 sphere:1 safko:1 equation:6 rohrlich:1 values:3 thin:1 mr:1 following:3 example:6 tau:1 impedes:1 renormalization:1 give:1 states:1 effectively:1 bend:1 mutually:1 rather:2 holds:1 write:1 very:1 vancouver:1 instead:1 coleman:1 parameter:2 sin:1 massive:1 simplicity:1 description:1 singular:1 may:4 immersed:3 orbits:1 fluxons:34 hence:1 fi:1 parallel:2 physical:1 effective:1 joint:1 spectra:1 lines:3 yielding:1 su:1 so:2 fundamental:1 sc:1 operate:1 order:8 typical:2 help:1 indeed:1 over:2 move:1 flips:2 already:2 london:1 agricultural:1 concentric:2 energetics:1 ln:6 seperation:1 actually:4 aviv:2 detected:1 degrees:1 systems:1 mail:2 main:1 defining:1 non:4 affected:1 landau:1 penetration:1 effects:3 half:1 now:1 φj:8 down:1 dirac:1 university:4 poole:1 2e:1 each:5 2l:1 found:4 soc:1 energetically:2 homogeneous:1 el:1 domain:2 mesoscopic:1 energy:17 einstein:1 reduce:1 related:3 wires:1 expect:2 impossible:1 quantum:2 our:2 operation:1 beyond:1 eq:5 special:1 canada:1 emerges:1 goldhaber:1 rep:1 since:3 induces:1 particles:6 acting:1 dxdy:1 denoted:1 rn:7 induced:5 issue:1 ri:2 rj:7 benefited:1 linear:2 interactions:2 voltages:1 free:2 effect:4 completely:1 complicated:1 detecting:1 generate:2 e2:1 pairs:3 interaction:10 θri:1 r1:13 r2:12 created:1 geometry:2 could:1 british:1 times:1 turn:1 length:7 exponentially:1 assumed:1 corrections:1 hadrons:1 condensate:1 south:2 first:1 origin:9 copper:1 initial:2 symmetry:1 number:4 antiquark:1 another:1 force:15 angular:2 aharonov:3 size:3 introduction:4 leading:1 interact:1 system:10 tot:1 triality:2 zeros:1 fermions:2 continuous:1 artifact:1 dyne:1 favorable:1 somewhat:1 off:1 requisite:1 freeze:1 than:1 modes:1 distance:5 higgs:3 see:1 determined:1 were:1 eγi:1 fcas:1 rewrite:1 quench:1 boston:1 unchanged:1 argument:2 summing:1 say:2 need:1 null:5 occupied:1 any:2 viewed:1 ray:1 rout:2 mechanism:1 note:2 ideal:1 potential:4 amusing:1 forces:11 finding:1 play:1 exactly:1 anandan:1 normal:2 compare:1 z2:1 simplify:1 regular:1 but:1 phase:2 baryons:1 nussinov:3 inserted:1 annulus:1 γi:1 considered:1 2πrdr:1 metal:1 kn:3 kr:2 electrons:7 exp:1 normally:1 fact:3 particularly:1 rings:1 terminate:1 anyway:1 dbz:1 gauge:4 reznik:3 trivial:1 find:4 ground:6 rev:1 finally:1 ratio:4 just:2 outside:2 topological:5 should:5 only:9 screening:12 factor:2 circle:1 carolina:2 2mr:2 do:1 between:18 overall:1 αi:1 cannot:1 reversal:2 international:1 aθ:1 dr:3 net:1 qq:6 fields:1 arxiv:1 yield:3 requirement:1 up:4 observed:1 ψαi:1 depends:1 individual:2 radius:5 heavy:1 particle:2 phases:1 detect:1 eigenfunctions:1 visiting:1 pattern:1 circulating:2 tend:2 symmetric:1 state:7 αe:1 closed:1 simplest:1 fluxon:19 invariant:3 boundary:1 solenoid:1 αn:1 screen:3 however:2 jl:2 vanishing:2 key:1 bose:1 suggested:1 both:4 prospects:1 last:1 many:1 region:5 infinitely:1 demanded:1 quantization:1 energies:4 φr0:1 casimir:4 exceeds:1 σr:1 passing:1 grounds:1 comment:2 cm:1 point:1 color:2 ca:1 dimensional:6 ab:1 simply:2 path:2 cancel:2 respect:1 mc2:1 conference:1 singlets:1 solenoids:1 equations:1 locally:1 due:7 been:2 screened:1 superconductor:2 interest:2 expected:3 ph:1 attractive:2 corresponding:1 coherence:2 photon:1 cos:1 locations:1 confinement:2 external:1 mcr:1 present:1 case:8 microns:1 frozen:1 profiles:1 will:12 near:1 suppose:1 promising:1 au:2 characterizing:1 a20:2 layer:3 n2h:4 coupled:1 thus:4 them:3 rin:2 disfavored:1 confining:4 il:1 aspects:1 vanish:1 duru:2 currents:7 perform:1 insofar:1 make:1 intrinsic:1 lett:1 same:6 clearly:1 shifts:5 parts:1 quant:1 virtually:2 modification:1 φi:3 dimensionless:1 several:1 used:1 columbia:2 trivially:1 numerical:1 upon:1 mutual:2 levels:2 implicitely:1 potentials:2 invariance:1 vaidman:1 schr:2 center:6 acknowledgement:1 charges:5 well:1 bohr:3 bohm:1 position:1 model:1 latter:2 charged:9 λs:13 distances:1 λp:2 popescu:2 generally:1 λy:1 λx:1 superconductors:1 shape:2 ftop:1 casher:1 using:2 yet:1 adding:1 density:8 photons:1 scales:1 add:1 location:1 easy:1 momentum:1 real:4 yukawa:1 around:3 putative:1 farach:1 rnf:3 forbidden:1 background:1 vacuum:2 confined:1 integer:3 insert:1 seperate:1 like:4 semi:11 sizes:1 manifest:1 separately:1 flux:2 continue:1 become:1 ha2:1 δe:5 webb:1 exceed:1 because:1 creation:1 some:1 emanate:1 choosing:1 fot:1 provided:1 scale:4 electromagnetic:1 quarks:1 integration:1 per:2 behave:1 tends:1 proc:1 refer:1 intial:1 jumps:1 radial:1 annular:1 2m:3 approximating:1 super:2 raise:1 conducting:2 origins:1 freedom:1 discussed:2 dependence:2 recalling:2 range:2 repulsion:1 greatly:1 act:1 introduced:3 consequently:1 considerations:1 equally:2 own:1 jθ:1 presence:1 h2:1 maxwell:1 into:2 three:1 assess:1 pair:3 references:1 nφ0:1 logaritmic:2 a3:2 log:1 area:1 nodal:1 there:5 transform:1 long:3 quadratic:1 bosons:3 ed:1 function:6 medium:1 form:2 feinberg:1 overlapping:1 compensating:1 neutral:1 hn:1 ec:3 hc:1 line:3 true:2 absent:1 made:1 circulation:3 inside:6 flip:1 us:3 paired:1 fermi:2 critical:1 fluctuations:1 problem:2 interplay:1 ac:1 required:2 constant:1 ai:2 abstract:1 contribute:2 metals:2 general:4 single:1 exist:3 wavelength:2 controlled:1 gradients:1 fill:2 again:1 functions:3 no:4 amounts:3 whereas:1 when:4 ne:2 nf:1 reality:1 field:4 other:4 role:1 department:2 nice:1 briefly:2 αem:4 a1:1 a0:8 generated:2 a2:3 ubc:1 astronomy:1 implies:2 coulomb:1 assume:3 physics:4 proposed:1 interval:2 persistent:1 together:2 having:1 factorizes:1 time:2 n2:4 strings:1 once:1
|
quant-ph9508019.txt |@word rev:21 magnetic:2 results:3 perelman:1 known:1 fig2:3 fig1:3 expressions:1 contributions:1 localized:5 scr:1 aug:1 subjected:1 tr:5 including:1 containing:1 squeezing:3 those:2 unnormalized:1 division:1 t12:1 returning:1 continues:1 stroud:6 wave:20 electron:1 figs:1 nieto:4 condition:1 presented:1 turns:1 t2:1 large:3 small:1 periodicity:5 direct:1 pulse:3 displays:1 further:1 what:1 appear:1 while:2 fractional:4 new:3 principal:2 method:1 evolving:1 full:5 respectively:2 gathered:1 here:3 atoms:11 free:1 based:1 strong:1 appears:2 change:2 studied:1 hughes:1 amount:1 survey:1 published:1 suitable:2 y10:1 plotted:1 via:1 spatially:3 plenum:1 highly:1 visible:2 plot:1 reflected:3 would:1 distinct:1 few:1 ψn:2 indiana:1 type:2 until:2 reflects:2 more:3 fractions:1 becomes:1 apparent:2 keplerian:2 berlin:1 particular:6 eccentricity:2 cases:1 derivation:1 me:2 states:27 permits:1 science:1 work:2 oscillator:1 crossed:1 den:3 meet:1 example:4 performed:1 figure:10 brown:1 process:1 attribute:1 ps:6 bommier:1 pieces:1 high:3 minimum:2 numbers:2 hydrogen:7 occur:1 provide:2 six:1 evidently:1 located:3 elliptical:1 instead:4 circular:2 oscillatory:1 product:12 description:3 replacing:1 after:3 orbits:3 expectation:1 produce:1 revealed:1 realized:1 short:6 outline:1 effective:1 correspond:1 sh:1 negligible:1 subsequently:1 pulsed:1 remnants:1 gradual:1 displayed:1 produced:3 nauenberg:2 experiments:1 pulses:2 statistical:1 still:1 excitations:6 its:7 outer:8 chosen:1 fix:1 coordinates:4 forms:1 absence:3 fig:6 persist:1 averbukh:1 supersymmetry:1 eventually:1 them:1 greater:3 conversations:1 yb:1 anticipated:1 framework:2 they:4 half:1 discuss:2 execute:1 2r:3 university:1 magnitude:1 2a:1 2b:1 radial:35 found:2 ters:1 mean:1 en:2 kleppner:1 ed:1 energy:3 used:2 measure:1 quantum:10 our:4 out:1 shown:3 robert:1 since:1 interference:1 re:1 goy:1 rational:1 ref:2 occurs:1 math:1 shows:3 turning:4 theory:1 interactions:1 hilfer:1 parame:1 possibility:1 minimized:1 formation:1 york:1 org:6 muller:1 skagerstam:1 r1:1 could:1 times:3 motion:5 turn:1 hence:1 undergo:1 first:3 origin:1 initial:3 features:3 probability:4 rydberg:15 variables:3 number:2 reaches:1 revive:1 restrict:1 intuitively:1 relations:1 mostowski:1 electronic:1 angular:10 illustrate:1 lagendijk:2 given:6 1r:2 ten:3 revival:5 similarly:1 tate:1 leading:1 system:1 adopted:1 1a:1 their:3 1c:1 1b:2 1e:1 1d:1 1g:1 1f:1 1i:1 1h:1 veff:1 collapse:3 centered:2 alan:1 part:1 somewhat:2 focusing:1 representing:1 than:3 png:12 oscillate:1 peaked:1 kind:1 1j:1 cyclic:1 zachary:1 trev:13 exhibit:1 obstacles:1 unchanged:1 defect:1 generalization:1 seem:1 orders:1 complete:1 depending:1 rout:5 note:1 potential:1 take:2 so:2 towards:1 relatively:1 electric:3 measures:1 involving:1 significant:1 successive:1 revivals:3 class:2 picoseconds:1 observation:1 bracken:1 later:3 metal:2 points:1 mechanical:1 velocity:1 scully:1 typically:1 fact:1 ritsch:1 parker:2 show:3 mains:1 attempts:1 minimizing:2 relation:4 enjoyed:1 ground:1 feng:1 ratio:6 parameters:4 duncan:1 should:3 values:1 colby:3 summarizing:1 indeed:2 parabolic:1 local:1 linden:3 do:1 dominant:1 means:1 overall:1 apsidal:5 ones:1 nonequilibrium:1 during:1 evolution:4 continuum:1 fields:11 arxiv:7 fixes:1 tcl:17 summary:1 europhys:1 analytical:8 through:2 thanks:1 set:1 imposing:1 packet:15 relative:2 see:2 college:2 gaeta:1 close:1 commutation:1 visiting:1 review:1 state:25 smallest:1 various:1 between:3 conditions:4 available:6 comparable:1 terms:1 nature:3 initially:2 attention:1 however:2 nsec:1 hydrogenic:18 problem:1 suggested:1 han:1 many:1 iγ1:1 uncertainty:19 equal:1 called:2 figures:3 hulet:1 argue:1 among:1 relevant:1 key:1 point:10 simple:1 harmonic:1 dimensional:2 exhibits:1 associated:2 pr:19 decohere:1 tint:3 described:1 geometries:2 due:1 been:2 springerverlag:1 wolde:3 expected:5 ph:7 lett:10 corresponding:4 frontiers:1 gay:2 radiofrequency:1 formed:1 photon:3 coherent:6 external:9 present:5 case:3 multi:1 laser:9 single:4 value:4 near:5 momentum:7 behavior:1 squeezed:35 situation:1 characterizing:1 psec:1 almost:2 ir:1 ii:1 itself:1 zhang:1 around:1 orbital:4 lengthy:2 ing:1 grant:1 perform:1 kosteleck:3 same:1 quant:7 units:2 several:2 grows:1 higher:1 amenable:1 eds:3 peaks:1 closest:1 singapore:1 kim:1 normalization:1 recent:1 center:1 charlie:1 variety:1 roughly:1 analysis:2 without:3 coordinate:1 self:1 usual:1 nanoseconds:3 obtain:1 shape:3 atomic:2 klauder:1 followed:1 eigenstates:2 halfway:2 rapid:1 zoller:2 density:2 excites:1 cl:1 other:3 treatment:1 excited:3 match:1 real:1 aspects:1 eigenfunction:1 format:6 possible:2 period:7 bluhm:1 five:1 world:1 noordam:3 mod:1 appearing:1 like:1 follows:1 reduces:1 performing:1 manifest:1 alkali:2 communications:1 either:1 mathematical:1 classical:11 some:2 gilmore:1 specified:1 oscillations:3 aspen:1 indirect:1 ourselves:1 generates:1 δn:1 provides:1 core:1 object:1 scientific:1 rep:1 each:1 oscillating:1 agreement:1 exciting:1 properties:1 constraint:1 http:6 dependence:1 o:1 alber:2 remains:3 range:2 peak:3 presence:2 previously:2 communication:1 into:1 washington:1 three:8 appropriate:2 determine:1 operator:3 uncertainties:2 van:6 additional:1 there:4 inner:2 bloomington:1 was:3 hare:1 function:8 elsewhere:2 form:7 fundamentals:1 but:6 construction:1 repeatedly:1 atom:3 subsidiary:2 longer:1 begins:1 made:2 coulomb:1 whether:1 characteristic:1 smooth:1 different:2 below:1 demonstrate:1 distribution:8 similar:2 display:2 separated:3 constant:1 moore:1 certain:1 describe:1 am:1 general:1 beats:1 periods:1 moves:1 distributions:1 physical:1 again:3 functions:4 no:2 wavefunction:1 when:3 matching:1 field:2 valid:1 details:1 department:2 nr:1 may:1 superposition:1 excitation:4 gross:1 generated:2 curvature:1 conover:1 decoherence:4 structure:1 delande:2 faster:1 l63:1 assume:1 physics:4 interval:1 packets:12 orbit:5 together:1 nasa:1 time:22 n2:3 n3:1 original:3 once:1
|
quant-ph9508020.txt |@word aided:1 represent:1 consider:6 interference:6 dynamic:1 results:18 perelman:1 zoller:2 leads:1 known:2 generalize:1 fig3:3 lewenstein:1 fig1:3 kurtosis:1 follow:1 expressions:5 symmetries:2 contributions:3 localized:3 scr:1 terms:13 aug:1 graph:1 workshop:1 technique:1 tr:2 contained:1 including:6 passage:1 presents:1 charge:1 squeezing:1 those:4 decomposition:1 delande:1 include:1 alber:2 applied:2 t12:1 b185:1 evolves:1 nanoseconds:3 peaks:4 reader:1 account:1 wave:74 trev:2 electron:10 witten:1 figs:4 reforms:1 experimentally:3 nieto:7 difference:2 exact:5 condition:2 look:1 four:3 hamiltonian:12 issue:2 dif:1 integrating:2 t2:5 solution:3 large:7 solved:2 convenience:1 vector:1 truax:1 small:2 eigenvalues:3 originally:1 png:18 application:1 strongly:1 smaller:4 periodicity:1 consistent:4 direct:4 pulse:14 ǫn:1 approximation:2 elegant:1 second:9 plenum:3 evaluated:2 pass:5 further:4 chem:1 odd:1 imposing:1 canonical:1 even:1 what:3 picoseconds:1 distance:6 d2:2 section:8 han:1 http:9 near:12 expressed:3 find:8 experiment:9 possibilites:1 issues:2 above:3 fractional:15 new:10 falling:1 increasing:2 method:4 body:2 full:13 den:2 alkaline:1 error:1 component:2 orbitals:3 atoms:37 ranges:1 explore:1 ramsey:1 nsec:12 address:1 ratio:4 along:1 equations:8 appears:1 change:1 obtained:14 remark:1 division:1 broken:1 gruber:1 shift:3 study:7 studied:2 completely:2 leaving:1 suggests:6 periodic:2 resulting:3 characterizing:1 published:1 action:1 california:1 conveniently:1 fourier:1 studies:2 y10:3 involves:2 plotted:7 via:3 useful:2 family:8 unsatisfactory:1 requiring:1 merely:1 vii:1 integrations:1 highly:1 conditions:2 decrease:1 opportunities:1 apply:3 clockwise:1 tools:1 remaining:1 derivatives:1 use:17 asymptotic:2 would:1 remains:1 spacings:1 predictions:1 next:3 process:1 nucl:1 call:3 therefore:9 taken:8 overviews:1 means:5 type:3 theoretical:11 reflects:2 more:4 fractions:2 skewness:1 ritsch:1 comparison:9 relevant:2 neglected:1 operators:2 factor:1 envelope:7 odinger:7 validity:1 long:1 normalized:1 particular:11 eccentricity:3 cases:6 iii:2 r1:5 me:2 high:4 none:1 quantized:1 permits:1 pursue:1 science:2 equation:15 work:4 oscillator:5 modified:2 mk:3 erf:2 gathers:1 values:15 evolved:2 determining:1 following:1 making:1 example:19 sinusoidal:2 ions:2 compare:3 figure:17 give:1 calculation:9 expanding:1 organized:1 purposes:4 bommier:1 states:50 effectively:1 minimum:18 rubidium:18 performed:4 past:1 specific:2 quantummechanical:1 hydrogen:30 evidently:3 axis:1 normalize:1 information:1 goal:1 provide:9 precessing:1 discussion:3 breaking:3 differences:2 eigenenergies:3 occur:3 write:1 maps:1 relative:2 get:2 elliptical:2 answer:1 symposium:1 absolute:7 parameter:6 indiana:1 circular:1 oscillatory:3 simplicity:2 product:11 wolde:2 description:10 may:7 broad:1 oscillators:1 after:7 orbits:6 expectation:8 hence:1 sven:1 mag:1 dominantly:1 date:1 summarize:1 choice:6 clearly:1 short:21 natural:3 effective:8 specialize:1 spectra:2 lines:1 correspond:3 element:1 generic:1 cannot:1 so:7 subsequently:2 playing:1 nonequilibrium:1 displays:3 pulsed:8 remnants:1 subsections:1 numbers:2 developed:2 over:5 insight:1 choose:3 feature:1 produced:4 course:1 nauenberg:2 experiments:6 through:8 motions:1 left:8 differs:1 captions:1 satisfies:1 still:1 excitations:3 its:19 before:3 revived:1 derive:4 outer:21 probability:12 sodium:1 supersymmetric:7 interesting:1 fix:1 presence:3 expectations:3 coordinates:7 forms:1 detected:1 distinguishing:1 fig:20 recombined:1 derivative:1 might:4 h0:2 supersymmetry:20 eventually:2 non:3 good:3 pure:2 combination:1 conversations:1 yb:1 processes:1 bound:1 break:1 framework:3 asymmetrical:1 they:10 half:2 front:1 mimicking:1 discuss:3 2t:1 eigenvalue:2 term:2 lithium:2 equality:1 2r:6 2er:1 fully:1 university:3 level:3 identified:3 accompanies:1 sin:1 orthonormal:2 2f:4 fringes:1 l2:3 trap:1 radial:73 2l:2 found:7 2n:3 t4:3 defects:10 subset:3 el:1 springerverlag:1 differential:2 ei:3 significantly:4 independent:2 generation:2 density:1 energy:12 hypergeometric:1 reduce:1 gaussian:2 conventions:1 seaton:1 investigated:2 expect:1 quantum:39 our:19 operation:1 tuned:1 eq:22 special:2 out:3 shown:12 hughes:1 literature:2 matrix:1 space:1 periodicities:4 electronic:2 robert:1 since:5 lagrangian:1 denotes:1 replacing:1 acting:2 papers:1 rational:2 zimmerman:2 rn:11 ref:15 occurs:1 math:1 shows:8 exactly:1 turning:15 theory:23 interactions:2 spectrum:1 attempt:1 stroud:6 standard:4 beyer:1 approaches:10 necessarily:1 formation:5 york:3 elsewhere:1 usual:4 initialize:2 org:9 generate:1 e2:3 incorporates:3 skagerstam:1 r0:6 derivation:4 r2:8 cowan:1 starts:3 could:1 transition:1 success:1 times:22 motion:23 turn:2 length:1 specification:2 consequence:2 uses:3 neglect:1 first:18 origin:8 there:1 features:11 symmetry:4 laguerre:1 rydberg:38 variables:5 number:8 reaches:2 nested:1 linden:2 done:2 nonperturbative:1 directly:1 mostowski:1 apparent:2 dunning:1 open:1 angular:11 constructing:1 dispersion:2 given:25 perturbation:7 ten:2 revival:13 needed:1 introduction:1 leading:1 eqs:3 system:3 relations:3 lagendijk:1 their:11 returns:1 nomenclature:1 normalization:4 calculations:4 realization:2 o:1 recovered:1 gives:3 shifted:1 e0:1 correlations:1 starting:1 collapse:2 predict:1 trapped:1 centered:5 tool:2 continuous:2 2p:1 alan:1 larger:2 part:10 because:3 somewhat:1 authors:1 shortly:1 dx2:1 than:9 coefficients:5 rss:79 salient:1 connections:1 kind:1 determines:1 third:1 holds:1 approximations:1 zachary:1 zero:5 determined:6 amplitude:5 were:5 sec:10 toward:1 distinguished:1 perturbative:6 exhibit:1 lowest:2 pointed:1 cn:5 few:2 separations:1 conventional:3 defect:10 interpretation:1 discussions:1 kepler:2 conjugate:3 need:1 seen:3 seem:1 constrained:1 seek:1 any:2 viewed:3 relatively:8 angle:1 key:3 convenient:2 rout:4 propagation:1 able:1 ideas:2 nonstandard:1 note:7 emphasis:1 potential:13 square:7 generalized:1 negligible:2 subject:1 primarily:1 accuracy:2 δn:6 begin:2 towards:3 aspen:1 electric:1 measures:1 satisfy:4 systems:2 gallagher:2 position:2 revivals:14 analytically:5 measured:1 class:2 eigenfunctions:5 peaked:2 constructed:2 especially:1 considered:2 mean:2 calculated:4 adopt:1 metal:19 disperses:2 order:1 graphs:7 proceedings:2 points:6 principle:2 exp:3 mechanical:2 prime:1 oscillates:3 penning:1 notion:2 fact:2 quantity:4 perspective:1 incorporate:3 parker:3 spaced:2 show:10 timedependent:1 probe:2 appearing:1 rotating:2 attempts:1 minimizing:2 relation:8 solutions:2 pump:1 earth:1 superalgebra:1 fine:1 agrees:4 ground:9 pick:1 partners:4 feng:2 finally:1 based:1 just:1 parameters:11 duncan:2 situations:1 reflection:1 specified:1 written:4 kleppner:2 moments:3 only:4 colby:3 subsection:7 molecules:1 ien:6 hamiltonians:2 curvature:1 characterization:1 do:3 intractable:2 move:1 handle:1 envelopes:2 notation:1 iωt:1 dependent:14 succeeded:1 overall:2 apsidal:14 yielded:1 tate:1 ferent:1 negative:1 despite:1 during:5 respectively:2 procedures:1 normalizable:1 evolution:19 precession:4 continuum:3 semimajor:1 introduced:3 fields:9 arxiv:10 effects:1 tcl:25 summary:2 greene:2 berlin:1 paper:3 cf:1 predicted:3 contain:1 analytical:27 pulses:4 fixed:5 approaching:1 reveals:3 requirement:1 set:6 counterclockwise:1 exists:1 principal:5 ldt:1 enjoyed:1 nicholson:1 packet:44 up:1 observed:3 see:6 individual:1 college:2 descriptions:3 eliminating:1 gaeta:1 separately:1 close:10 thanks:1 meet:1 kinetic:1 incorporating:2 situation:2 closer:2 satisfying:1 commutation:3 visiting:1 review:1 complementary:1 dipole:3 fano:1 naturwissenschaften:1 state:21 difficulties:1 various:2 closed:1 between:9 progress:1 halfway:1 approach:5 generators:1 available:10 recently:2 reproduced:2 extend:1 nature:1 initially:3 modify:1 weak:2 however:13 interfere:1 vanishing:1 substantially:1 here:6 hydrogenic:14 p2r:1 interface:1 rapidly:1 understanding:1 distribution:16 concentrated:1 both:8 cos:3 piece:1 last:1 candidate:1 brown:1 many:3 iγ1:4 uncertainty:30 equal:6 dominant:1 called:4 chosen:2 objects:1 figures:2 context:4 exceeds:2 variance:1 passing:1 candidates:2 expression:4 excites:1 experimental:3 otherwise:1 arbitrarily:1 among:1 solving:1 unnormalized:7 point:27 simple:11 berkeley:1 narrower:1 period:23 dimensional:3 exhibits:3 right:8 away:1 constant:6 rep:2 throughout:1 broadens:1 pr:27 ps:9 ensures:2 configuration:1 described:3 ylm:3 bertrand:1 three:13 been:9 int:5 reduction:1 describes:4 treat:1 interest:8 basic:2 expected:8 grant:1 ph:11 algebras:1 oscillate:2 generating:2 describe:1 partly:2 frontiers:1 gay:1 bracken:1 quantities:6 sufficient:1 formed:3 photon:3 depend:1 t3:4 bulk:1 coherent:11 external:2 decreased:1 2n2:1 c0:2 present:7 case:10 multi:1 replaces:1 laser:30 splits:1 washington:1 defining:1 akad:1 appearance:2 examine:1 value:19 transformation:2 deferred:1 while:7 rau:1 momentum:12 behavior:26 promising:1 squeezed:21 exist:1 located:1 leaves:1 procedure:3 klauder:2 real:2 detailed:3 psec:31 approximate:1 simons:1 vi:2 refs:6 wkb:2 thus:1 iv:5 ii:3 eigensolutions:1 attributed:1 ia:1 partner:1 zhang:1 conover:1 around:1 orbital:26 different:9 thereby:1 multiphoton:1 prior:1 perform:2 acknowledgments:1 kosteleck:9 format:9 lett:6 same:8 approximately:2 member:2 shifts:3 another:1 parts:1 quant:11 units:1 several:5 higher:2 development:1 reexpress:1 used:10 eds:7 unconventional:1 closest:1 singapore:2 averbukh:1 initialization:4 numerical:7 hand:1 average:1 moment:2 levels:3 moving:2 kim:1 potentials:1 infinite:1 six:2 expand:1 recent:1 strinati:2 suitable:2 schr:7 center:2 ed:1 largely:1 disappears:1 corresponds:4 2dr:1 well:2 inquiry:1 analysis:5 off:1 philos:1 solve:2 sets:1 coordinate:4 comparisons:2 model:5 recombine:1 latter:1 charged:1 spherical:1 world:2 construct:2 proposed:1 being:2 accurate:1 labeled:1 obtain:7 actions:1 shape:4 intervals:2 atomic:14 predicts:1 immediately:2 followed:1 alternative:1 eigenstates:1 previous:4 adding:2 now:2 signal:2 integer:5 conclusions:2 similarities:1 regarded:1 cl:2 spread:1 treatment:2 easy:1 theorem:1 nicolai:1 scully:1 excited:11 match:3 take:3 identical:1 exhibited:1 aspects:1 eigenfunction:1 rnl:2 evaluate:3 breaks:1 spatial:1 possible:1 harmonic:5 early:1 matters:1 increases:2 bluhm:2 kash:1 background:3 press:1 using:7 accepted:1 fig2:3 mod:1 necessary:1 like:1 particle:7 shaped:1 follows:8 reduces:2 performing:1 serves:1 alkali:19 similarly:2 l63:1 either:1 warned:1 evolutions:1 inter:1 reduced:2 replacement:1 specifies:1 polarization:1 methods:1 classical:43 charlie:1 some:13 back:3 bounce:2 therein:1 gilmore:1 inequivalence:1 choosing:1 moreover:1 oscillations:3 treatments:1 matching:1 generates:1 shapes:2 scale:1 describing:3 demonstrates:1 future:1 integration:4 nlm:1 magnitude:2 connecting:1 provides:4 prog:1 demonstrated:1 refer:1 core:5 object:1 quantph:1 obey:5 power:1 plot:1 equivalent:1 each:2 oscillating:2 agreement:6 expansion:3 hss:5 tint:2 polynomials:1 although:8 substitution:1 analyses:1 includes:1 properties:14 stage:1 integers:1 about:12 valence:1 central:9 carried:1 extension:1 reappear:2 basis:2 discussed:6 dependence:6 greater:1 1r:3 range:5 extensions:1 discusses:1 slightly:1 gamma:2 truncating:1 sh:1 muller:1 rev:34 inclusion:2 orders:2 material:1 into:8 within:3 numerically:7 attains:1 due:1 down:2 appropriate:2 en:14 references:2 determine:4 operator:2 ellipse:1 often:1 uncertainties:3 van:4 comparing:2 initial:12 transform:1 stark:1 rcl:3 width:1 much:2 strayer:1 inner:3 series:1 bloomington:1 scientific:2 was:4 propagator:1 function:34 complete:4 form:10 energies:2 fundamentals:1 potassium:7 regard:1 but:1 idea:1 repeated:1 construction:5 crank:1 atom:13 subsidiary:1 line:1 inverted:1 true:2 collapses:3 observation:1 made:1 presented:5 qualitative:1 intuitive:1 versions:1 characteristic:1 inside:1 maximum:3 us:1 2πn:1 international:1 below:3 frequency:3 limit:3 how:1 sum:4 autocorrelation:19 demonstrate:1 problem:6 define:2 similar:3 agree:2 examples:7 mechanics:1 separated:2 result:3 later:1 associated:6 moore:1 ln:4 defined:3 certain:4 decreases:3 sidestep:1 am:1 direction:1 metals:1 general:2 supersymmetries:1 single:10 ensuing:2 periods:2 dθ:1 corresponding:12 reflecting:1 moves:2 distributions:3 eigenstate:1 physical:3 vertical:1 again:5 functions:18 compared:2 eventual:1 no:4 asymmetry:1 fixing:2 whereas:1 wavefunction:1 when:8 spectroscopy:1 field:9 other:12 role:2 details:1 becomes:4 department:2 nr:2 concerning:1 polar:1 elements:1 conventionally:1 excitation:7 provided:2 models:1 excite:2 radially:1 variation:1 prepared:2 noordam:3 spatially:1 generated:1 keplerian:3 sqm:3 variable:5 decoherence:1 structure:2 nasa:1 implies:3 coupling:1 coulomb:12 examination:1 perturbatively:1 physics:5 statistical:1 required:1 packets:37 orbit:14 governed:2 otsuka:1 dr:3 gross:1 cambridge:2 littman:2 time:71 avoids:1 n2:2 n3:3 requires:2 original:2 once:1
|
quant-ph9508021.txt |@word represent:2 evidence:1 gr:6 caused:1 brownian:4 results:6 existing:1 four:1 roy:2 scalar:2 mile:1 entropy:4 go:1 follow:1 gm:1 causes:1 consider:2 whose:5 depend:2 aug:1 description:2 equivalence:9 relating:5 environment:1 summarised:1 does:6 weyl:1 present:1 th:1 under:1 stochastic:20 norm:3 division:2 conjecture:1 amplitudes:1 bedford:2 far:5 frequencies:1 2re:2 reader:1 springer:2 iτ0:1 wave:15 me:1 every:3 experimentally:3 emphasized:1 difference:1 condition:1 hagelin:1 leads:3 caesium:1 exponential:1 hamiltonian:5 did:1 criterion:1 proposals:2 large:13 vector:10 science:1 small:15 relation:3 inertial:1 rested:1 smaller:3 says:1 decoherent:2 consistent:3 estimates:1 qmw:1 modified:1 elegant:1 zero:3 noise:2 further:1 dynamics:9 even:4 what:1 nonlinear:2 appear:4 apparatus:1 itˆ:8 section:9 interactions:1 bergman:2 expressed:1 uniform:3 current:1 version:1 dilation:2 new:9 preserved:1 contrast:1 satisfy:7 full:1 never:2 component:4 here:5 atoms:1 behaviour:1 objects:3 smearing:3 108b:1 represented:3 equations:11 appears:1 change:2 contraction:1 obtained:3 great:1 4ns:1 institute:1 hartle:2 study:1 changed:2 through:6 leaving:1 prior:1 recently:3 resulting:1 stimulating:1 california:1 domains:1 surely:1 fourier:6 spacetime:1 subjected:1 sci:1 pearle:6 uniquely:1 deterministic:1 griffiths:2 scales:12 requiring:1 replace:1 durham:1 localizes:1 planck:25 unit:2 involving:1 takes:1 would:7 commun:2 probabilities:1 continuous:1 contains:2 predictions:1 next:5 classically:1 explicitly:2 therefore:1 taken:3 conservation:1 associated:1 tell:1 more:10 flat:5 excluded:1 becomes:1 ascribe:1 odinger:8 curvature:3 berlin:2 rigid:1 normalized:4 foundations:5 must:9 nondifferentiable:5 high:1 account:1 quantized:2 quantize:1 ρh:1 equation:24 constraint:2 ρl:1 theories:28 reviews:1 remain:3 regions:1 values:4 publications:1 concepts:1 believed:2 spontaneous:2 example:4 slightest:1 something:1 point:3 weaker:1 wang:2 lρ:1 calculation:1 relativistic:1 role:1 neglected:2 violations:1 states:5 sphere:1 lorentz:5 numbers:1 want:2 mohanty:3 sharp:11 times:5 guarantee:1 needs:1 end:1 rather:1 imprecision:2 di:10 ghirardi:6 feature:1 hampered:1 very:5 copyright:1 unites:1 low:1 acta:1 ordinary:9 constraints:1 frenkel:2 displacements:1 isotropic:1 continues:1 intended:1 may:5 earlier:2 derived:9 containing:2 applications:1 wrong:1 produce:3 1993b:3 1993a:4 coming:1 date:1 representations:2 constants:1 changes:1 short:2 dynamical:4 resemble:1 physik:1 light:1 parameter:5 lost:1 introducing:1 cosmology:1 si:3 so:20 automatically:1 fundamental:1 things:1 representation:4 order:3 ito:1 theme:1 interpretation:5 help:1 produces:2 mds:1 developed:2 over:3 despite:1 vary:1 satisfied:2 years:1 whilst:1 raman:1 experiments:10 london:2 statistical:2 differs:1 existence:4 satisfies:3 still:1 its:3 humboldt:1 write:1 derive:1 group:2 thank:1 osi:10 how:1 energies:1 masses:2 relativity:8 blurring:1 pritchard:1 forms:1 omn:2 distinguishing:2 microscopic:1 systems:17 ours:1 might:6 kasevich:2 overcome:3 them:3 delocalization:1 weakness:1 detectable:1 processes:5 introduce:3 break:1 p12:1 hamilton:1 effects:5 they:9 foot:1 now:3 falsifiable:1 nor:1 worlds:3 term:7 always:1 university:5 ensemble:4 micro:2 magnitude:1 reasonable:1 each:2 universit:1 d47:1 side:1 referred:1 domain:1 differential:15 england:1 significantly:1 generation:1 series:1 energy:9 revised:1 principles:7 related:3 frames:4 used:2 search:1 expect:3 measurement:5 quantum:112 our:14 happen:1 transitions:1 nonlinearities:1 mdw:1 special:1 out:3 try:1 shown:6 dominates:2 space:69 restricted:1 since:6 rev:11 chaos:1 diffusive:1 traversed:1 dominated:3 dowker:2 conjectured:3 herder:1 size:1 math:3 shows:2 foundation:2 numerical:2 theory:50 localization:13 hull:1 gardiner:5 contain:1 given:4 free:6 standard:2 difficulty:2 base:1 complicated:1 york:1 put:2 asi:1 e1:1 milburn:2 care:2 incorporates:1 interaction:2 derivation:5 geometry:2 could:4 srednicki:1 feasible:2 motion:6 length:2 relativistically:1 place:1 diffuses:1 freiburg:2 retain:1 think:1 already:1 features:1 variables:1 primary:11 transform:1 philosophical:1 done:2 approximately:1 directly:1 speculatively:1 open:3 spread:3 idea:1 little:2 ian:1 observer:1 needed:4 introduction:2 adjoint:3 system:9 relations:7 their:5 intermediate:1 master:6 normalization:1 wirzba:1 white:1 gives:2 shifted:1 collapse:3 radiation:1 exactly:1 albert:1 plane:2 transverse:1 assumption:1 part:2 permanent:1 too:2 consult:1 july:1 abandoning:1 representing:1 than:4 diffusion:49 distance:2 determines:1 showed:2 penrose:5 was:8 depends:1 halliwell:3 matter:12 elementary:1 determined:3 stp:2 frustrating:1 maybe:2 naturally:1 treated:1 distinguished:1 rimini:6 journey:1 fluctuation:5 dynamically:1 modern:1 mind:1 say:2 unlikely:1 need:1 seem:2 unaffected:2 any:8 contents:1 relatively:1 helpful:1 built:2 convenient:5 self:2 responsible:1 gravity:17 mechanism:1 contact:1 note:1 emphasis:1 internal:1 forces:1 objective:1 hgc:1 rate:1 calculus:5 lectures:4 added:1 ray:1 opposite:1 price:1 who:3 phases:1 most:3 gravitation:8 germany:1 significant:3 phase:7 ludwigs:1 acknowledgements:1 intrinsic:2 herman:1 es:2 sub:2 wiley:1 consequences:2 dordrecht:1 chosen:1 later:1 stronger:1 drive:1 feynman:4 principle:11 grishchuk:2 effect:1 physics:5 laws:1 precise:1 particularly:1 show:1 violation:1 agreed:1 queen:1 helv:1 gauge:2 inconsistent:1 subtle:1 speakable:1 find:1 decade:4 trying:1 based:4 just:3 parameters:6 much:3 less:2 written:1 universal:3 should:6 only:9 experiment:7 generators:1 factor:7 isham:4 local:5 pointed:1 hope:1 do:3 his:2 means:1 dependent:1 simplest:2 expectation:1 nevertheless:1 cannot:2 dz:1 invariant:1 dw:3 dt:16 conjunction:1 ds:3 alexander:1 evolution:7 unacceptably:1 arxiv:1 paper:5 common:1 wormholes:2 including:4 gell:2 approaching:1 coefficient:3 applied:1 set:4 reference:2 frame:1 uses:1 packet:3 observed:1 nuo:4 see:1 individual:3 college:1 us:3 fail:1 close:3 nuc:1 fails:1 said:2 interacting:1 ul:1 nature:1 consequence:1 chu:2 state:49 future:2 between:11 probably:1 neither:1 luk:5 conditions:3 wide:2 preserve:1 multiplied:2 terms:4 missing:1 grassi:2 were:3 however:5 histories:3 hypothesis:3 key:1 distinguish:5 rapidly:1 come:1 problem:3 undetermined:1 both:4 essentially:2 dtp:1 many:6 region:4 equal:3 propagation:1 manifestations:1 hρ:1 whole:1 comes:3 cm:1 nonrelativistic:4 simple:1 guaranteed:1 semiclassical:2 confirmed:1 respect:1 semigroups:1 described:1 transformations:7 basis:1 addition:1 skew:1 locally:2 due:1 been:3 cvitanovic:1 reduction:9 describes:1 hawking:2 basic:1 nato:1 ph:1 extreme:2 mary:1 define:1 suggested:2 direction:3 corresponding:3 indeterminacy:2 qsd:1 prospects:1 worked:1 general:6 unpredictability:1 spirit:1 those:6 pilot:2 case:2 replaces:2 look:1 unlike:3 developing:1 decades:1 value:3 will:3 near:1 cosmos:1 suppose:1 weber:2 applies:3 squeezed:1 property:1 falsified:1 guide:2 unitary:2 coupled:4 metric:2 formulation:5 thus:1 non:2 according:1 ih:2 itself:1 commonly:1 technology:1 different:3 suggests:1 il:1 suggest:1 formulations:1 problems:2 indistinguishable:1 same:5 princeton:1 unity:2 complex:9 quant:1 pauli:2 modification:1 nanopoulos:4 gets:1 neutron:1 difficult:1 development:1 independent:2 weinberg:2 eds:2 trajectories:1 differing:1 possible:5 usually:1 moving:1 hospitality:1 infinite:1 changing:1 invariance:1 spreads:1 identity:2 suitable:1 schr:8 largely:1 adξ:1 macro:3 well:1 bohm:1 de:2 without:4 experimental:4 components:3 coordinate:1 position:5 model:2 dimension:1 usual:6 distances:2 1994b:2 proposed:2 1994a:3 wagner:1 obtain:1 rest:2 press:2 atomic:2 world:1 localize:1 alternative:5 macroscopic:2 stratonovich:1 previous:1 adw:1 generous:1 poses:1 preprint:1 kluwer:1 density:5 bell:4 had:2 except:2 discuss:1 signals:1 parts:2 valid:2 transformed:2 lett:2 mann:2 extensive:1 apart:2 transformation:22 momentum:4 real:2 tests:3 fluctuating:11 around:3 represents:6 read:1 nonphysical:1 showing:1 haus:2 psd:33 test:2 know:1 vacuum:2 confined:1 using:6 bit:1 unique:1 vdt:2 dimensional:4 necessary:1 like:6 particle:4 follows:2 brun:1 communications:1 history:1 either:2 become:3 works:1 reduced:1 towards:1 replacement:1 accessible:1 heisenberg:1 because:4 methods:1 classical:17 foreseeable:2 squires:2 some:4 stat:1 stimulated:1 broglie:2 paragraphs:1 intact:1 absent:1 provided:1 scale:20 ellis:6 sufficiently:6 unavoidable:1 langevin:6 critical:6 provides:3 particles:1 proc:2 measuring:1 destroys:1 replaced:1 run:1 nonuniform:2 uniformly:3 equivalent:4 hazy:1 agreement:1 expansion:1 br:1 handbook:1 imaginary:1 stay:1 super:2 properties:4 von:1 stage:1 about:2 extension:1 rederived:1 universe:29 theorems:1 introduces:1 dependence:3 o:8 d46:1 acs:5 range:3 a2:2 ensure:2 connected:2 mean:8 slightly:1 road:1 soc:2 cambridge:2 letter:1 presence:1 previously:1 pergamon:1 into:4 within:5 functional:1 latter:1 down:3 included:2 square:2 references:2 einstein:2 operator:12 proportional:3 strasse:1 letts:3 rely:1 statistics:2 additional:2 probabilistic:1 support:1 there:19 approximate:1 long:1 dispersion:5 absolutely:2 accordingly:1 quadratic:1 quanta:1 physicists:2 sections:2 interferometry:8 function:5 medium:1 complete:2 form:5 dξr:1 differences:1 but:22 displacement:1 volume:1 failure:1 larger:3 hc:1 lindblad:4 removed:1 true:2 oxford:3 he:2 pull:1 made:1 minkowski:15 gravitational:14 smooth:7 up:1 differentiable:4 theoretical:1 azy:8 below:2 books:1 fluctuations:25 percival:14 similar:2 agree:1 gisin:10 mechanics:27 constant:7 discussed:1 defined:2 abstract:1 describe:1 influence:1 resultant:4 dξ:14 right:1 laboratory:4 physical:2 again:1 compared:1 cim:4 no:20 objection:3 whereas:1 when:5 detail:1 field:8 other:8 detected:1 details:1 spatial:1 department:2 you:1 picture:1 briefly:1 star:1 generates:1 models:2 time:91 drift:6 includes:1 rise:1 important:3 validity:1 velocity:4 variable:2 westfield:1 structure:13 longer:3 dψ:4 normally:1 required:2 packets:3 together:1 mass:5 resembles:2 decoherence:9 requires:5 original:5 unspeakable:1
|
quant-ph9508022.txt |@word consider:4 remarkable:1 rev:7 brownian:1 results:3 acknowledgements:1 entropy:1 go:4 localized:3 certainly:1 terms:8 4ns:1 deterministic:1 tr:2 nonlocal:1 environment:2 finally:1 present:1 ti:14 tf:12 stochastic:2 applied:1 supported:1 string:1 advantage:1 orthogonal:1 very:14 frequencies:1 continues:1 percival:8 wave:2 lyapunov:1 2γx:4 difference:1 exact:1 vast:1 paz:1 entire:1 hamiltonian:6 having:2 t2:1 t0:14 damped:7 hartle:5 discrete:2 vector:1 phase:17 small:3 optics:1 caltech:1 attracting:1 prevent:1 strongly:2 work:8 force:3 decoherent:13 approximation:1 zero:7 pass:1 rigorous:1 further:4 dynamics:5 seth:1 quite:1 linear:2 even:5 index:1 what:3 nonlinear:7 appear:1 giving:1 d2:1 section:15 brief:1 cell:1 version:1 above:1 new:5 ever:1 method:1 contrast:1 temperatures:1 full:1 spacing:1 here:2 diagonal:3 explore:1 smearing:2 address:1 path:2 strong:1 equations:2 appears:1 extreme:1 every:1 great:1 aug:1 institute:1 study:8 studied:5 through:1 leaving:2 amount:2 periodic:7 ρtotal:1 usually:2 complicated:1 suitable:1 involves:1 york:2 holmes:1 attractor:4 technique:1 useful:1 divide:3 scales:3 natural:1 highly:1 brought:1 rarely:1 imaginary:1 readily:2 tn:1 use:1 handled:1 would:7 probabilities:5 continuous:2 contains:1 negative:2 next:2 classically:5 sample:1 explicitly:1 iαi:2 taken:1 exhaustive:1 e2:3 type:1 wipes:1 more:12 sort:4 becomes:6 operators:4 kδ:1 odinger:1 needed:1 sharply:2 particular:4 33d:1 potential:3 must:2 high:2 springer:1 smears:1 quantized:2 effectively:1 equation:13 averaged:1 oscillator:14 measures:5 remain:1 values:4 ρt:2 resembles:2 following:1 my:4 example:6 stimulating:1 history:8 beautiful:1 grained:2 transition:2 figure:7 give:1 calculation:1 neglected:1 involve:1 weighting:2 arise:1 absolute:2 rather:2 scarring:1 get:2 regions:1 how:4 instead:3 ordinary:1 verlag:1 sin:1 map:9 description:3 may:5 oscillators:3 earlier:1 space:13 orbits:2 collection:1 expectation:1 reflect:1 applications:1 phenomenological:1 summarize:1 choice:1 types:1 diffusion:7 short:1 quasiclassical:7 coarse:10 effective:1 resemble:1 light:2 grant:1 explicit:2 correspond:3 projectors:1 duffing:7 baggage:1 switch:1 cannot:1 so:5 specifying:3 fundamental:2 correlation:3 representation:1 order:2 exclusive:1 wigner:7 closely:2 reservoir:8 cutoff:2 developed:1 over:11 murray:1 course:3 attitude:1 xi:6 london:1 statistical:1 differs:1 its:6 environmentally:1 dξ0:1 derive:1 group:1 termed:1 interesting:3 jim:1 exhibits:1 fruitful:1 better:1 strange:4 degrees:3 systems:23 persist:1 er40701:1 might:1 correspondence:1 them:4 combination:1 irreversible:1 numerically:1 effects:1 they:4 own:1 now:2 discuss:3 easily:1 february:1 indeed:2 always:2 level:1 identified:1 pinv:5 possibilities:1 sufficiently:1 lorenz:1 each:5 found:1 side:1 characterized:1 mean:1 subsystem:1 differential:1 england:1 doing:2 series:5 energy:2 displacement:1 related:2 gutzwiller:1 investigated:1 expect:4 todd:1 quantum:53 our:1 approximated:1 t1:1 special:1 out:6 large:3 shown:5 matrix:4 driving:3 factors:1 restricted:1 since:3 induces:1 chaos:19 generation:1 looking:4 re:1 socalled:1 dowker:1 induced:2 correct:1 inevitably:1 trajectories:3 theory:11 little:2 treatments:1 fractal:4 indices:1 completely:2 threedimensional:1 california:1 term:5 advisor:1 attendant:1 dx0:1 e1:1 inevitable:1 additional:4 guckenheimer:1 enormous:1 interaction:2 could:1 similarly:1 times:12 motion:9 ordering:1 length:1 consequence:1 onto:2 think:1 first:3 size:1 indebted:1 initial:3 daunting:1 probability:14 variables:5 computers:1 number:2 clear:1 done:5 least:2 another:1 pablo:1 impossible:2 open:1 illustrate:2 given:6 ian:1 temperature:3 width:1 introduction:2 nondissipative:1 behaves:1 system:22 approximately:3 their:6 assumption:1 master:4 too:1 calculations:1 analytical:2 leggett:3 exponents:1 gives:3 kolmogorov:1 collapse:1 centered:3 distribution:11 tool:1 exactly:1 eliminates:1 part:1 x2:1 off:2 x0:6 x1:3 than:3 specify:3 dynamical:1 peaked:4 wide:1 kind:1 molecular:1 isolation:1 second:1 halliwell:5 preparation:1 states:2 lloyd:1 pqn:2 measure:2 treated:3 distinguished:1 projections:2 exhibit:5 ρdt:1 fashion:1 reproduces:1 fluctuation:1 ann:1 turned:1 already:1 qualitatively:1 need:1 seen:1 seem:1 clearly:2 chirikov:2 forced:7 γk:1 studying:1 isolated:1 note:2 ideal:1 without:2 absorbed:1 quantizing:1 finding:1 towards:2 allow:1 trace:2 though:7 any:1 who:1 most:3 retaining:1 analytically:1 extremely:2 why:1 exponent:1 enumerating:3 average:1 physica:2 doe:1 feynman:3 points:10 undeniably:1 exp:6 mechanical:2 ueff:1 typically:2 sum:3 laws:3 phenomenon:1 show:2 queen:1 friction:2 solutions:3 goes:2 x3:1 fine:3 find:4 help:1 based:2 knowledge:1 dp0:1 dissipative:14 guidance:1 histories:29 should:2 freedoms:1 only:11 going:1 x4:1 ambiguity:2 quasiperiodic:1 equivalents:4 hamiltonians:1 interested:2 achieve:1 do:3 his:1 gains:1 means:2 zurek:3 de:1 fluid:1 bear:1 truly:2 pq1:2 conceptual:1 unimportant:1 ones:1 foremost:1 dx:3 dt:14 du:1 ds:3 coth:1 evolution:8 exhibiting:1 continuum:2 fields:2 arxiv:1 thermal:4 yield:1 underlying:1 common:4 qi:5 including:1 qk:2 fixed:3 gell:5 view:1 kernel:2 set:7 thesis:1 correlations:1 connections:2 see:7 individual:5 college:1 usefulness:1 discussions:1 close:5 vint:2 analog:4 techniques:1 surfaces:1 caldeira:3 eigenfunctions:1 schack:1 currently:1 tend:1 state:14 closed:2 between:3 crude:1 invariant:6 approach:6 interpretational:1 recently:3 initially:3 suppresses:1 however:1 wi:3 interfere:1 vernon:3 jr:1 fluctuations:1 multivariable:1 alters:1 both:2 ssys:8 realizable:1 limits:1 many:5 taking:2 density:6 according:1 connection:1 grain:1 argue:2 mann:5 among:3 nonrelativistic:1 reasons:1 ca:1 others:5 harmonic:2 121a:1 assertions:2 lagrange:1 polynomial:1 broadens:1 considers:1 considering:3 decohere:2 pq:1 described:2 addition:2 trajectory:5 locally:1 due:1 been:8 quickly:1 springerverlag:1 much:2 treat:3 interest:4 basic:1 ph:2 pi:12 pn:1 mary:1 choose:1 field:1 generating:1 describe:1 corresponding:3 quantities:1 cos:4 maps:2 coherent:5 those:4 bifurcations:1 case:8 attractors:1 p0:6 p1:7 look:2 value:2 choices:1 will:11 while:7 match:1 behavior:8 hωk:1 discretize:1 larger:1 chaotic:10 averaging:1 thus:3 non:4 surface:6 ik:1 ij:1 vanish:3 technology:1 substructure:3 different:3 juan:1 inc:1 author:1 perhaps:1 distributions:3 make:5 poincar:2 parts:1 quant:1 widely:2 finite:2 coarsegraining:1 difficult:2 evolve:1 used:5 peaks:1 paths:1 numerical:9 effect:1 hand:1 action:2 moving:1 scale:2 intended:1 infinite:1 sres:2 ideally:1 lower:1 task:1 schr:1 nevertheless:2 acknowledge:1 well:5 analysis:1 thought:1 contact:3 solve:1 experimental:1 sets:3 position:1 model:7 reward:1 arising:4 dimension:1 usual:6 just:1 less:2 generally:2 rest:1 ideas:1 assigned:2 intervals:4 summed:1 shorthand:1 alternative:1 yet:1 projection:3 nicolas:1 like:3 preprint:1 conclusions:2 workers:1 point:5 except:1 simple:3 valid:1 lett:2 theorem:1 stable:2 extensive:1 profitably:1 euler:1 take:4 unravelled:1 casting:1 around:1 rules:2 sums:1 possible:10 corresponds:1 indicative:1 wojciech:1 using:6 amply:1 unique:1 occurring:1 displaced:1 necessary:1 δx:5 particle:1 follows:1 collective:1 unstable:5 integrals:2 become:2 4mm:1 mathematical:1 traced:1 methods:1 classical:39 sequence:3 pαi:1 some:8 zheng:1 choosing:1 specified:1 oscillations:2 neglecting:1 provided:1 total:1 unavoidable:1 integration:1 best:1 eliminate:1 provides:2 demonstrated:2 noise:15 obey:4 power:1 equivalent:1 paper:1 step:1 diosi:2 cα:2 properties:2 takes:1 about:6 pα:2 carried:1 freedom:3 am:1 dependence:1 o:3 simulation:2 practical:1 convenient:1 range:3 fell:2 extensions:1 obeys:1 underway:1 αi:2 other:3 seeing:1 twi:1 dξ1:1 offdiagonal:1 presence:3 into:7 within:1 integral:1 functional:13 variable:3 appropriate:1 because:2 references:2 operator:6 statistics:1 deal:2 area:1 there:12 approximate:4 brun:4 restricts:1 quadratic:1 low:2 way:5 was:3 pasadena:1 damping:4 function:8 complete:2 form:4 becoming:1 but:9 sophisticated:1 delta:1 fg03:1 true:3 considerable:3 condition:3 jonathan:1 versions:2 2πi:2 cells:3 up:3 us:2 until:1 ωk:2 frequency:3 limit:21 demonstrate:1 problem:6 define:4 calculated:2 gisin:6 mechanics:4 separated:1 interval:2 constant:2 debye:1 dp:1 defined:3 certain:6 abstract:1 measurement:1 influence:3 general:1 dξ:1 single:3 right:1 together:1 simulations:2 formalism:12 graham:2 defines:1 functions:2 compared:1 qδ:1 no:3 when:2 application:2 unparalleled:1 details:2 normal:1 department:2 forcing:1 draw:1 elements:1 calculating:1 savage:2 kt:1 shepelyansky:1 includes:2 generated:2 important:2 suppression:2 dissipation:9 generalized:1 westfield:1 structure:4 nonintegrable:2 regime:1 algorithm:1 physics:4 required:1 orbit:1 rule:1 graining:10 volumes:1 time:12 decoherence:27 izrailev:1 original:2 evenly:1
|
quant-ph9508023.txt |@word consider:5 sagdeev:1 results:3 computation:1 go:1 causes:2 whose:2 depend:1 γn:2 γm:1 under:3 applied:4 amplitudes:2 far:1 frequencies:2 rise:4 wave:5 mixing:2 exact:2 condition:4 level:9 cause:2 solution:5 t0:40 solved:1 small:5 eigenvalues:1 strongly:1 hk2:1 hk1:1 direct:1 past:1 second:4 quite:1 nonlinear:1 appear:3 section:2 version:2 above:5 new:3 increasing:1 method:4 full:2 respectively:2 lem:1 here:2 explore:1 possibility:1 strong:8 equations:3 appears:2 obtained:2 exemplified:1 clarify:1 shift:1 p2:2 accomplished:4 stressed:2 via:1 useful:1 substitution:1 nk2:1 redefining:1 would:1 prove:1 remains:1 next:2 comparing:3 taken:1 introducing:1 company:1 odinger:3 validity:1 known:2 must:1 springer:1 quantized:2 henri:1 equation:5 following:2 example:2 give:3 calculation:1 neglected:1 numbers:2 arise:1 verlag:1 turn:1 write:1 how:1 parameter:1 oscillatory:1 may:2 derived:1 inst:1 waves:4 meaningful:1 stress:1 continuos:1 so:5 fundamental:1 order:19 developed:1 pointed:2 ities:1 paper:3 through:2 resummed:1 kinetic:1 still:2 derive:2 till:1 fix:1 actually:2 harmless:3 systems:1 penn:1 main:4 them:2 now:1 realize:1 eigenvalue:1 term:10 indeed:1 hamiltonian:5 each:1 2m:3 mean:1 exemplify:1 ei:5 series:5 energy:4 poincare:1 quantum:12 our:3 avoided:1 eq:7 out:3 shown:1 nuovo:3 rev:4 chaos:1 increase:1 acting:1 ref:8 integrated:1 shows:2 benjamin:1 theory:19 assured:1 free:2 standard:5 difficulty:1 surely:1 york:1 put:1 e1:5 e2:6 interaction:4 could:5 introduction:1 nω2:1 retain:1 neglect:1 first:4 origin:2 already:1 directly:1 open:2 given:5 perturbation:22 ordering:1 leading:9 structured:1 system:5 least:1 perturbations:9 too:1 gives:4 lot:1 part:3 x2:1 eliminated:1 wide:1 kind:1 showed:3 cimento:3 submitted:1 matter:1 perturbative:1 behaviors:1 rewrite:1 ann:1 modern:1 spectrum:1 seen:1 linked:1 able:1 k2:3 k1:2 forces:1 sakurai:1 switching:1 unperturbed:2 any:1 rhs:3 cummings:1 phase:4 class:2 considered:3 average:1 face:2 normally:3 show:5 v12:12 anyway:2 solutions:1 zaslavsky:1 should:7 only:1 going:4 factor:2 goes:1 means:2 dt:19 du:1 adiabatically:1 evolution:8 turbulence:1 arxiv:1 view:1 set:1 sep:1 see:5 sec:6 result:2 analog:2 cole:1 away:2 iγn:1 drawn:1 reading:1 conditions:1 joye:1 publishers:1 terms:3 attention:1 however:5 jr:1 js:1 jm:3 jn:3 uψ:1 cos:2 tractable:1 attributed:1 contribution:2 comes:1 otherwise:1 mechanics:7 cn:4 pendulum:2 point:3 simple:2 simply:3 polynomial:2 considers:1 publishing:1 due:4 harwood:1 ph:2 define:1 v21:2 arises:1 corresponding:1 determination:1 case:2 exponential:1 resummation:1 evaluated:1 will:3 behavior:1 unitary:4 chaotic:1 vm:1 vn:9 frasca:6 different:2 verified:1 k2v:1 same:1 orders:4 beside:1 shifts:10 quant:2 arguments:1 higher:7 development:2 independent:1 effect:5 v1:11 v2:11 levels:3 recent:1 schr:3 well:2 academic:1 without:1 solve:1 roma:1 model:6 arising:1 just:3 being:10 summed:1 eigenstates:1 conclusions:2 easy:2 theorem:2 eigenstate:1 marco:1 easily:3 showing:1 sums:1 possible:3 using:1 like:1 particle:6 systematically:1 reduces:1 adiabatic:8 yields:1 become:1 works:1 methods:2 classical:4 some:2 examples:1 apply:2 ported:1 avoid:1 does:2 assuming:1 bessel:1 prob:1 limitations:2 although:1 found:1 perturbed:1 h0:26 operator:9 strictly:1 question:3 philadelphia:1 noticed:1 italia:1 way:2 was:1 function:2 form:1 but:1 partially:1 ponderomotive:1 us:1 limit:2 mk1:1 problem:11 similar:1 called:1 originating:1 constant:2 computing:1 recognize:1 abstract:1 general:3 again:1 functions:1 compared:2 no:1 when:1 application:1 mathematics:1 picture:3 problems:3 deriving:2 treatable:1 mω1:1 suffers:1 assume:2 physics:1 rule:1 4m:2 mass:1 time:7 understand:1 having:2
|
quant-ph9508024.txt |@word limited:1 consider:3 ceases:1 squared:2 results:7 perelman:1 four:1 fig2:4 fig1:4 constants:1 displaying:1 localized:2 scr:1 depend:3 aug:1 graph:1 recurrence:1 those:2 unnormalized:1 division:1 amplitudes:1 t12:1 relatively:1 wave:66 electron:2 figs:1 reforms:1 experimentally:3 difference:1 presented:1 culminating:1 large:5 small:3 noted:1 approximately:2 periodicity:9 pulse:6 second:1 displays:1 further:1 canonical:3 even:1 what:1 appear:4 apparatus:1 sum:2 localization:1 expressed:1 agrees:1 experiment:3 ψcl:2 above:2 fractional:26 new:9 method:2 coefficient:3 full:24 christian:1 chose:1 respectively:2 here:2 atoms:4 ionization:1 explore:1 others:1 alone:1 appears:3 change:1 obtained:1 technical:1 study:1 larger:1 later:1 periodic:1 published:1 hospitality:1 suitable:1 der:1 plotted:3 azimuthal:1 scales:4 noordam:1 visible:1 org:8 apply:1 total:1 predicted:2 plot:2 use:3 would:3 distinct:5 predictions:1 few:1 ψn:2 therefore:2 indiana:2 associated:1 type:2 theoretical:2 more:7 fractions:5 commences:1 comparison:1 snoek:1 keplerian:2 normalized:1 known:1 actual:1 cases:1 hold:2 must:1 me:1 defines:2 science:1 equation:1 work:1 slices:1 macroscopically:3 values:7 evolved:1 example:7 performed:1 figure:20 expanding:1 purposes:1 states:1 indicates:2 numbers:2 feasible:1 hydrogen:6 occur:2 absolute:5 generally:1 end:1 quantph:1 rather:2 eigenenergies:1 write:2 instead:2 explains:1 circular:10 simplicity:1 product:1 description:2 may:3 earlier:2 orbits:1 stroud:7 plane:2 demonstrating:1 waves:1 types:1 short:2 outline:1 effective:1 resemble:2 sr:3 lines:1 correspond:2 sh:1 so:1 decreasing:1 subsequently:1 order:4 typical:1 ϕk:4 hierarchy:2 indeed:1 insight:1 feature:1 produced:1 nauenberg:1 experiments:4 through:2 still:1 its:2 delay:4 group:1 chosen:1 sα:1 exhibits:2 detected:2 fig:3 remarked:1 tsr:16 them:2 greater:11 thereby:1 conversations:1 outlined:1 yb:1 primary:1 effects:5 they:3 half:1 represents:1 term:8 several:3 den:2 university:2 radians:1 labeling:1 magnitude:2 2a:2 reasonable:1 radial:9 found:3 square:7 evolve:1 series:4 energy:2 gaussian:2 related:1 expect:1 sectional:2 quantum:8 our:4 beyond:1 eq:2 special:2 out:1 shown:2 dominates:1 factors:2 periodicities:9 robert:1 since:5 interference:1 time1:1 weighted:1 rational:2 size:2 ref:5 occurs:1 shows:8 after:6 theory:2 written:2 possibility:1 reason:1 formation:8 hep:1 definition:1 fixed:1 created:2 determining:1 could:3 times:22 motion:2 produce:1 undergo:1 exhibited:1 first:7 key:1 there:1 features:3 rydberg:17 averbukh:1 number:3 smaller:2 defects:2 directly:2 angular:4 illustrate:1 1q:2 passes:1 given:4 1t:1 revival:33 indicate:2 tate:1 system:2 construct:1 1a:2 their:2 1c:1 1b:1 1e:2 1d:1 scheme:1 structures:4 way:2 mostly:1 asymmetric:2 explanation:2 alan:1 reflecting:1 than:20 coefficients:5 oscillate:1 peaked:1 observed:4 third:2 likely:1 amplitude:1 were:2 radius:1 treated:1 trev:38 spectrum:1 seen:5 orders:3 collapse:1 angle:1 depending:1 studying:1 responsible:1 k3:1 k2:1 take:1 modulus:2 begin:1 multiple:2 though:1 microseconds:1 involving:1 letter:1 phase:4 clear:1 adopt:1 metal:4 exp:4 kt:2 oscillates:1 physics:3 3q:1 ritsch:1 parker:2 spaced:1 show:2 detection:1 probe:1 purely:1 find:2 principal:2 q3:1 duncan:1 state:2 should:3 only:2 explicitly:1 colby:3 png:16 ien:2 mechanics:1 local:1 do:1 dominant:1 notation:1 means:2 dependent:2 expectation:1 closely:4 installed:1 evolution:2 consist:1 arxiv:9 tcl:13 consisting:2 paper:2 noncanonical:1 including:1 cycles:2 view:2 reveals:1 moduli:1 set:2 exists:1 undergoes:1 unpublished:1 enjoyed:1 packet:50 maximum:2 relative:1 college:2 result:1 close:2 αs:1 detect:2 reform:1 currently:1 pump:1 smallest:1 various:2 between:2 propagated:1 approach:2 available:8 terms:4 initially:1 however:5 nsec:7 hydrogenic:1 interface:1 reappears:1 configuration:1 concentrated:1 both:4 taking:1 equal:1 called:1 energies:2 figures:2 expression:1 ck:3 among:1 relevant:2 cn:4 timescale:1 cl:2 appeared:1 harmonic:1 coordinates:1 moreover:2 ps:8 agree:1 three:2 been:1 quickly:1 much:6 wolde:1 ph:12 lett:6 photoionization:1 corresponding:2 quantities:1 photon:1 defect:1 observe:1 present:3 case:7 hughes:1 laser:6 look:1 expanded:1 single:3 value:10 eigenstate:2 near:3 reformed:2 behavior:4 squeezed:1 zande:1 fielding:1 procedure:1 noel:1 thus:2 orbital:1 different:2 grant:1 suggest:1 kosteleck:4 cross:2 same:3 quant:11 largest:1 finite:2 independent:1 used:1 http:8 peaks:5 levels:1 changing:1 expand:1 recent:1 lower:1 lagendijk:1 charlie:1 well:4 without:1 coordinate:1 usual:4 µsec:14 just:1 less:1 commensurability:1 nanoseconds:1 obtain:2 shape:3 underlying:1 thanks:1 predicts:1 gaeta:2 eigenstates:1 multiples:2 previous:1 note:1 zoller:2 absorption:1 point:1 simple:2 corresponds:3 mod:2 excited:5 momentum:2 generalized:2 around:3 format:8 evaluate:1 comparing:1 period:7 bluhm:3 five:1 picosecond:1 integer:5 occurring:3 appearing:1 follows:1 signal:1 serves:1 alkali:4 either:2 reduced:1 because:2 often:2 classical:8 sequence:2 phenomena:1 duration:1 proofs:1 nonzero:5 provided:2 gradually:1 scale:5 does:4 provides:1 refer:2 2b:2 rep:1 2c:2 conventional:2 expansion:3 bs:10 losing:1 plots:1 exciting:1 properties:1 integers:1 about:1 central:2 reappear:1 discussed:2 alber:2 introduced:1 equally:3 rev:18 letters:1 presence:2 previously:1 into:3 within:1 revivals:19 en:1 determine:1 theoretically:1 van:5 classically:1 assumed:1 initial:6 long:3 width:1 fraction:1 bloomington:1 ten:1 naturally:1 function:35 elsewhere:1 form:1 femtosecond:1 some:1 delayed:1 but:2 pumpprobe:1 atom:3 subsidiary:8 line:2 true:1 collapses:3 illustrative:3 evident:2 2πi:3 characteristic:1 uv:1 up:2 below:1 autocorrelation:26 demonstrate:1 distribution:4 unequally:1 similar:3 display:1 strongly:2 linden:2 taylor:1 proved:2 defined:2 certain:1 peres:1 examine:4 lifetime:1 4q:1 distributions:1 physical:1 again:1 compared:2 when:5 interested:1 department:2 happens:2 superposition:1 excitation:5 centered:2 resembles:3 radially:1 slice:2 peak:1 conover:1 included:1 structure:11 l63:1 required:1 packets:20 orbit:3 original:3 uncovered:1 weights:1 time:40 crosssectional:1 n3:1 furthermore:2
|
quant-ph9508025.txt |@word limited:1 parker:1 ceases:1 show:1 rev:4 detection:1 atom:1 results:4 perelman:1 installed:1 shape:2 paper:4 through:1 integer:1 denotes:1 find:5 multiples:1 principal:1 expansion:3 delay:3 number:2 aug:1 energies:1 excites:1 editors:1 collapses:2 forms:2 detected:2 experiment:1 colby:3 lett:3 versa:1 ien:1 derivative:1 include:2 tsr:6 excited:3 alber:1 case:1 vii:1 greater:4 dependent:1 could:1 yb:2 term:4 wave:28 modification:1 ϕn:3 detunings:3 effects:5 closely:2 summarized:1 during:1 occurring:1 prime:1 evolution:3 presented:2 university:2 arxiv:1 tcl:3 culminating:1 method:1 alkali:3 experiments:2 each:1 including:1 entirely:1 cycles:1 optics:2 reduced:1 mean:2 possibility:1 because:2 occurrence:1 classical:4 sequence:1 series:3 energy:2 direct:1 packet:16 certain:1 see:1 college:2 quantum:9 beyond:3 eigenstates:1 provided:1 scale:1 appear:1 apparatus:1 reform:1 periodicities:4 robert:2 currently:1 use:1 time1:2 expressed:1 its:2 below:1 state:1 does:2 rational:1 fractional:8 new:6 foundation:1 induced:1 occurs:2 refer:1 coefficient:1 1q:1 particular:1 full:7 terms:2 written:2 initially:1 radial:1 seventh:1 however:1 here:1 atoms:3 pump:1 formation:1 york:1 hydrogenic:3 found:2 3q:1 stroud:1 additional:1 obtained:1 zoller:1 created:1 work:1 many:1 study:1 discussed:1 plenum:1 times:9 motion:4 prior:1 bluhm:3 periodic:2 wolf:1 published:1 expand:2 undergo:1 first:1 examining:1 relevant:1 cn:2 scales:5 rydberg:10 into:1 within:1 period:4 three:2 en:8 references:1 defects:6 determine:1 moreover:1 recombines:1 conference:1 conventional:1 long:2 smaller:1 n3:2 revival:24 indicate:1 distinct:2 initial:3 system:1 been:1 few:1 detuning:1 much:4 mandel:1 time:25 indiana:2 ph:4 type:1 national:1 ritsch:1 more:2 fractions:2 photoionization:1 corresponding:2 commences:2 furthermore:3 concerning:1 coherence:2 delayed:1 alan:2 part:1 pulse:1 bloomington:2 known:1 subsidiary:1 line:1 level:1 than:6 those:2 nauenberg:1 me:2 evolves:1 laser:6 science:1 nsec:2 mimicked:1 single:1 value:2 probe:1 macroscopically:1 examined:1 values:1 behavior:2 sum:1 under:1 stages:1 called:1 trev:15 function:5 required:1 packets:8 refs:1 functions:1 thus:1 weighting:1 examine:1 kepler:1 performed:1 eberly:1 around:1 different:3 rescaling:1 end:1 grant:1 supported:1 sh:1 kosteleck:5 noninteger:1 when:2 note:1 ny:1 interested:1 quant:3 generalized:1 department:4 instead:1 defines:2 used:1 multiple:1 description:1 may:1 averbukh:1 after:4 june:2 orbits:1 possible:1 phy:1 detect:1 keplerian:1 hep:1 revivals:9 rochester:2 summarize:1 200a:1 structure:9 feasible:1 short:1 third:1 vice:1 lines:1 usual:2 metal:3 disperses:1 e2π:1 order:1 cannot:2 exp:1 resembles:3 example:1 oscillates:1 physics:4 original:2 nearly:1
|
quant-ph9508026.txt |@word consider:3 varying:1 results:4 perelman:1 consists:1 ψcl:1 scr:1 depend:1 aug:1 conditions:1 wave:51 drexel:2 experimentally:1 nieto:3 difference:1 presented:1 correct:1 large:1 smaller:1 occurrence:1 periodicity:4 pulse:3 approximation:1 likely:1 pass:1 established:1 what:1 appear:1 apparatus:1 section:1 experiment:2 above:1 fractional:9 new:6 method:2 full:9 here:1 atoms:6 objects:1 along:1 quite:1 equations:1 appears:1 change:1 technical:1 shift:3 studied:2 prior:1 periodic:3 permit:1 resonance:2 suitable:1 plotted:1 family:1 scales:1 apply:2 tools:1 use:1 asymptotic:1 would:1 distinct:3 ψn:2 therefore:2 indiana:2 type:3 theoretical:2 more:4 commences:1 quant:3 keplerian:2 particular:1 known:4 must:1 me:2 evolves:1 keeping:1 oscillator:1 macroscopically:1 values:2 figure:2 purposes:1 states:10 weighting:1 minimum:1 performed:2 feasible:1 hydrogen:3 absolute:1 eigenenergies:1 delay:1 how:2 fourth:2 symposium:2 parameter:1 circular:1 oscillatory:1 product:1 description:3 modulation:1 after:1 orbits:1 stroud:1 waves:1 date:1 types:1 short:5 outline:1 third:2 lines:1 correspond:1 sh:1 order:1 talk:4 pulsed:2 ϕk:1 september:1 installed:1 produced:1 nauenberg:1 experiments:2 through:3 lasers:1 its:1 write:1 outer:1 chosen:1 exhibits:1 recombines:1 forms:1 detected:1 systems:1 derivative:1 tsr:7 averbukh:1 supersymmetry:2 greater:5 yb:2 detunings:1 effects:3 represents:1 term:1 university:2 level:3 orthonormal:1 radial:14 found:1 entirely:1 mean:1 en:7 series:2 energy:9 gaussian:1 quantum:14 our:5 eq:1 might:1 shown:2 periodicities:2 robert:2 since:1 rev:9 may:13 reader:1 illustrate:1 ref:1 occurs:1 shows:2 theory:6 localization:1 differ:1 possibility:1 standard:1 approaches:1 formation:2 generate:1 times:8 motion:7 first:3 features:1 render:1 rydberg:15 variables:1 number:1 philadelphia:1 defects:3 another:1 electronic:1 angular:1 size:1 1q:1 given:1 perturbation:1 revival:20 introduction:1 construct:1 final:1 pump:1 centered:2 alan:2 part:3 than:9 coefficients:1 observed:1 kind:1 determines:1 second:1 trev:18 defect:7 substantial:1 seen:1 clearly:1 rout:2 note:1 k2:1 multiple:1 index:1 culminates:2 phase:1 k3t:1 metal:7 disperses:1 looked:1 proceedings:1 exp:2 kt:1 physics:4 3q:1 ritsch:1 parker:1 show:4 probe:1 find:6 principal:1 based:2 parameters:1 state:10 controls:1 should:1 only:2 colby:3 ien:1 centrally:1 do:1 dominant:1 quantph:2 dependent:1 express:1 apsidal:2 ϕn:4 nearly:1 closely:4 evolution:5 fields:1 arxiv:1 shape:2 tuned:1 analytical:1 set:2 packet:26 detection:2 college:2 detect:1 written:1 difficulties:1 between:1 approach:1 terms:4 however:2 nsec:5 hydrogenic:4 both:2 zoller:2 many:1 invited:1 uncertainty:2 equal:1 energies:1 context:6 ck:1 among:2 cn:2 point:2 period:4 moreover:1 pr:2 described:5 three:1 been:1 detuning:4 much:3 expected:1 ph:4 define:1 photoionization:1 adopted:1 sufficient:1 excite:1 coherent:2 observe:1 coherently:1 2n2:1 those:4 case:4 laser:10 defining:1 expanded:1 appearance:1 examine:1 value:3 eigenstate:1 kepler:1 match:1 behavior:3 squeezed:14 iγ1:1 procedure:1 larger:1 refs:3 wkb:1 thus:1 different:5 suggests:1 generic:1 kosteleck:7 shifts:1 parts:1 speaker:1 units:1 used:3 singapore:1 numerical:1 levels:3 moving:1 expand:2 off:1 well:4 model:2 usual:1 nanoseconds:1 tcl:6 atomic:1 integer:2 eigenstates:2 candidate:1 similarities:1 spread:1 lett:3 profitably:1 excited:5 momentum:1 around:3 possible:2 harmonic:1 bluhm:4 background:1 world:1 particle:1 follows:1 alkali:7 either:1 nonintegrability:2 because:1 methods:1 classical:4 sequence:3 some:1 examples:2 oscillations:1 proofs:1 matching:1 generates:1 provided:1 scale:7 does:4 t12:1 refer:3 run:1 scientific:1 rep:1 equivalent:1 expansion:3 analyses:1 2n:1 comparison:1 central:1 carried:2 rederived:1 dependence:2 alber:2 referred:1 ψnlm:1 material:1 into:2 revivals:9 appropriate:1 square:3 references:2 determine:1 rely:1 hep:1 additional:1 initial:10 question:1 approximate:1 long:2 width:1 pa:1 fraction:1 bloomington:2 function:12 complete:1 form:3 governs:1 delayed:1 but:2 idea:2 construction:2 atom:3 subsidiary:2 line:1 consist:1 2πi:1 characteristic:2 sum:2 autocorrelation:5 distribution:1 similar:1 strongly:1 taylor:2 constant:3 certain:2 describe:1 single:1 arises:1 ensuing:1 functions:3 no:1 fixing:1 whereas:2 noninteger:2 generally:1 field:1 other:1 department:4 out:2 superposition:2 resembles:4 peak:1 variable:1 structure:8 assume:1 packets:20 orbit:2 original:1 time:24 n2:1 furthermore:1 external:1
|
quant-ph9508027.txt |@word exponentiation:10 reversibility:2 entropy:1 totient:1 consider:6 whose:4 violate:1 aug:1 speeded:1 under:4 rise:2 every:6 affect:2 logarithmically:1 school:1 solution:2 vector:13 deutsch:10 miller:2 likely:7 rigorous:1 implemented:2 machines:17 even:5 negates:1 errorcorrecting:1 above:18 designing:1 negated:1 ever:1 coefficient:1 margolus:3 never:2 here:6 atoms:1 represented:6 path:2 calculate:1 digits:1 inefficiently:1 study:4 changed:1 schnelle:1 permit:1 fourier:20 settled:1 offs:1 divide:3 classification:1 explained:1 replace:2 rφ:1 pp:62 brc:1 linearly:1 solovay:3 plot:1 would:28 likelihood:1 call:1 therefore:1 25th:1 type:2 los:9 decomposable:1 fractions:2 holy:1 reversibly:5 reversible:34 hold:4 must:10 springer:5 word:4 room:1 work:16 concepts:1 example:7 give:15 bennett:14 organized:1 involve:1 want:2 times:5 absolute:5 motion:1 end:1 turn:3 imprecision:3 machine:25 how:11 gate:69 beach:1 brassard:5 description:6 replacing:1 turing:22 after:6 minimized:2 minimizes:1 law:1 parallel:1 types:1 third:7 summing:2 complexity:14 algorithms:26 suggest:2 tantalizing:1 order:27 operations:3 over:14 vary:3 murray:1 xi:2 london:8 thesis:18 japan:1 satisfies:3 before:5 somewhere:1 stimulated:1 writing:1 better:2 differently:1 potentially:3 hidden:2 easier:1 them:5 xa:12 tained:1 amenable:1 effects:1 they:14 structural:2 represents:1 40q:2 each:26 mean:2 independent:3 principles:1 literature:1 combining:1 clauses:1 onhage:8 divincenzo:5 rq:1 crucial:1 rb:3 rc:22 rl:4 ri:4 rj:6 numerical:1 turning:1 linear:1 assured:1 given:15 standard:4 vazirani:5 estimate:1 r0:3 r1:4 r2:4 decohering:1 machining:1 tempting:1 corrections:2 resetting:1 already:3 restrict:1 clarity:1 rewritten:2 similarly:3 top:1 approximately:2 needed:3 compromise:1 too:4 hypothetical:1 somewhat:3 showed:2 divisible:1 approximations:1 second:13 classes:3 kth:1 powers:12 extracting:1 manner:3 emphasizing:1 canny:2 seen:3 seem:2 tells:2 seminar:1 relatively:7 indexed:3 effectiveness:1 nobody:1 though:3 denominator:2 accurately:2 involving:1 germany:1 obermayer:1 phase:15 iterate:1 acknowledgements:1 points:1 principle:2 consumes:1 channels:1 signatures:1 random:12 nand:3 keywords:1 substituting:1 proposed:5 implementation:3 explain:1 thermodynamically:1 coefficients:1 constant:13 hamiltonians:1 do:20 cryptography:1 de:4 stop:1 simpler:1 congruent:1 reversal:2 despite:1 report:1 du:4 dq:1 runs:1 fields:1 method:18 bad:2 architecture:2 pointers:1 transforms:5 zahlen:1 observed:9 depends:2 result:18 fail:1 disturbing:1 best:9 techniques:3 exponent:2 discovery:1 preserve:1 terms:5 weak:1 however:18 extent:1 separately:1 34th:1 adapting:1 cos:5 colloquium:1 logic:7 exceeds:1 distinction:2 contribution:2 adapted:1 1982a:2 1982b:2 appeared:3 dissipating:1 polynomial:41 conference:2 basis:18 three:2 been:29 quickly:2 much:9 basic:1 expected:3 θk:1 coherent:1 2n2:1 spin:1 applied:4 say:2 transformation:7 euclidean:2 near:1 suppose:3 viii:1 aid:2 35th:4 leaves:9 procedure:1 ii:2 il:1 recover:3 perform:7 things:3 make:13 complex:6 quant:1 split:1 several:2 grows:2 fairly:1 schumacher:1 hand:1 programs:1 changes:2 academic:3 materials:1 greatest:1 endif:3 quantitative:6 left:5 teich:2 just:4 farther:1 yamamoto:1 yet:5 previous:1 adding:1 candidate:5 had:3 wright:6 easy:2 gave:3 reuse:1 advances:1 possible:21 possibly:1 performance:1 advanced:1 coarseness:1 performing:1 specific:2 informative:1 steps:8 arbitrary:2 nonintegrability:1 beneficial:1 right:3 deal:1 people:1 successfully:1 escape:2 confusing:1 precomputed:1 bpp:2 comments:1 asking:1 unit:3 shamir:2 sherman:2 algorithmic:3 pose:1 confer:1 substitution:1 post:4 super:1 properties:5 chapter:1 o:26 distinct:2 misleading:1 considerations:1 raised:1 statements:1 obtaining:4 bound:5 down:3 multiply:8 acad:2 formidable:1 amsterdam:1 reducing:4 often:2 suffice:1 transform:15 class:8 physicists:1 fraction:10 resulted:1 was:14 lowest:3 form:2 converse:1 failure:1 true:4 reset:2 arrays:14 devices:2 stages:2 proved:1 zeno:1 computing:26 abstract:1 evidence:1 peres:4 exist:1 simulations:1 check:1 physical:9 nj:1 nm:1 no:8 agreeing:1 na:1 ekert:6 when:16 reality:1 ny:1 interested:2 digital:6 test:1 superposition:10 models:8 palma:3 variable:3 faster:4 assume:2 bottom:1 together:1 time:62 serious:1 n2:2 quantity:2 logarithms:14 remarkable:1 roy:6 computation:74 primes:8 inverse:2 depend:3 technique:9 environment:1 rightmost:1 efficiencies:1 bqp:1 analogous:3 division:1 advantage:1 dokl:2 choice:2 drexel:1 entries:1 exact:4 riemann:1 presented:1 did:6 leave:3 discrete:22 recall:4 vetter:1 phrasing:1 upper:1 says:1 dealing:1 cost:5 substitute:1 adds:2 appear:9 uniform:4 goes:1 international:2 satisfy:1 alone:1 along:2 sieve:5 appears:4 change:8 box:1 institute:2 popescu:1 studied:3 bob:1 automaton:1 studies:1 plotted:1 useful:9 santa:3 extra:7 merely:1 logical:2 inverses:1 alamitos:9 working:2 prove:1 going:1 memory:5 theoretical:4 outputs:4 apparent:1 cases:1 logarithm:3 ibm:2 originally:1 hardest:1 values:15 cal:1 following:5 making:7 trans:1 nearest:3 figure:2 sample:2 allowed:2 distinguishable:1 occur:1 redundancy:2 fortunately:1 discussion:2 s0:6 grosser:1 write:2 subroutines:2 criterion:1 fourth:1 optimal:1 divides:4 inputs:1 product:3 designer:1 emde:3 may:14 fed:1 residues:3 produce:1 lenstra:11 representations:1 data:1 grow:2 natural:3 johnson:1 purification:1 sj:7 switch:1 so:18 sl:3 increase:6 indeed:3 fredkin:12 soc:8 course:1 experiments:1 cold:1 still:2 ieee:11 group:6 thank:2 interesting:2 correspondence:1 non:12 processes:1 introduce:1 scaling:1 half:4 arriving:1 nov:1 now:19 maintaining:1 factorising:1 term:6 equality:1 stabilize:1 crypto:1 inaccuracy:2 possibilities:2 classify:1 square:4 ed:7 sov:1 approximates:1 shown:9 factors:9 rounding:2 furthermore:2 interference:2 looking:1 contained:1 investigation:2 correct:2 shows:4 earlier:2 theory:18 seventh:2 possibility:4 quite:2 complicated:4 remainder:5 benioff:2 programming:2 3r2:3 thing:1 place:1 gordon:3 think:2 first:39 xk:10 intuition:1 simplifies:1 clause:1 pseudocode:5 symbolic:2 requirement:4 approximate:3 long:6 directly:3 xr:12 impossible:2 array:26 open:3 size:11 little:1 necessarily:2 checked:1 unruh:3 dissipate:1 bits:40 hardwired:1 gives:11 way:5 obtained:2 date:2 x2:5 eliminated:1 copy:2 representing:2 than:24 intrinsically:1 effective:1 encrypting:1 require:1 were:4 outcome:1 nozaki:1 20q:4 ann:1 turned:3 argument:2 1992a:2 1992b:2 weinfurter:5 any:30 computationally:3 efficient:3 converges:1 note:10 sciences:1 potential:4 take:9 new:6 strengths:1 switching:1 channel:1 multiple:5 track:2 knew:1 pair:5 especially:1 considered:1 later:2 feynman:3 laws:7 precise:5 shor:21 show:14 discovered:4 log2:1 fifth:1 feng:1 specifically:1 only:46 explicitly:1 black:1 1995b:4 get:10 truly:1 cannot:3 nearly:2 trade:1 prime:30 resource:2 circuits:6 umesh:1 mapped:2 ignored:1 physically:5 comparable:1 ignores:1 euclid:1 fails:2 satisfying:3 ways:3 subsequent:1 enough:10 un:1 jth:3 between:10 αi:3 justified:1 reading:1 notice:2 jq:2 jr:2 comm:1 multiplier:1 realizable:4 implementing:1 many:7 personal:3 expression:10 characterization:1 maintained:1 cancel:1 boas:3 considers:1 noisy:5 configuration:1 workshop:3 direction:5 enable:3 andrew:1 observe:5 those:2 paying:1 promising:1 worry:1 binary:7 different:1 develop:1 same:16 arguments:1 pai:5 investigated:1 closest:1 running:3 entanglement:1 invariance:1 faithful:1 ıvely:1 without:2 solve:7 components:2 very:5 model:5 whereas:2 researchers:2 gates:37 unsolvable:1 being:6 generally:5 rest:3 aspect:1 ithaca:1 multiples:3 zoller:3 photons:1 seems:6 improvement:1 lett:6 suominen:1 around:3 read:1 papers:4 early:1 np:6 using:19 ams:1 accepted:1 mod:78 particle:1 steiglitz:4 reduces:2 benefit:1 either:6 multiplicative:4 output:33 reduced:3 conditional:1 deduce:2 erase:4 table:8 extensively:1 conservative:1 critical:1 adleman:9 measuring:3 reasonable:9 power:26 kyoto:1 calmet:1 found:4 repeating:1 rearranging:1 central:1 choi:2 discussed:1 meaning:2 acm:5 practical:2 greatly:2 mixed:1 acyclic:2 mannheim:1 perturbed:1 communication:4 dissipation:1 references:2 stabilisation:1 elementary:4 watchdog:1 technically:1 log:44 there:36 start:2 low:2 complete:8 smolin:2 cloned:1 trying:1 irreversible:1 longer:1 applying:2 agree:2 multiplications:1 expect:1 ac:4 cirac:3 ai:6 certain:2 describe:3 general:4 aq:9 formulation:1 corresponding:5 again:2 drafts:1 field:7 mathematics:2 you:1 briefly:1 odlyzko:2 a0:3 important:3 bounded:2 building:6 decoherence:10 evenly:2 original:1 represent:3 sci:3 forget:1 chinese:3 program:2 bakker:1 case:3 amplitudes:5 far:1 supercomputer:1 bottleneck:1 condition:5 treating:2 hamiltonian:4 list:1 large:18 small:16 zero:4 design:1 further:12 canonical:2 residue:4 what:3 generator:7 section:5 brief:3 version:5 scientists:3 public:4 leeuwen:2 component:3 ranges:2 modular:10 directions:1 strong:1 observing:7 divisor:3 inspired:1 allows:2 amount:8 permutation:1 uniquely:2 invalidate:1 via:1 requiring:1 ask:2 send:1 sch:8 takes:9 levine:2 probabilities:4 finally:2 automata:6 correspondents:1 taken:3 entails:1 more:19 knows:1 particular:9 known:9 foundations:7 producing:1 presumed:1 keeping:2 science:18 equation:8 remain:1 changeover:1 history:1 ions:1 compare:1 suggestions:1 accept:1 states:19 minimum:1 numbers:24 sense:1 information:4 needs:2 breaking:1 algebra:1 weaknesses:1 derived:1 mapping:2 fe:2 contrived:1 short:1 generalizations:1 register:11 fundamental:4 rounded:1 ith:4 developed:1 fft:1 pseudorandom:1 paper:13 through:4 berthiaume:4 its:8 continued:1 solving:2 cryptology:2 actually:5 squaring:2 microscopic:1 systems:3 might:6 alter:1 good:26 universality:1 sssr:1 knuth:10 oxford:1 speculate:1 yu:1 easily:5 gets:1 2p:2 2q:4 2r:1 always:2 2d:1 inequality:1 2l:5 inherent:1 2n:6 polynomially:3 2i:4 2j:3 2k:9 constructing:2 energy:3 hard:6 reduce:4 idea:1 slowdown:1 wires:4 obtains:1 measurement:3 quantum:214 operation:4 try:4 solved:3 since:29 research:3 hill:1 issue:1 occurs:1 difficulty:3 reason:2 imagine:1 put:3 beginning:1 definition:6 pairs:3 optics:1 computers:34 round:1 exponentially:1 circuit:2 probability:43 number:49 done:9 construct:1 distributive:1 introduction:3 leading:2 least:32 statement:1 scheme:2 relationship:1 trapped:1 akad:1 luckily:2 part:3 translation:1 believe:3 convinced:1 kind:1 nonreversible:1 cyclic:4 determined:1 treated:1 comput:5 substantial:1 conjugate:2 elsevier:1 paths:1 built:12 depending:1 zp:1 internat:2 costs:1 build:4 analogy:1 finding:11 english:1 reach:1 most:24 assoc:1 significant:1 nothing:1 measured:1 mach:1 kc:1 clear:3 sometimes:3 exp:29 physics:10 particularly:1 registers:3 relation:1 find:20 depended:1 dividing:6 exponentiations:1 pomerance:2 penalty:1 generators:3 factor:16 circle:1 bernstein:5 columns:3 abelian:1 notation:1 dependent:1 zurek:2 fastest:1 closely:1 during:1 him:1 arxiv:1 factorization:7 common:6 caise:1 set:14 art:1 potentiality:1 tended:1 plausible:1 see:9 close:6 11th:1 theoretic:1 analog:7 mechanically:1 currently:6 various:1 conditions:9 15th:2 knowing:1 recently:1 initially:1 untouched:1 both:16 paradigms:2 improved:1 reverse:6 desired:3 solely:1 annual:12 sensitive:1 context:1 whole:2 finds:1 experimental:1 point:3 simple:6 asymptotically:9 cryptosystem:1 corresponds:4 dimensional:2 adaptation:1 church:15 addisonwesley:1 throughout:1 expensive:2 worthless:1 pq:3 described:3 transformations:14 lattice:1 due:1 reduction:1 coarse:1 ph:1 pi:6 addison:1 convert:1 else:1 understand:1 practicality:1 classifications:1 look:1 exponential:10 expanded:1 while:10 replaced:1 behavior:1 error:11 landauer:3 unitary:17 laflamme:1 vol:6 itself:2 italy:1 randomization:1 widely:7 higher:1 development:3 used:12 mountain:1 uses:4 purpose:1 robust:1 lower:4 underlies:1 analysis:1 person:1 endfor:3 entry:6 comprise:1 alternative:1 letting:1 tables:3 kluwer:2 readers:1 scales:2 theoret:2 theorem:10 input:38 ruled:3 solvable:2 remaining:1 euler:1 generalized:1 showing:2 isomorphisme:1 philos:1 eiθk:1 integer:12 bit:37 projects:1 helpful:1 pertinent:1 improbable:1 envisioned:1 follows:9 ignore:2 imposes:1 yields:1 spins:1 mathematical:5 sketch:1 methods:3 some:18 back:1 b0:1 examples:2 28th:1 scale:1 describing:1 measurements:5 integration:1 behave:1 connecting:1 proc:7 bd:5 run:1 bc:6 bl:1 processing:2 bi:1 bj:3 bk:1 bt:1 step:6 br:7 dictated:1 hilbert:3 superpositions:2 integers:5 pα:8 anything:1 completing:2 simulation:2 range:1 preset:2 block:1 seeing:2 computational:4 into:19 within:1 integral:9 appropriate:1 proportional:1 coppersmith:4 rows:3 few:3 question:6 fast:7 handbook:1 analyze:1 considerably:1 cryptanalysis:1 repeatedly:1 russian:1 line:2 2πib:2 2πi:11 up:3 us:9 2πiw:1 2πiv:1 sum:12 called:2 associated:1 worthwhile:1 defined:1 specified:3 single:1 codes:2 fixing:1 application:4 arithmetic:1 elements:1 gf:1 problems:24 polynomials:1 generated:2 allowing:3 vectors:4 structure:8 feasible:2 independently:1 algorithm:50 required:5 tradeoff:1 oracle:3 requires:10 having:5 once:2 code:3 partial:1 results:7 existing:1 illustrated:1 eds:5 go:2 simon:7 knill:2 deterministic:2 factoring:35 languages:1 dickinson:1 include:2 resources:4 implicitly:1 putting:2 cellular:3 matrices:7 positions:2 notes:4 deals:1 seminumerical:1 barbara:1 mahler:1 smaller:2 imply:1 dynamics:3 correspond:5 odd:7 giving:1 3r:2 expressed:1 networks:1 access:1 experiment:4 respectively:1 teleportation:1 gilles:1 believed:4 objects:2 others:1 consideration:1 implicit:1 simulating:3 great:1 larger:3 resulting:2 postprocessing:1 implement:3 makes:4 heart:1 hardy:6 addressed:1 boneh:3 apply:7 use:29 asymptotic:3 toffoli:14 next:7 classically:3 duplicate:1 themselves:1 stage:4 ofman:2 started:2 challenge:1 obvious:1 proof:1 weaker:2 calculation:2 purposes:1 pieces:1 high:5 something:1 gcd:7 holds:5 arrangement:1 varies:3 instead:4 blocks:2 db:1 factored:2 productive:1 multiplication:21 efficiently:9 22nd:1 computations:11 counter:2 arrow:1 element:4 allow:1 s1:1 produced:2 mathematicians:1 including:1 looks:1 chosen:2 willing:1 choose:2 designs:1 pure:1 dan:1 practice:4 realize:1 february:1 university:1 lagarias:1 sufficiently:1 magnitude:2 l2:3 l3:2 truth:6 subset:1 illuminate:1 map:1 doing:4 society:11 computable:15 measure:1 our:23 robot:1 special:2 out:13 matrix:14 res:1 rev:13 performs:1 fran:1 lecture:4 cause:1 math:5 statist:2 undo:1 completely:5 york:5 jozsa:7 shortest:2 interaction:2 geometry:1 determining:1 could:16 keep:4 length:7 swapped:1 powerful:5 randomized:1 improvements:1 ser:6 simulated:3 πi:2 system:10 πr:1 their:8 intermediate:1 siam:3 perfectly:1 reversed:1 exactly:6 rsa:3 rivest:2 simulate:7 manipulation:1 july:1 subroutine:4 distinguishes:1 submitted:1 amplitude:10 unchanged:3 comfortable:1 discussions:1 unlikely:1 need:27 clearly:1 viewed:1 able:13 si:4 subject:1 lipton:3 unless:4 πaj:1 who:2 but:26 preliminary:1 device:7 why:3 tensor:1 looked:1 proceedings:19 workspace:2 mechanical:8 fact:11 charles:1 bring:1 planning:1 chuang:6 lloyd:4 trivial:2 q1:3 based:4 should:10 jan:1 bases:1 pascoli:1 local:1 hope:1 karatsuba:2 1995a:4 means:3 overall:2 joint:1 ones:1 words:1 compute:16 amer:1 evolution:1 ended:1 numerous:1 reif:2 nauk:1 qd:1 contain:3 fixed:4 view:1 moduli:1 multiplying:7 modulo:5 computed:5 operates:2 computer:109 primality:1 phases:1 nuclear:1 state:52 difficulties:3 progress:1 counterexample:1 publishers:2 ends:1 barenco:5 ability:1 transpose:2 efficiency:5 hypothesis:1 key:4 sleator:5 ket:1 distribution:1 david:1 limits:1 taking:1 equal:4 grail:1 otherwise:4 ck:3 huang:1 cl:1 ca:11 news:1 respect:3 addition:4 yap:1 yao:3 treat:1 define:2 aj:8 controlled:3 sufficient:3 coherence:1 essentially:5 last:5 present:3 harder:1 value:10 will:58 wilf:1 almost:2 thus:48 hardware:2 raison:1 ave:1 greater:2 ˆetre:1 perhaps:1 parts:2 largest:3 finite:2 twelfth:4 difficult:7 effect:1 architectures:1 infinite:1 identity:1 off:2 reflection:1 obstacles:2 well:1 thought:1 patterns:1 sets:2 scho:3 less:7 accurate:2 obtain:16 macroscopic:1 rapid:1 preprint:2 jeff:1 reasons:1 add:2 book:1 nato:1 tests:1 increased:1 know:11 press:13 turbulence:1 necessary:4 like:4 success:2 wooters:1 become:6 accessible:1 indications:1 because:18 classical:42 sequence:3 growth:2 choosing:3 peter:1 happens:1 est:1 lead:1 avoid:1 does:19 summand:1 assuming:1 transmitted:1 ensures:1 expansion:2 wesley:1 although:6 worthy:1 approximating:1 hiding:1 about:2 actual:3 carried:1 getting:1 universe:1 strassen:6 software:2 combinatory:1 equally:1 keeps:1 functional:1 en:1 tiny:1 thwart:1 van:5 additional:5 faithfully:2 applegate:1 function:4 extended:1 hu:1 repeated:7 construction:4 versatile:1 he:5 count:2 made:8 wise:1 whether:6 smooth:2 record:7 below:1 limit:2 problem:13 piece:1 cryptosystems:4 mechanics:19 universal:11 functions:8 trials:3 other:9 details:1 pollard:1 symposium:12 june:1 variation:1 precision:16 qπ:1 chance:5 space:25 rule:1 bcc:1 cleve:3 augmented:1
|
quant-ph9509001.txt |@word limited:1 consider:4 maximum:3 varying:1 trigonometric:1 existing:1 leads:2 jawaharlal:1 quadrature:7 invariably:1 consists:1 expressions:4 compact:13 preserves:1 inverse:2 depend:3 subjected:1 equivalence:2 finally:1 according:1 squeezing:15 under:12 eiα:1 case:15 straightforward:2 orthogonal:2 far:1 frequencies:1 implicitly:1 results:6 probability:1 handling:1 every:1 entries:1 experimentally:2 difference:2 matrices:2 condition:2 look:1 four:2 conjugating:1 level:4 ρu:2 scalar:2 large:1 vector:9 irreducibly:1 manifestly:1 optics:3 application:1 originate:1 ten:1 10b:1 10c:1 10a:1 measurable:1 sign:1 past:1 likely:1 evaluated:1 equal:2 qualitatively:1 canonical:3 even:3 aim:2 appear:2 ak2:1 section:5 favour:1 expressed:2 henceforth:1 experiment:1 above:7 new:3 acknowledgments:1 contrast:3 temperatures:4 lee:1 degree:1 respectively:7 never:1 component:1 here:4 behaviour:1 explore:1 simon:3 sinh:24 others:1 active:2 consideration:1 appropriate:2 quite:1 z1:40 z2:41 obtained:6 search:1 ref:1 antisymmetric:1 institute:2 involved:6 leaves:1 studied:2 denominator:6 amount:1 survey:1 action:4 implement:1 studies:2 york:2 formulated:1 followed:2 classification:3 9a:1 basel:1 9c:1 9b:1 9d:1 achievable:1 ϕu:51 apply:2 total:1 unit:4 plot:4 takes:2 would:1 nehru:1 covariant:4 iαt:1 contains:2 negative:6 hilbert:2 explicitly:2 kinematics:1 therefore:6 taken:1 simpler:1 theoretical:1 more:12 separated:1 anticorrelation:1 becomes:4 operators:21 stone:1 appendix:2 everywhere:1 basically:1 particular:9 cases:2 iii:2 vj:1 eβ:10 ρa:9 obeying:1 keeping:2 quartic:1 sphere:4 ed:1 science:2 equation:2 work:1 fock:4 subpoissonian:9 minimisation:1 concepts:1 following:1 arrive:1 figure:15 give:2 distributions:1 sps:23 india:4 increasingly:1 states:47 indicates:3 minimum:9 numbers:1 want:1 sense:3 occur:1 rather:1 discussion:1 six:1 feature:1 orthogonality:1 till:1 nontrivial:2 pure:1 parameter:24 ensemble:1 classify:1 u21:2 oscillatory:1 map:1 product:1 magnitudes:3 description:5 algebra:5 may:4 earlier:1 derived:1 lengthy:1 applications:2 explored:1 fd:1 minimizes:2 choice:6 meaningful:1 short:1 natural:1 moments:1 whenever:1 sp:20 explicit:1 su:21 st:1 ones:6 used:4 correlation:1 taking:1 representation:4 order:2 superscript:1 least:1 interpretation:1 help:2 considerations:1 developed:2 over:5 displayed:3 choose:4 interpreted:1 combinations:1 thermal:9 paper:5 through:9 statistical:1 left:1 benjamin:1 its:5 group:6 lc:1 singular:3 how:1 chosen:1 interesting:5 ll:1 lj:3 lk:3 conjugation:2 actually:2 resort:1 detected:1 parts:1 systems:3 main:1 decades:1 maximal:7 non:41 motivated:2 combination:5 polarizations:1 material:1 fig:6 obeyed:1 walls:2 effects:4 they:1 now:4 wiley:1 february:1 e2β:3 2s:1 always:1 university:1 presented:1 identified:1 displacements:10 possibilities:1 mccall:1 inequality:1 l2:1 mode:86 reasonable:3 each:11 side:1 mean:1 homogeneous:2 ei:1 weight:3 independent:4 there:1 displacement:8 related:8 recapitulate:2 extended:3 changed:1 quantum:5 our:6 eq:2 out:7 predefined:1 shown:4 lastly:1 matrix:14 rr:2 space:3 since:4 research:2 looking:1 acting:1 suffices:3 shows:3 disclose:1 after:2 linear:7 sudarshan:1 diagonal:7 possibility:1 standard:1 term:3 ǫjkl:1 8s:2 generate:1 definition:4 qj:1 r2:6 could:2 hyperbolic:1 bl1:1 v2:7 nonnegative:1 isotropic:1 u22:2 signature:4 hence:4 onto:1 exhibited:1 first:5 already:1 features:1 symmetry:3 variables:2 number:17 rank:2 exact:1 done:2 construct:1 another:4 carry:2 4b:3 precisely:1 illustrate:1 given:22 cartesian:3 temperature:3 their:5 introduction:1 leading:2 antibunching:2 amsterdam:1 system:4 relations:5 1a:1 needed:1 statement:2 eqn:6 john:1 gives:1 relative:4 larger:1 optical:2 jordan:1 review:9 yurke:1 eliminated:1 cosh:38 representing:2 than:3 intrinsically:3 center:1 detection:1 kind:1 holland:1 require:1 second:2 annihilation:8 determined:4 amplitude:1 dutta:2 minus:1 displays:1 generality:2 fluctuation:1 unchanged:1 curves:1 conjugate:1 need:2 north:1 element:2 twomode:1 any:10 elsewhere:3 reaches:1 zero:3 min:1 convenient:2 responsible:1 k3:1 mix:1 k1:1 so:1 components:3 lion:1 though:2 σj:1 reach:1 most:7 involving:5 phase:11 analytically:2 class:4 tensor:2 unequal:2 kk:3 kj:7 clear:4 kl:1 part:1 exp:11 mechanical:1 typical:1 physics:4 notion:7 fact:2 signatures:2 phenomenon:1 show:4 v12:2 dependences:1 minimizing:1 relation:1 definable:1 calculable:1 subtle:1 d2:2 q1:4 q3:9 q2:3 based:1 parameters:10 series:1 situations:3 explain:1 hkj:1 written:9 rjj:1 analytic:1 only:5 indian:2 generators:8 arvind:4 factor:3 equally:1 covariantly:1 achieve:1 do:2 mixture:1 dependent:2 vary:1 ϕv:51 overall:2 expectation:4 2a:15 q32:2 cannot:1 progress:1 dv:1 applying:1 represented:2 regarding:1 fields:10 arxiv:1 2b:13 mapped:1 qk:1 fixed:4 distinguishes:1 thanks:1 set:5 computed:1 sep:1 physically:2 undergoes:4 j0:7 j1:1 j2:1 j3:1 observed:1 see:2 individual:1 terms:15 incorporating:1 phases:4 mechanically:1 commutation:5 ways:1 away:1 tend:1 symmetric:4 state:46 various:2 closed:1 between:4 invariant:23 neither:1 email:1 available:1 βab:2 nature:11 attention:1 however:2 jl:2 implementing:1 extent:3 jk:1 sξ:1 both:5 essentially:3 last:1 region:2 density:7 ilj:3 ilk:1 propagation:1 figures:9 expression:2 generalisation:1 relevant:1 jj:6 point:5 simple:1 poissonian:1 q12:1 directions:1 grants:1 coordinates:3 wider:1 respect:3 factors:1 along:2 considering:1 described:4 transformations:16 three:4 been:11 commission:1 reduction:1 much:1 treat:1 interest:1 basic:2 ph:1 define:4 v22:1 generating:2 arises:1 corresponding:12 received:1 sufficient:1 photon:20 requires:1 coherent:34 representative:3 demand:1 denote:1 irrelevant:1 spirit:1 present:4 p2:1 multi:1 p1:1 splits:1 defining:1 expanded:1 examine:2 value:7 choices:2 will:8 while:2 preselected:2 squeezed:26 situation:1 property:4 study:1 stoler:1 a21:5 a22:5 unitary:7 played:1 vol:1 von:1 thus:7 them:4 surface:4 iv:2 ii:2 turns:3 theta:1 qj2:1 ernet:1 alone:2 agarwal:1 different:12 develop:2 commuting:1 make:3 radiation:4 same:3 clearly:3 complex:8 quant:1 emphasize:1 largest:1 decreases:1 higher:2 hermiticity:1 exhaust:1 literature:1 somewhere:1 numerical:2 upon:4 hand:4 effectively:1 v1:22 running:1 birkhauser:1 purpose:1 invariance:4 concluding:2 lower:2 modes:29 minimize:1 changes:1 depending:2 well:2 analysis:4 without:2 machinery:1 incapable:2 arising:2 polynomial:1 subgroup:9 teich:1 drawn:1 maslov:1 minima:1 being:8 generally:1 obtain:2 distinguishing:1 via:2 transforms:3 klauder:2 quartics:1 λj:1 minimized:1 hjk:2 previous:1 note:2 k2:1 photons:4 conclude:1 character:1 passive:6 iψ:2 transformed:12 treatment:1 theorem:1 skl:1 apart:1 sin:83 transformation:14 scientific:1 real:13 depends:1 alternatively:1 iα:1 showing:2 possible:3 iη:3 increases:2 varies:1 makes:1 vacuum:3 using:3 unique:2 advanced:1 prominent:1 loss:2 necessary:1 like:2 follows:3 qualitative:2 manifest:1 sab:1 collect:1 continue:1 index:1 either:1 arbitrary:2 become:1 iδjk:1 pertaining:1 satisfactory:1 because:6 neumann:1 classical:41 creation:8 some:9 calculated:2 q22:1 examples:1 kimble:1 happens:3 specific:1 scale:1 describing:1 electromagnetic:2 centre:1 recorded:1 does:4 disappears:1 l3:1 measuring:1 noise:1 obey:1 minimization:4 location:1 equivalent:3 l1:1 weil:1 nowhere:2 yuen:1 plots:20 bangalore:3 super:1 properties:7 stage:1 comparison:1 about:5 actual:2 carried:1 extension:1 algebraic:1 column:3 freedom:1 numerator:2 dependence:5 mukunda:4 important:1 wolf:1 act:1 mixed:2 referred:1 block:1 subset:2 conserving:3 vergne:1 letters:5 into:4 numerically:2 chooses:5 remarks:3 hermitian:4 involvement:1 primarily:1 operator:13 financial:1 next:1 classicality:7 theoretically:1 unambiguous:1 statistics:9 area:1 assumed:1 support:1 initial:1 u1:24 transform:2 u2:69 quadratic:5 mandel:20 way:5 irrespective:1 call:1 analyze:1 naturally:1 function:25 maximally:1 complete:5 form:5 fundamentals:1 regard:1 but:2 change:4 magnitude:2 delta:2 line:4 squeeze:6 rjk:1 considerable:1 arranged:4 iisc:1 uv:2 up:1 below:1 limit:1 uj:1 distribution:12 similar:4 called:1 mechanics:1 defined:7 u4:4 general:13 single:6 ar:4 saleh:1 formulation:1 formalism:3 nonhermitian:3 physical:13 again:1 functions:4 compared:2 faithful:1 no:3 cos:104 whereas:1 subfigures:1 when:16 rs:1 field:7 other:11 role:1 department:2 polar:2 elements:8 superposition:10 kt:1 nonconserving:1 covariance:1 a1:18 generated:2 a2:15 graphically:2 vectors:3 variable:1 ξa:5 ξb:3 implies:1 factorized:2 assume:1 values:18 required:1 original:4 lying:1 simplicity:1 n1:15 n2:15 4a:3 starting:1 having:4 normalized:4
|
quant-ph9509002.txt |@word similarity:6 four:2 consists:3 fronts:1 calculate:1 γu:1 aus:1 under:18 ℜn:3 worth:2 rescue:1 every:3 quadratics:2 ρu:2 solution:1 convenience:1 vector:8 specially:2 second:7 haake:1 even:6 ˆr:8 ˆs:4 dept:1 ˆa:1 above:9 new:15 ˆj:1 consisting:1 ˆn:1 κn:13 guillemin:1 notions:5 equals:1 here:19 reported:1 active:5 κr:9 obtained:1 property:5 study:6 changed:1 suitable:9 changes:2 explained:1 brs:1 plenum:2 brought:1 total:2 univ:1 unit:1 would:7 negative:1 definiteness:1 call:6 therefore:3 type:1 nonunique:1 auv:1 odinger:3 berlin:1 correspondingly:3 hold:1 must:5 obeying:3 springer:1 rα:1 work:2 theories:1 suggestive:1 mp:5 concepts:4 elegantly:3 root:1 example:5 contragredient:1 give:6 relativistic:1 preserving:1 india:4 involve:2 bonafide:1 provide:1 verify:1 feature:1 transitively:1 nontrivial:4 significance:2 answer:4 classify:1 description:5 after:2 law:6 types:1 effective:1 order:5 interpretation:1 eigen:1 over:5 vary:1 london:1 production:1 hidden:2 bunching:1 maximal:10 them:8 they:8 multidimensional:1 eigenvalue:4 reasonable:1 each:14 series:1 principles:7 carry:1 poincare:1 rr:1 rs:12 restricted:1 urbana:1 content:1 re:4 reader:2 rk:8 turning:2 linear:13 free:3 necessarily:4 onto:2 already:1 features:3 rank:9 restrict:1 another:7 cartesian:2 xii:1 eqs:1 too:1 eqn:1 john:2 centred:4 classes:2 feeling:1 rao:1 spectrum:3 manner:2 iσ2:3 seen:8 seem:1 quadrature:1 convenient:6 latter:8 responsible:1 antihermitian:2 though:2 object:1 bsr:1 extending:1 involving:3 cummings:1 phase:18 definitely:3 rivista:1 sum:2 reprinted:1 dover:1 nonuniqueness:1 dependences:1 subtle:2 d2:3 spite:1 situations:1 hamiltonians:2 dn:5 do:7 db:2 dq:1 covering:2 nicely:1 twice:2 transforms:2 projections:1 fail:1 techniques:3 said:1 exponent:2 symmetric:20 cooperation:1 simplest:2 drawn:1 encounters:1 wg:4 terms:16 nature:5 however:9 extent:1 essentially:4 uncertainty:11 exceeds:1 distinction:1 argue:1 adapted:1 basis:8 simplification:3 three:8 been:7 much:5 basic:5 expected:3 algebras:2 families:3 quantities:1 concerning:1 coherent:7 lesser:2 euclidean:9 suppose:3 viii:1 balance:2 leaves:1 iy:8 ix:1 played:2 iq:2 ip:1 iu:2 iv:4 ii:3 im:3 ic:2 ib:4 nonunitary:2 confirmed:1 make:2 utilitarian:2 complex:20 quant:1 split:3 several:4 hermiticity:2 independent:1 i1:4 numerical:3 hand:4 unimodular:1 subgroups:15 mentioning:1 fourier:1 academic:2 possesses:1 just:5 aside:1 identify:1 thanks:1 yet:1 previous:1 adding:2 nilpotent:1 regarded:1 passive:7 belongs:3 transformed:2 easy:4 iπ:1 apart:4 iβ:1 possible:6 possibly:1 unique:5 advanced:2 occurring:1 unnecessary:1 arbitrary:1 right:1 old:1 wwm:12 2nπ:2 icq:1 shamir:1 meanings:1 illustration:1 bangalore:4 properties:12 takes:3 zuv:2 o:11 mukunda:12 plus:1 considerations:1 soc:1 vergne:1 statements:2 dyson:1 δus:2 obtaining:1 bound:1 lies:1 hermitian:19 ξˆa:18 often:2 transform:1 physicists:2 way:9 iˆ:2 form:51 becoming:1 differences:2 true:1 absent:1 coset:2 iisc:1 maximum:3 ln:2 abstract:1 wybourne:1 xiii:1 exist:1 commuting:2 check:2 physical:10 faithful:1 no:6 naturwiss:1 when:12 vanishes:1 unambiguously:1 role:4 ξo:1 ξa:6 ξb:3 longer:1 assume:5 xr1:2 together:1 time:2 characterising:1 n2:7 concept:2 remarkable:1 global:6 leads:2 devoted:1 certainly:2 inverse:1 noncompact:9 passage:1 finally:1 orthogonal:8 geometrical:2 entries:2 solves:1 presented:1 irreducible:3 discrete:1 irreducibly:1 science:4 says:1 dealing:2 sign:2 generalisations:2 adds:1 appear:4 groups:20 alone:2 along:2 appears:1 galilei:1 institute:3 shift:1 studied:1 poisson:2 usually:1 studies:4 useful:13 coinciding:1 post:1 handled:2 covariant:5 positive:19 going:1 y4:1 compactly:1 theoretical:2 uau:1 everywhere:1 effort:1 valued:1 oscillator:1 cat:1 fock:1 values:2 following:8 allowed:4 rescaling:1 conversely:1 rays:1 requirements:1 s2:5 s1:4 write:3 criterion:11 pure:11 parameter:6 product:9 may:21 δvs:1 applications:2 produce:1 representations:3 sy:1 sx:1 natural:1 remember:1 sr:6 sp:124 explicit:1 sv:4 su:4 sk:10 inform:1 sh:8 so:30 representation:32 sg:10 acts:2 submatrices:1 indeed:4 wishing:1 stability:1 course:4 omitting:1 differs:2 group:27 sξ:1 interesting:7 forms:7 main:3 correspondence:1 non:6 rotations:1 introduce:2 hamilton:1 half:6 nov:1 now:11 discuss:1 term:1 name:3 establishing:1 possibilities:1 morandi:1 entirely:1 square:1 ed:1 gaussian:14 happen:3 eq:20 narducci:1 shown:3 space:20 lagrangian:1 contained:5 formula:1 correct:1 shows:4 theory:3 quite:3 language:1 βs:3 impose:1 turn:3 place:3 view:1 think:1 βj:3 first:10 origin:1 xi:1 xn:3 symmetry:4 u1:1 variables:5 xx:1 xy:1 directly:4 xr:2 xs:1 xt:1 given:22 1r:1 checked:2 antibunching:1 cosϕ:2 convention:1 structures:2 speaking:2 1n:4 continuous:2 x2:4 x3:1 eliminated:1 x1:4 than:10 x4:1 zsu:1 third:3 zsr:1 require:1 were:1 pre:5 generality:1 sab:4 argument:3 say:6 buried:1 recover:1 saw:1 any:37 ideas:2 note:3 sciences:1 coincide:1 begin:2 opposite:2 caustics:1 paid:1 remarks:3 america:3 inequalities:2 later:2 implications:1 abraham:1 typically:1 precise:1 show:1 marmo:1 spaces:3 decompositions:3 ground:2 state:29 analytic:1 only:13 explicitly:3 arvind:4 equipped:1 get:4 cannot:6 invariant:14 racah:2 mapped:3 kernel:14 physically:3 namely:4 unaltered:1 commutation:8 ways:7 review:10 definite:13 justifies:1 label:1 between:6 geometric:2 reading:1 gives:1 βab:5 tuv:1 article:1 come:2 x2n:1 many:2 vuv:1 propagation:1 expression:2 comes:4 among:3 v2t:3 maintained:1 moreover:1 schleich:1 aˆ:6 wrs:11 6a:1 direction:1 6c:1 photon:2 dimensionalities:1 stems:1 former:8 those:2 paying:1 variances:1 engineering:1 arnold:1 squeezed:14 situation:4 metric:2 middle:1 theta:1 ernet:1 different:1 develop:2 distributions:2 same:5 antisymmetry:1 arguments:2 status:1 sudarshan:5 siegel:2 arose:1 invariance:7 cr:3 modes:2 without:3 components:4 model:1 dimension:11 being:10 generally:1 actions:4 aspect:1 generator:1 except:1 interested:1 real:45 aspects:1 read:2 department:2 using:10 2q:1 particle:1 deta:3 detb:3 detg:1 either:5 integrals:1 dets:1 detu:1 detv:1 gilmore:2 respect:1 eiα:2 dimensions:9 eiθ:1 wuv:1 decomposition:25 expressing:1 scientific:2 retains:1 equivalent:5 wavefunctions:3 symp:8 assemble:1 comparison:1 stone:3 kinematic:2 y2n:1 theorems:4 discussed:1 develops:1 greater:2 practical:1 mutually:1 wolf:1 act:3 mixed:2 iwasawa:9 cambridge:2 helgason:1 jβ:3 implementable:2 qrs:2 references:1 elementary:2 ηy:1 normalised:3 strictly:3 there:11 start:1 disposes:1 complete:8 fundamentals:1 regard:3 displacement:2 marsden:1 arranged:1 ωs:1 ωv:1 detailed:1 ac:1 ab:3 ad:2 certain:4 describe:9 6b:1 ao:3 general:30 aq:4 examine:1 multiplicatively:1 gruber:1 again:1 mathematica:1 field:1 valid:3 d2n:2 mathematics:3 polar:4 briefly:1 separate:1 a1:1 a2:2 suited:1 mass:1 resolution:1 original:1 consider:3 jawaharlal:2 scalar:4 follow:2 expressions:1 preserves:2 equivalence:1 preserved:2 th:2 case:22 belonging:2 very:8 translations:1 sons:1 difference:1 condition:9 generalised:7 conjugating:2 hamiltonian:1 list:3 wsr:5 wsu:1 generalises:1 zero:3 irreducibility:1 pass:3 further:8 canonical:18 bilinear:4 what:2 sub:2 brackets:2 diag:6 section:22 nondegeneracy:4 subspaces:3 method:1 contrast:4 revealing:1 edited:1 full:2 component:2 behaviour:6 concluding:2 diagonalised:3 antisymmetric:5 allows:2 pick:2 action:5 uniquely:4 via:3 family:13 requiring:1 vii:1 ask:5 jrs:2 establish:1 proceed:1 nehru:2 contains:1 pˆs:4 taken:4 more:13 operators:21 problem:2 basically:2 particular:8 known:2 foundations:1 keeping:1 recall:1 det:3 del:1 nonsingular:3 beautiful:1 stated:5 states:16 minimum:1 numbers:1 sense:4 axis:1 information:1 rather:4 breaking:1 acta:1 explains:2 upto:1 simplicity:1 tried:1 algebra:5 wiley:3 choice:2 specifying:1 fundamental:2 help:2 through:2 y1:4 existence:1 y3:1 y2:4 its:12 conjugation:1 actually:2 wrr:1 systems:7 jacobi:1 might:1 motivated:3 yn:3 framework:1 walls:2 motivates:1 easily:6 2v:1 gets:1 hereafter:1 always:3 level:1 2a:1 turns:4 2n:156 weight:1 reduce:1 expect:2 quantum:30 organised:1 beyond:1 nuovo:1 since:6 preserve:1 research:2 acting:3 δrs:2 annihilates:1 benjamin:3 asr:1 pythagoras:1 asv:1 asu:1 reason:1 put:1 definition:10 pairs:5 retained:1 tru:1 nonnegative:1 american:2 consequence:3 undergo:1 exhibited:2 major:1 relate:1 number:14 done:2 introduction:1 leading:1 construct:2 statement:5 calculations:1 relationship:1 part:2 jordan:1 schr:3 believe:1 kind:1 cyclic:1 contravariant:1 annihilation:2 aat:1 determined:1 conjugate:2 lie:10 built:2 generalized:1 play:2 added:1 quote:1 kan:1 most:5 experiences:1 zrs:7 extremely:1 unequal:1 clear:6 sometimes:3 coincides:1 optical:3 exp:23 realised:1 physics:6 lying:2 particularly:1 cdt:1 multiplicities:1 relation:2 carefully:1 find:6 parameters:2 generators:26 factor:17 circle:1 huygens:1 abelian:4 notation:3 dependent:3 express:5 methods:3 combinations:7 arxiv:1 factorization:1 common:2 set:16 aru:1 arv:2 achieved:1 undergoes:2 see:15 individual:1 descriptions:1 close:2 theoretic:1 mechanically:2 distinctive:1 noncompactness:1 various:8 pn:1 conditions:7 available:1 recently:1 complement:4 attention:2 moyal:2 δad:1 vanishing:1 both:17 last:1 connection:1 symplectic:43 context:1 finds:1 point:3 simple:8 corresponds:1 dimensional:14 simply:4 suppressing:1 pr:3 described:8 pw:1 due:1 pb:2 describes:1 change:11 pj:2 ph:1 xad:2 generating:1 partly:1 wheeler:1 covariance:1 representative:6 demand:1 p1:1 look:2 expanded:1 while:9 replaced:2 behavior:1 δsu:4 nonrelativistic:1 unitary:33 von:3 encountered:1 reads:3 itself:1 vanish:2 twofold:1 belong:3 emphasize:1 products:1 composition:4 calculation:2 used:4 moment:1 purpose:2 eigenvectors:1 lower:2 analysis:1 obviously:1 concrete:1 exponentials:2 entry:1 stating:1 profoundly:1 questions:1 alternative:1 informal:1 theorem:11 totally:1 transformation:24 euler:4 characterise:1 philos:1 integer:1 emergence:1 exakt:1 follows:5 manifest:2 separately:2 continue:1 indication:2 essential:1 mathematical:2 neumann:3 creation:2 some:20 back:2 b2:2 δbd:1 describing:3 shall:6 integration:1 connecting:1 proc:1 bd:1 bb:1 bc:2 virtues:1 restrictive:2 weil:2 relating:1 hilbert:3 range:1 ranga:1 block:4 into:9 within:6 integral:6 uncertainties:1 sequence:1 question:2 bialynicki:1 elsewhere:2 properly:1 delta:1 line:1 collapses:1 intuitive:1 uz:2 uu:1 characteristic:5 uv:2 up:9 us:7 fluctuations:1 similar:4 called:5 choosing:1 defined:8 cover:1 specified:2 single:3 pˆ:14 formalism:1 grs:1 amounts:1 points:2 ergeb:1 realisable:4 nice:1 elements:21 problems:3 lens:3 meaning:1 allowing:1 vectors:8 birula:1 structure:4 multimode:1 independently:1 implies:1 practically:1 orbit:2 notion:1 equivalently:1 overcompleteness:1 xbd:2 xba:2 having:3 partial:2 gq:1 diagonalisable:3 results:7 go:4 gl:9 compact:21 simon:10 pˆn:1 uniqueness:2 pˆr:6 squeezing:18 mehta:1 wave:4 mixing:1 matrices:25 arrange:1 entire:2 fewer:1 pˆ1:1 manifestly:2 eigenvalues:2 trs:4 optics:8 trv:1 zn:1 incidentally:2 dynamics:2 zr:9 index:3 expressed:7 indian:2 3b:1 3a:1 exercise:1 degree:2 respectively:5 z1:1 z2:1 extreme:1 vba:2 involved:6 larger:1 leaving:2 survey:1 makes:1 involves:5 transformations:16 integrations:1 xca:2 apply:1 use:6 usa:1 remains:1 next:6 few:1 themselves:1 stage:1 reflects:1 becomes:4 normalized:2 iii:3 account:4 obvious:2 xcb:2 weaker:1 xcd:2 process:1 lorentz:1 holds:1 parametrised:1 reinstated:1 pair:5 blocks:1 singular:1 counter:1 lines:1 element:11 divided:1 wigner:7 including:1 mentioned:2 la:1 chosen:3 degrees:3 choose:1 defining:9 setting:2 semisimple:1 fourth:1 outlined:1 material:1 maslov:2 rotation:2 february:1 university:2 traced:1 identified:1 sufficiently:1 l2:1 mode:13 homogeneous:1 weyl:2 doing:1 related:4 operator:13 our:7 special:4 out:7 matrix:47 behaviours:1 socalled:1 ref:2 noncanonical:1 diagonal:32 york:11 aˆr:4 aˆs:2 geometry:9 could:4 times:2 counterpart:1 length:2 isotropic:11 hence:1 retain:1 metaplectic:19 possessing:1 intuitively:1 ars:5 precisely:2 ordering:1 system:4 relations:13 their:13 dutta:5 sternberg:1 sinϕ:2 cimento:1 lion:1 mobius:2 distinguished:1 result:11 symmetries:1 unchanged:1 delineated:1 apparently:1 clearly:4 angle:2 able:3 instance:4 subject:4 heisenberg:4 centre:3 gξ:1 who:1 qˆr:7 qˆn:1 connected:1 definitions:1 intrinsic:1 tensor:1 consequences:1 mechanical:3 normally:1 fact:8 xr2:1 q1:5 based:1 basel:1 should:4 bases:1 ambiguity:2 inπ:1 achieve:3 perpendicularity:2 means:6 familiar:6 generalise:1 ones:4 words:1 evolution:2 qr:9 differential:2 contain:1 qj:2 qn:4 strengthened:1 multiplying:1 geometrically:1 phases:2 madras:1 attempting:1 nondegenerate:1 nuclear:1 written:7 correctly:1 progress:1 email:1 vrs:9 ends:1 vrv:1 vru:1 importance:2 implementing:2 key:2 subgroup:29 configuration:3 tensors:2 limits:1 taking:2 equal:3 etc:2 sβ:3 passing:2 otherwise:1 unitarily:2 aa:1 relevant:3 co:8 cd:1 table:1 geometries:7 addition:2 compensating:1 define:4 arises:1 corresponding:3 sufficient:2 coherence:2 subspace:10 present:3 semidefinite:5 subsets:4 tsr:1 appearance:1 will:9 vi:2 thus:17 vu:3 conserve:4 descriptive:1 generic:1 radiation:1 member:1 unity:1 parts:1 finite:4 infer:1 upon:1 effect:2 v1:60 v2:7 v3:8 birkhauser:1 variance:8 infinite:1 identity:3 off:2 reflection:1 nevertheless:1 0n:2 well:12 sets:2 position:1 preprints:1 usual:5 spherical:2 less:5 moments:2 obtain:3 klauder:1 density:3 supply:2 add:1 conjugated:1 know:2 press:7 intersection:2 loss:1 necessary:3 like:3 lost:1 exploiting:2 become:1 vsr:1 because:2 classical:12 2qq:1 convey:1 proper:1 proofs:1 happens:2 subramaniam:1 lead:1 does:1 noise:15 obey:5 journal:5 expansion:2 qˆ:14 imaginary:3 simpler:1 about:1 column:2 freedom:7 introduces:1 carries:1 important:7 transitive:1 subset:5 equally:1 letters:2 additional:1 stucture:1 vab:6 vaa:1 intention:1 quadratic:3 diagonalisation:1 naturally:2 function:10 williamson:12 but:13 camb:1 hb:1 squeeze:1 xab:9 made:3 society:3 whether:2 wish:1 below:3 distribution:5 display:1 mechanics:15 inadequate:1 universal:1 meaningless:1 denote:1 campus:1 nongeneric:1 functions:4 variety:1 reiθ:1 detail:2 illinois:2 other:14 details:2 normal:12 misconceptions:1 ubu:1 expressible:1 ranks:2 factors:14 rule:6 4b:1 4a:1
|
quant-ph9509003.txt |@word gv:7 otherwise:1 protocol:7 help:1 just:2 being:1 storage:2 areas:1 vacuum:1 results:1 existing:1 four:1 stored:1 identify:1 worth:1 eavesdropping:2 computers:1 differs:1 oldest:1 ieee:2 its:2 reduced:1 redirect:1 access:2 discloses:1 copy:1 based:1 thank:1 density:2 chosen:2 exact:2 photons:2 state:1 controls:1 actually:1 common:2 only:5 does:1 suspicion:1 fig:2 input:1 must:1 oct:1 sent:1 first:2 identical:2 non:1 supported:1 peres:2 risk:1 cryptography:2 orthogonal:12 very:1 propose:2 practice:1 possible:2 investigated:1 choice:2 inspection:1 cannot:1 example:1 know:1 they:2 drawn:1 using:1 bit:6 distortion:1 matrices:1 unfounded:1 essential:1 materialize:1 notations:1 beamsplitters:1 particle:2 proc:1 signal:1 arxiv:1 eve:12 summary:1 asher:1 protocols:2 she:7 each:3 small:1 accompanied:1 announces:1 refer:1 optics:1 ports:1 view:2 accessible:2 performing:1 delayed:2 achieved:1 sends:1 problem:1 carrying:1 successfully:1 moving:1 lior:1 crypto:1 ct:1 interferometer:3 second:2 interferometers:1 measurement:1 quantum:8 israel:2 choices:1 advance:1 out:1 widely:1 shown:1 scale:1 matrix:1 apparatus:1 function:1 restricted:3 review:1 measurements:2 rings:2 while:1 instantaneous:3 sr2:1 waiting:1 version:2 york:1 between:3 new:2 order:1 ref:1 method:1 announced:1 fibers:1 disclose:1 exactly:1 processing:1 theory:1 respectively:1 team:1 haifa:1 however:2 here:1 quite:1 step:1 no:2 lev:1 imagine:1 represented:4 bangalore:1 standard:1 security:1 department:1 wait:1 obtained:1 both:1 essentially:1 piece:1 sender:1 getting:2 eavesdropper:1 many:2 could:4 thence:1 meaning:1 times:1 caption:1 carrier:1 coiled:1 receives:1 receiver:1 discard:1 bob:9 shaded:1 spacetime:1 alice:11 rev:1 letters:1 features:2 point:2 into:2 tracing:1 sign:1 corresponds:1 reaches:1 perturbing:1 declare:1 done:1 numbers:1 moreover:2 message:1 clarity:1 interesting:1 research:1 gerard:1 kets:1 use:4 classical:1 her:5 basis:7 there:2 center:1 their:3 bases:1 bz:1 relativistic:1 ph:1 goldenberg:3 was:3 final:1 store:1 more:2 separated:1 introducing:1 graphical:1 bennett:1 corresponding:1 option:1 eavesdrop:1 observable:1 detail:1 acquire:1 photon:7 emission:2 but:1 eavesdroppers:1 tested:1 optical:1 encouragement:1 known:1 encoded:1 line:1 detects:1 representing:1 than:1 those:2 he:1 randomly:1 resulting:1 publicly:2 pacs:1 work:1 bb84:6 namely:1 value:1 until:3 windows:1 easier:1 delay:3 values:4 were:2 interpolating:1 gives:1 similar:3 certainty:1 cryptosystems:1 distance:1 claim:2 would:2 toward:1 figure:3 mirrors:2 process:1 likewise:1 consecutive:1 received:1 india:1 them:2 additional:1 general:1 states:15 technion:1 single:1 sr1:1 conf:1 seen:2 technology:1 any:2 physical:1 chance:1 information:9 different:3 secure:1 carriers:2 latter:2 when:2 feature:1 same:2 machine:1 other:5 quant:1 split:1 branch:5 test:2 instead:3 most:1 brassard:1 either:1 lett:1 used:2 paths:2 may:2 after:3 institute:1 systems:1 zigzag:1 hand:2 diagram:1 steps:1 wrong:2 uses:2 letter:2 velocity:1 wave:2 recent:1 dummy:1 branches:2 longer:2 fund:2 discarding:1 physics:1 later:2 lines:1 packets:1 vaidman:3 without:2 principle:1 time:7 international:1 bounced:1 swope:1 avoid:1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.