text
stringlengths 0
190k
|
|---|
quant-ph9801046.txt |@word secondly:1 consider:12 global:1 focus:3 leads:6 edu:1 go:2 follow:1 contributions:1 causes:2 inverse:6 depend:7 re:1 respectively:3 equal:2 technique:1 tr:12 ts:7 finally:1 those:7 under:2 γc:1 td:29 include:3 8m:1 straightforward:1 kτ:1 very:4 frequencies:3 assuming:1 springer:2 results:15 sons:1 fall:1 experimentally:2 difference:1 exact:36 collett:2 condition:9 treating:1 presented:7 12th:1 solution:12 large:12 solved:2 convenience:1 small:3 markov:70 optics:18 noted:1 upper:2 dilute:1 publications:2 approximation:48 zero:17 value:9 realistic:4 further:2 dynamics:7 goes:2 even:8 rewritten:1 nonlinear:1 const:1 giving:1 section:18 abk:1 remain:1 agrees:1 consistently:2 version:2 absolute:2 above:6 capital:1 required:3 ground:1 waveguide:2 method:4 contrast:2 thin:1 satisfy:1 edited:1 evolving:1 full:3 led:1 becs:1 here:13 atoms:41 behaviour:9 following:2 olshanii:1 possibility:2 separation:1 eikx:1 alone:1 consideration:1 quite:1 equations:33 change:10 obtained:15 2aρ:1 involved:2 larger:2 allows:4 commonly:1 ignoring:3 resulting:3 interac:1 usually:2 suitable:1 changes:2 involves:4 plotted:1 appropriately:1 useful:3 requiring:1 castin:1 vii:2 replace:1 texts:1 inequality:3 condensates:1 use:8 quasi:1 would:9 dalibard:1 remains:3 lasing:3 negative:2 adequacy:1 comparing:1 linear:1 therefore:3 taken:1 australian:2 leaky:1 type:1 theoretical:2 reflects:1 more:5 flat:1 becomes:5 operators:8 stable:3 odinger:1 validity:9 berlin:2 everywhere:1 labelled:2 particular:8 cases:1 hold:1 iii:6 emphasising:1 must:9 ρa:1 keeping:1 eiω0:12 science:1 equation:60 work:3 modified:1 theories:1 reproduce:1 erf:2 values:9 temperatures:2 burnett:1 already:1 making:6 spontaneous:1 example:3 grained:1 compare:3 figure:9 give:5 arise:2 near:1 states:1 effectively:1 assumptions:1 numbers:3 allowed:1 tions:1 ratio:1 information:1 goal:1 provide:1 revivals:1 discussion:1 breaking:1 write:1 how:1 opt:1 instead:1 ignore:5 parameter:13 sin:2 exponentially:1 ψa:4 description:5 may:15 demonstrates:3 earlier:4 derived:5 different:9 pfau:1 produce:3 fi:1 wave:2 kurn:2 short:4 interscience:2 light:3 explicit:1 correspond:1 s3:1 ones:1 so:8 fundamental:2 correlation:19 operate:2 order:7 typical:3 pulsed:1 reservoir:59 produces:4 allegrini:1 over:3 eqs:2 satisfied:2 presence:2 thermal:2 paper:3 through:7 lasers:10 affect:2 still:1 asymptotes:1 derive:2 rapidly:4 probability:1 decay:22 chosen:2 interesting:1 solving:1 edge:1 forms:1 spreeuw:1 mπ:3 systems:6 pergamon:1 quant:1 carmichael:1 kasevich:1 non:15 good:2 motivated:1 combination:1 numerically:1 material:1 regarding:1 band:3 walls:2 repulsive:3 effects:11 they:4 half:4 oxford:1 1b:2 now:7 discuss:13 february:1 dirac:9 always:1 university:1 traced:1 leak:1 sufficiently:2 magnitude:1 differing:1 mode:13 2m:4 higher:3 lorentzian:1 neglects:1 schemes:2 ei:1 significantly:3 energy:1 frequency:4 gaussian:11 related:2 extended:2 interplay:1 substantially:1 our:18 approximated:4 eq:53 out:2 ketterle:2 leave:1 shown:4 space:7 furthermore:2 since:1 rev:10 replacing:1 rf:2 cause:1 correct:7 shows:5 asymptote:1 wiley:3 theory:3 interactions:6 disagree:2 gardiner:2 mechanisms:1 pumping:3 free:7 standard:7 reason:1 york:1 estimate:1 lambropoulos:1 universally:1 milburn:1 iω0:9 interaction:12 derivation:2 could:1 transition:3 times:4 motion:9 turn:1 place:1 derivations:1 hence:2 pitaevskii:2 facilitate:1 neglect:1 first:4 major:1 initial:4 features:2 symmetry:1 variables:6 number:23 approximate:1 entanglement:1 done:2 approximately:2 another:1 σk2:1 impossible:1 open:1 size:1 given:32 necessarily:1 temperature:1 similarly:2 introduction:1 condensate:2 achieved:4 system:56 relations:8 1a:2 their:3 assumption:9 master:46 john:1 final:1 townsend:2 gives:4 molmer:1 relationship:1 tool:1 exactly:2 zeroth:1 accurately:1 transverse:2 optical:27 simulate:1 schr:1 eliminated:1 unrealistic:2 than:5 traps:4 wide:1 determines:1 holland:1 ubiquitously:1 bec:7 approximations:26 rate:1 modelled:1 annihilation:1 determined:1 intensities:1 opens:1 were:1 iωk:3 descriptions:1 function:37 fig:7 generality:1 cohen:1 alongside:1 turned:1 spectrum:2 discussions:1 variable:1 manner:2 qualitatively:1 seen:1 constrained:1 any:5 strength:11 latter:2 able:1 gravity:15 mechanism:2 note:3 instance:4 k0:11 analogy:1 finding:2 destroy:1 require:1 tannoudji:1 heisenberg:5 begin:2 towards:2 allow:1 though:1 falls:1 most:2 significant:2 device:1 kb:1 found:6 kg:2 failure:2 considered:2 sometimes:1 steady:2 part:4 verlag:2 exp:2 multiparticle:1 physics:4 sum:1 fact:5 intensity:1 show:4 delta:10 dependant:1 rotating:2 relation:10 solutions:16 find:4 principal:1 aρ:6 fibre:2 based:8 quoted:1 parameters:14 much:1 outside:3 hg:4 being:1 only:12 explicitly:1 population:1 interested:1 hope:3 equilibrium:1 do:6 dk:11 untrapped:1 means:5 dependent:1 familiar:1 lifshitz:1 sasso:1 expectation:7 beam:1 cannot:6 dx:1 despite:1 combinations:1 dt:12 written:1 durfee:2 evolution:7 continuum:3 approach:1 arxiv:1 bay:2 investigate:5 experiments:1 mewes:2 predicted:2 analytical:2 including:4 thirdly:1 transforms:2 hκ:1 redefine:1 statistical:3 reference:1 sep:1 physically:1 undergoes:1 national:1 correlations:5 up:1 become:1 depends:8 sec:4 result:2 ignores:3 fail:7 recently:1 uncorrelated:1 incorporating:1 inversely:1 fails:4 potential:1 inequalities:1 ways:1 subsequent:1 away:1 definite:1 below:1 tend:5 initially:8 state:19 various:2 correctly:2 between:16 affecting:1 conditions:3 email:1 available:1 sections:1 terms:13 extend:1 nature:1 importance:1 however:23 glenn:1 huang:1 demonstrate:1 bose:2 cirac:1 holds:2 σk:16 restrictions:1 many:3 region:1 infinitely:2 according:1 laplace:6 context:2 whole:1 hτ:1 andrews:2 timescale:31 cl:7 reasons:4 address:1 corresponds:3 hollow:2 dimensional:3 ab:1 applicability:1 dependance:1 moreover:4 ct:1 considering:4 destroyed:1 described:7 second:2 agree:3 addition:1 due:10 been:7 int:1 describes:2 damping:3 interest:1 expected:1 ph:1 territory:1 empty:6 define:2 rather:2 corresponding:5 both:5 suppress:1 coherence:2 photon:3 new:3 gap:2 coherent:3 understand:2 external:2 kicks:1 denote:1 present:8 case:16 laser:24 look:1 exponential:8 anu:1 solid:3 examine:1 evaluated:1 transformation:1 will:16 while:4 suppose:1 viii:1 au:1 property:1 taking:1 identical:3 coupled:5 almost:1 vi:3 vk:1 thus:7 saturation:1 iv:3 ii:5 coupler:1 itself:1 containing:1 formalism:1 generic:1 suggest:2 make:4 radiation:3 same:6 orders:2 shorter:1 nonmarkovian:1 potentially:1 arguments:1 wilkens:1 finite:4 couple:1 difficult:2 breakdown:1 used:9 infinity:2 see:6 trajectories:1 indicies:2 effect:6 possible:1 action:1 running:1 harris:1 uses:1 infinite:1 fourier:1 off:3 modes:14 nevertheless:2 makes:2 well:2 without:3 solve:2 comes:1 firstly:1 position:3 model:38 self:2 left:1 proposed:1 increasingly:2 generally:2 obtain:6 photonic:2 press:1 shape:1 atomic:10 world:1 alternative:1 speed:3 previous:3 zoller:1 density:5 photons:9 except:1 other:8 lett:3 input:1 wiseman:3 remaining:1 momentum:5 real:2 moy:4 australia:1 around:1 louisell:1 iγ:1 term:13 know:2 vacuum:6 confined:1 using:13 u0:2 loss:4 success:1 particle:4 alternatively:1 reduces:1 strictly:1 pt2:1 specific:2 continue:1 either:3 fully:1 output:38 essential:1 because:3 often:1 creation:3 some:5 back:1 born:75 added:1 choosing:2 mirror:1 treatments:1 exists:1 nonzero:2 savage:3 scale:1 proceeding:1 lead:5 icl:1 cavity:18 affects:1 avoid:3 integration:1 does:15 tends:3 proc:1 demonstrated:2 trap:3 conference:1 noise:1 2µm:1 equivalent:7 martin:1 analysed:1 bk:8 hsr:4 although:1 accompanied:1 imaginary:2 normalisation:1 properties:2 comparison:6 about:1 cavities:2 extension:1 extending:1 tracing:1 basis:2 discussed:10 dependence:4 o:5 practical:3 range:2 a2:1 plus:1 miesner:1 considerations:1 conserving:1 letters:2 markovian:12 inclusion:3 previously:4 ωe:1 into:6 integral:7 three:3 down:1 phase:2 appropriate:5 square:1 references:1 trs:4 einstein:2 operator:10 proportional:1 next:5 bosonic:1 methods:2 europhysics:1 statistics:1 assumed:1 unchanging:2 there:8 transform:4 long:7 dispersion:17 width:8 cauchy:1 way:1 was:2 assumes:1 coarse:1 raman:2 form:14 hr:4 hs:4 differences:4 nonexponential:1 but:1 hk:2 hi:1 gain:1 atom:64 line:6 collapses:1 made:6 qualitative:1 whether:1 wish:1 gravitational:2 maximum:1 devices:1 ωk:10 decays:7 limit:20 spectroscopy:1 continuously:1 highlight:1 semiclass:1 similar:5 emit:1 regimes:17 mechanics:1 later:3 constant:6 moore:1 introducing:2 defined:11 describe:9 guzman:1 general:8 quantum:8 single:11 pˆ:2 laboratory:1 hamiltonian:7 check:1 defines:1 incorrect:1 again:2 functions:2 compared:9 us:1 no:6 dashed:3 whereas:2 wavefunction:1 when:5 field:5 valid:12 compares:2 department:1 conclusion:3 picture:4 inguscio:1 gross:1 models:3 gas:1 time:25 problems:1 includes:1 deriving:2 important:4 suppression:1 included:4 describing:10 15m:1 structure:1 independently:1 correlated:1 regime:3 coupling:62 fluorescence:1 assume:6 typically:5 dτ:9 factors:2 dρ:2 broadband:24 4m:1 mass:5 broad:2 meystre:1 requires:2 having:1 normalized:3
|
quant-ph9801047.txt |@word represent:1 partial:1 consider:2 results:3 existing:1 four:7 eds:2 drastically:1 go:1 sci:1 compact:2 increase:1 certainly:1 inverse:4 depend:1 iii:4 show:2 experimentally:1 quasi:3 does:2 th:2 stable:23 summarizes:1 division:1 r14:2 r12:1 r13:3 returning:1 very:13 unavoidably:2 decide:1 ma:5 em:6 difference:2 convexity:8 presented:1 did:1 eve:6 large:3 discrete:1 adjust:1 mλ:2 small:4 upper:1 force:2 version:1 sign:4 approximation:1 consists:1 zero:4 rigorous:4 chem:1 even:1 established:1 what:4 errors:1 const:2 appear:1 richard:13 celebrated:1 while:2 expressed:1 a234:1 experiment:1 goes:2 new:4 equivalent:1 mp:2 body:23 notions:1 whose:1 honour:1 residual:1 here:1 understanding:1 believed:1 q2:53 separation:1 others:1 represented:3 ratio:1 along:5 equations:1 implicit:1 z2:4 z3:4 obtained:1 dividing:2 cern:4 study:1 trial:4 published:1 implement:1 mz:1 studies:2 e13:2 marc:1 seifert:3 useful:1 marked:1 total:1 tools:1 linearly:1 use:7 charge:13 eψ:1 would:3 prove:2 remains:2 positive:3 contains:1 finally:3 scenarios:1 few:3 a52:1 m1:3 therefore:7 m3:13 memory:1 survive:1 theoretical:2 andr:1 clever:1 becomes:3 schrader:2 odinger:1 everywhere:1 particular:4 known:1 rare:1 cases:3 iv:1 producing:2 potential:1 must:1 me:2 topic:2 word:1 mc:2 mb:5 science:1 equation:1 work:4 protons:1 london:1 remain:1 obvious:3 three:19 morgan:1 following:1 europhysics:1 my:1 example:3 proof:10 ions:2 dedicated:2 figure:10 give:4 calculation:1 permutations:1 define:1 pieces:1 states:5 minimum:2 spruch:3 degenerate:1 sense:2 rescaling:3 hydrogen:4 absolute:6 needs:1 r24:2 r23:3 get:1 off:1 regions:4 far:2 pure:1 answer:1 instead:2 roy:1 divides:1 circular:1 fr:4 tried:1 may:4 dx3:1 diagram:1 tries:1 plane:3 horizontal:1 realized:1 natural:2 remember:1 third:1 lines:1 correspond:1 their:1 so:2 martina:1 allow:1 decreasing:1 playing:1 talk:2 triton:1 lighter:1 considerations:1 pointed:1 cosh:1 satisfied:2 stability:31 course:5 paper:1 including:3 thesis:4 omitting:1 mentioned:1 still:2 its:1 le:1 rapidly:1 energies:4 masses:14 late:1 attraction:3 strange:1 choose:1 mail:2 might:1 image:2 them:2 someone:1 return:1 practice:1 noticing:1 introduce:1 scaling:5 band:2 repulsive:1 they:2 half:8 thus:1 now:5 discuss:2 represents:2 february:1 january:1 university:2 concave:3 drake:2 sufficiently:1 inequality:3 found:4 went:1 european:1 heavy:2 reactions:1 domain:2 disregarding:1 energy:16 ea:1 idea:1 related:1 joined:1 investigated:1 quantum:2 our:1 oppenheimer:7 ep:4 neighbourhood:4 really:1 shown:8 unbound:1 kiev:2 sector:1 unnatural:2 ponomarev:1 since:4 rev:12 particles:11 replacing:1 hill:6 math:3 conjecture:1 linear:2 assured:1 interactions:3 diagonal:1 completely:6 ect:1 york:1 besides:1 estimate:1 e0:1 e2:5 definition:1 bates:1 persons:1 could:1 persists:1 times:1 produce:1 fleck:1 leading:1 hence:5 neglect:2 first:3 exotic:1 major:1 already:2 urich:1 xb:10 xc:12 variables:8 xa:10 number:5 xe:9 xy:1 done:1 gases:1 another:1 xp:9 precisely:2 angular:1 given:5 similarly:1 introduction:1 lapp:1 system:30 carson:1 indicate:1 fermions:1 calculations:10 variational:2 too:4 geneva:1 exactly:1 part:2 x2:6 x3:7 x1:7 representing:1 than:8 positively:1 center:1 distance:1 kind:1 sectors:1 showed:1 princeton:2 see:3 submitted:1 annihilation:2 future:1 coulombic:1 doubly:2 a41:1 negatively:1 gives:1 treated:1 trento:1 a49:1 lowest:2 sees:1 explicit:1 ann:1 spectrum:1 chen:1 say:3 cleaned:1 seem:4 constrained:1 border:1 any:11 seminar:1 subsystems:3 mostly:1 ohlich:4 convenient:1 able:1 isolated:1 note:1 instance:3 concerns:2 take:6 wonder:1 adjusting:1 hyperfine:1 differences:1 fundamental:1 opposite:3 collaboration:2 molecule:3 systems:21 algebraic:1 plus:1 plays:1 analytically:2 segment:7 why:1 unequal:4 clear:1 later:1 coincides:1 feynman:3 points:2 organise:1 principle:1 exp:1 charged:3 physics:4 review:2 fact:5 joining:1 2m2:1 2m3:1 2m1:1 distances:3 dissociate:3 purely:1 threshold:2 find:2 ground:1 q1:1 q3:36 believe:3 based:2 knowledge:1 parameters:2 pdµ:2 e12:6 enough:1 should:1 jan:1 only:6 explicitly:1 constant:4 hope:1 do:1 his:1 triangle:18 above:1 means:2 familiar:1 de:1 overall:1 q32:3 cannot:2 words:1 international:2 during:1 respectively:1 areas:1 budapest:1 conclusion:1 approach:1 arxiv:1 wightman:3 method:1 predicted:1 gribov:2 through:3 fixed:8 valid:1 graf:1 satisfy:1 exists:1 lifetimes:1 unpublished:1 grosse:3 relative:2 depends:1 decided:1 quantitatively:1 fail:1 close:2 observed:1 subject:1 preparation:1 said:1 interacting:1 nuclear:1 away:1 definite:1 symmetric:1 state:6 various:2 between:4 a42:1 conditions:1 multiplied:2 notice:3 terms:1 vertical:1 nature:1 weak:2 however:6 interpolate:1 wu:6 derive:1 both:5 essentially:1 many:4 region:8 hint:1 equal:12 etc:1 eth:1 whole:2 fix:1 comes:1 ch:2 groups:1 point:9 simple:3 excess:1 narrower:1 corresponds:5 proton:5 respect:3 speak:2 mention:2 estimating:1 pz:1 due:3 been:4 hellmann:3 much:1 treat:1 pe:8 ph:1 fig:9 direction:1 corresponding:1 sufficient:2 wheeler:2 collaborators:4 argument:1 singly:1 spin:2 present:3 case:12 myself:3 processes:1 value:9 will:17 near:3 replaced:1 applies:2 situation:2 property:4 real:1 vol:1 a29:1 binding:18 freund:1 according:4 ii:7 reads:1 experts:1 orbital:1 different:1 glaser:2 same:7 concavity:8 quant:1 arguments:1 pauli:1 gets:1 start:1 difficult:1 used:2 infinity:1 positronium:1 numerical:6 hand:1 ion:2 levels:1 uses:1 vieux:1 infinite:2 changing:1 totally:1 lower:3 schr:3 varga:2 pµ:4 charges:16 com:1 well:1 increases:1 finds:1 more:8 without:2 jean:1 left:11 muon:2 just:2 less:5 being:2 generally:1 armour:2 obtain:1 relevant:1 atomic:2 questions:1 λm:1 previous:2 heuristic:1 dissociation:2 infinitely:3 nonrelativistic:1 had:1 except:1 improvement:1 reasons:1 other:5 lett:4 easy:1 theorem:16 role:1 save:1 excited:1 momentum:1 useless:1 identical:1 rescaled:1 around:1 breaks:1 possible:5 e123:4 fusion:1 know:5 press:2 using:5 unique:2 like:4 particle:10 shaped:4 follows:1 qualitative:1 continue:1 unstable:20 either:4 integrals:2 martin:4 works:1 mathematical:1 parity:4 because:11 old:1 namely:1 some:9 algebraically:1 born:7 q22:3 acad:1 2z:1 convex:3 recently:1 2e:1 avoid:2 shall:5 critical:2 disappears:4 tends:2 proc:1 q2c:1 pletely:1 arbitrary:2 illustration:1 restrictive:1 step:2 instability:16 properties:3 takes:1 actual:3 carried:1 ader:2 most:3 theorems:1 repulsion:1 efforts:1 lieb:4 subsystem:5 soc:1 own:1 ppe:1 into:6 definitely:1 bound:9 negative:9 right:2 references:1 refined:2 gerstein:4 strictly:1 there:23 question:1 transform:1 long:3 strict:2 workshop:3 way:2 subregions:1 gusev:1 was:5 combined:1 function:4 academic:1 himself:1 form:1 becoming:1 m2:13 but:10 sophisticated:1 implies:1 line:9 true:1 considerable:1 snodgrass:1 places:1 whether:1 inside:1 up:2 us:4 bethe:2 below:1 exerts:1 limit:7 problem:7 walter:5 similar:1 calculated:1 mechanics:1 proved:1 defined:1 certain:4 abstract:1 describe:1 condition:1 covers:1 general:2 exist:5 lifetime:1 moves:1 simplest:2 tedious:1 again:5 functions:1 dotted:1 no:14 eα3:1 when:2 application:1 interested:1 annecy:1 special:2 holding:1 electrons:1 out:1 metastability:2 a46:1 star:5 thirring:4 meaning:1 important:2 variable:2 sides:1 feasible:1 ago:1 simon:1 subdivision:1 longer:1 coulomb:4 assume:2 values:1 baker:1 curve:1 together:1 original:1 summit:10 mass:7 time:2 nuclei:1 starting:1 having:1
|
quant-ph9801048.txt |@word essay:1 represent:1 partial:2 consider:6 remarkable:1 limited:1 caused:3 green:2 particular:3 results:4 produce:1 leads:2 scalar:1 grateful:1 consists:1 follow:2 cτ:1 weakly:1 localized:1 inverse:1 const:2 calculate:14 zone:1 quantenphysik:1 producing:1 technique:2 interact:1 finally:7 does:5 infinitesimally:1 present:2 excluded:1 γl:21 include:1 ζx2:1 overlaps:1 supported:2 straightforward:2 far:6 reader:1 p0:14 wave:23 electron:1 k0:24 refractive:1 resonant:4 affect:3 entire:1 moderate:2 impressive:2 hamiltonian:16 positions:1 t2:27 solution:1 fewer:1 occurs:1 large:7 solid:1 kx2:3 small:3 enhance:1 markov:3 trr:21 optics:11 lines:2 lˆ:6 application:2 ruostekoski:3 smaller:1 2k0:7 lewenstein:4 findings:1 obtained:1 ψi:1 consistent:2 os:1 l3:1 approximation:7 lian:1 rate:14 noise:6 video:1 traveling:1 further:1 ter:1 analogue:1 canonical:12 even:1 index:2 ˆr:2 nonlinear:1 plays:3 appear:1 apparatus:3 section:10 localization:2 brief:1 expressed:3 d3:29 suspect:1 above:7 new:2 momentum:2 method:5 contrast:22 pioneering:1 condensed:8 degree:2 respectively:3 concepts:1 component:3 residual:3 here:6 atoms:27 canonically:1 objects:1 focused:1 andrews:2 eikx:6 ignore:1 along:2 ρir:2 observing:2 appears:2 change:1 box:1 great:1 stark:1 institute:2 shift:2 study:4 studied:1 allows:2 approaches:1 contradiction:1 atom:11 resulting:1 commutators:1 action:1 shifting:1 conveniently:1 fourier:6 studies:1 involves:1 appropriately:1 formulated:4 ikx:2 stenholm:2 elaborated:1 tr:1 castin:1 prefer:1 iϕ:1 replace:2 poissonian:1 issue:1 condensates:13 apply:8 total:6 research:2 cloud:1 shlyapnikov:1 derivatives:2 use:7 proceed:3 would:5 dalibard:1 positive:2 contains:3 negative:2 properties:2 few:4 unpleasant:1 call:1 therefore:11 memory:3 taken:2 means:4 type:1 theoretical:2 more:7 outweighs:2 becomes:1 operators:2 factor:3 envelope:1 odinger:11 leonhardt:1 iid:1 berlin:1 appendix:6 varying:1 reformulate:1 verified:1 iii:4 must:5 states:3 k02:6 k03:1 evolution:1 quantized:2 ih:1 ρi:9 science:3 equation:31 averaged:1 modified:1 glauber:1 ρr:2 obvious:1 thin:2 ulm:3 following:1 arrive:2 example:5 4i:1 2γl:2 compare:2 employs:1 figure:4 chosen:1 calculation:3 cited:2 share:1 sample:9 contradicts:1 satisfactory:1 minimum:1 performed:1 cτ0:5 sense:1 occur:2 calculated:1 information:1 ti:2 monitoring:1 caption:1 rather:1 technology:1 discussion:2 acts:4 utilize:6 write:1 how:3 2ik0:2 repulsion:1 priori:1 simplicity:1 product:2 express:3 description:1 influenced:1 may:6 broad:4 after:4 containing:1 hence:2 plane:8 waves:4 ζx:1 ky2:3 forschungsgemeinschaft:1 short:2 quasiclassical:1 remember:1 effective:4 2iω0:1 light:68 explicit:2 deutsche:1 si:1 maintain:1 so:9 ρˆr:3 allow:1 verify:1 sackett:2 order:9 se:1 prefactor:2 houston:1 holds:1 reservoir:4 produces:2 gradual:2 over:9 dy:2 meter:5 interpreted:1 produced:1 course:1 paper:3 through:3 statistical:1 experimentally:1 mentioned:1 existence:2 satisfies:1 still:3 condensation:1 lf:4 derive:4 measuring:1 decay:2 ln:1 lm:3 τc:6 exhibits:1 late:2 estimating:1 absence:2 otv:1 differently:1 lp:2 potentially:1 bradley:2 freely:1 might:2 into:6 virtually:1 character:1 non:9 crucial:1 affected:1 safe:1 performance:4 budapest:1 introduce:2 attains:1 oll:3 walls:2 repulsive:1 effects:1 they:1 singularity:1 transparent:3 dielectric:5 susceptibility:2 term:14 finite:3 trac:9 fully:2 university:2 kerr:1 appropriate:1 2z:4 dominance:1 orthonormal:2 javanainen:3 magnitude:2 l2:4 stockholm:1 deplete:1 each:1 contours:2 2m:3 universit:1 commutation:2 characterized:1 mean:2 differential:1 significantly:4 formulate:1 populated:2 series:4 energy:2 sov:1 gaussian:1 snapshots:1 breakthrough:1 elementary:1 frequency:3 expect:2 measurement:10 quantum:61 our:28 beyond:2 eq:23 out:2 travels:4 ultimately:1 matrix:4 space:5 gradient:1 restricted:1 furthermore:5 since:7 lagrangian:6 barchielli:1 denotes:3 particles:1 collisions:1 posteriori:1 dominated:1 i0:8 formula:2 induced:3 ref:4 integrated:1 shows:3 foundation:1 numerical:1 theory:35 interactions:1 gardiner:4 free:4 standard:1 reason:2 perturbation:3 imaging:19 dynamics:1 imagine:1 put:2 estimate:3 milburn:2 iω0:4 definition:2 interaction:20 derivation:1 language:2 kn:3 could:1 insert:1 motion:3 turn:6 length:5 disturbed:1 nondemolition:2 transfer:1 consequence:1 uses:1 pitaevskii:1 neglect:5 first:12 origin:1 kz2:1 already:2 humboldt:1 probability:4 feel:1 variables:2 ez:11 number:13 transform:1 restrict:1 entanglement:1 set:2 simplified:1 nonperturbative:1 ihm:2 mixing:1 force:3 ibid:13 open:1 causing:1 dispersive:1 given:7 long:2 fascinating:2 correlation:4 their:5 introduction:1 cambridge:4 condensate:49 behaves:2 magnifying:1 system:2 indicate:4 conservation:3 rates:2 observations:3 calculations:3 time:11 show:1 master:12 ordered:1 scheme:2 final:1 low:2 shifted:1 progr:1 mostly:1 ohberg:1 continuous:2 imprinted:1 immediate:1 employ:1 assumption:1 optical:41 differentiate:1 authors:3 x2:33 off:1 x1:31 than:3 specify:1 modes:7 diffusion:17 kind:1 determines:1 third:1 roles:1 double:5 summary:1 eik0:1 likely:1 utilizing:1 annihilation:2 matter:24 sweden:1 future:1 kth:1 amplitude:1 were:7 gives:1 solely:3 extracting:1 collecting:1 function:20 absorb:1 γp:26 appreciate:1 measure:1 spectrum:4 graham:1 agen:1 say:1 re:1 depleted:1 conjugate:1 need:1 seen:2 seem:1 clearly:2 vulnerable:2 strength:1 zero:2 tends:1 latter:1 governs:1 able:1 consortium:1 converges:1 polarization:4 hr:3 ideal:1 without:2 take:2 forces:1 finding:1 destroy:1 singh:1 strengths:1 ζy:1 m2:1 accuracy:1 heisenberg:2 spectral:1 play:1 induces:1 altered:1 electric:1 normal:1 object:13 interatomic:1 consistency:1 exploited:1 germany:1 ensure:1 significant:2 phase:57 appl:1 measured:1 why:3 probes:1 cause:1 give:2 observation:5 average:9 later:1 detectors:1 heat:1 face:1 traditional:2 part:15 exp:14 pictures:2 kz:7 ky:2 typical:2 physics:4 sum:1 fact:2 quantity:1 precise:1 incorporate:1 emerging:1 drastically:1 particularly:1 phenomenon:1 disturbances:1 his:1 delta:8 scattered:5 converge:1 developed:2 corney:1 minimizing:1 relation:4 svistunov:1 hungary:2 d4:1 uniform:3 d2:3 find:13 ground:3 slow:1 ratio:4 hf:7 enough:1 should:2 analytic:2 only:8 explicitly:2 indeed:4 integrate:3 employed:1 inφ:1 hamiltonians:1 local:2 interested:1 lynch:1 do:4 cube:1 dominant:1 goes:1 notation:1 get:7 davis:1 familiar:4 de:1 overall:3 account:1 da:1 beam:1 cannot:2 dz:7 nearly:1 dx:3 ˆi:1 dv:1 during:2 dt:5 du:1 aν:1 justified:1 lossless:2 alexander:1 processes:6 reading:1 transversal:2 lengthy:1 arxiv:1 microscopy:1 ˆm:2 experiments:1 bec:1 fixed:3 inside:2 thanks:1 monochromatic:1 ignored:2 ik0:16 reference:1 acquired:1 national:1 testing:1 operates:1 observed:3 zez:1 intensity:10 individual:1 radius:1 result:8 localize:1 specialize:1 dµ:16 springer:1 belavkin:1 subject:1 suffer:1 interacting:2 resonantly:2 purpose:1 scattering:3 review:1 complementary:2 justifies:2 yet:3 state:11 determined:1 vectorial:1 closed:1 between:5 δn:1 geometric:3 previous:1 approach:4 speed:1 sections:1 notice:1 ihr:4 terms:8 ability:1 nature:4 attention:2 weak:2 however:9 equals:1 incident:17 systems:1 invisible:1 bose:18 jetp:1 distribution:5 both:4 prospects:1 last:1 limits:1 desired:1 biquadratic:3 many:8 region:1 uncertainty:2 equal:1 attributed:1 quantization:2 approximative:1 propagation:20 iv:1 hulet:1 sketch:1 refraction:1 exceeds:2 variance:1 nent:1 estimation:3 expression:4 rokhsar:1 experimental:7 ansatz:1 abbreviate:1 conclude:2 runs:1 seems:1 lagrangians:1 depletes:1 dimensional:8 grants:1 simply:2 adding:1 xi:2 sequences:1 wider:1 respect:6 schleich:1 ct:2 hω0:11 strong:1 described:1 transformations:2 second:7 basis:3 addition:2 equations:4 due:1 been:4 z1:2 detuning:3 describes:11 z2:2 extends:3 ph:1 hardly:3 fig:2 ϕˆi:12 direction:3 describe:9 flight:2 samples:1 observable:1 droplets:1 carmichael:1 coherence:2 gas:4 remark:1 depend:2 bulk:3 fund:1 coherent:1 dramatic:1 understand:4 external:2 c2:5 evidence:3 those:1 case:5 encircles:1 intriguing:1 gustafsson:1 laser:2 look:1 exponential:1 frozen:1 defining:1 estimations:2 appearance:2 t0:2 value:5 expelled:2 will:12 safely:1 behavior:2 applies:1 squeezed:1 balance:1 property:2 inspired:1 procedure:2 terminology:1 real:1 cylinder:1 larger:4 vogel:2 phenomenological:1 averaging:2 von:2 t1:17 thus:6 quanta:1 according:1 ii:11 quantize:1 itself:2 im:1 dkx:1 illustrates:1 otka:1 ic:1 dky:1 interacts:3 situ:1 shorthand:1 acknowledgments:1 different:2 develop:2 impossible:1 lengths:2 media:4 make:1 radiation:1 hecht:1 same:1 any:1 shifts:2 complex:3 quant:2 arguments:1 largest:1 units:2 dimensionless:1 gets:1 higher:2 independent:4 clear:1 infinity:1 see:31 rightfully:1 comprehensive:1 a2z:1 faces:1 effect:7 hand:5 effectively:1 moving:3 delicate:3 potentials:1 infinite:3 robust:1 focal:2 electromagnetism:3 lower:3 narrow:1 schr:11 center:1 nevertheless:1 marte:2 politzer:1 well:2 roughly:3 dispersionless:1 temperature:1 easily:2 very:1 position:1 model:7 otherwise:2 usual:2 less:2 being:5 when:3 residue:1 obtain:25 acknowledge:1 vanishes:5 sources:1 shape:2 via:2 atomic:21 immediately:1 regardless:1 giorgini:1 macroscopic:5 eigenstates:1 convolution:1 note:3 enters:1 signal:6 zoller:2 density:31 absorption:8 photons:5 point:2 royal:2 discuss:3 ψˆi:7 simple:1 add:1 potential:6 transformed:3 lett:8 easy:2 theorem:2 electrical:1 mod:1 illumination:5 remaining:2 euler:2 divided:1 identical:2 iλ:4 references:2 depends:3 represents:1 evaluate:1 dark:1 test:5 caves:1 entangled:1 a2x:1 vacuum:2 press:3 using:7 highly:1 apart:1 loss:2 necessary:1 like:3 particle:5 qualitative:1 serves:1 manifest:1 specific:1 flux:1 δl:5 steps:1 stringari:2 integrals:2 characterizes:1 mode:11 reduced:1 imprints:1 δa:1 mathematical:1 indications:1 because:12 neumann:1 classical:5 what:2 lagrange:2 some:2 begin:1 calling:1 born:4 mirror:1 images:1 neglecting:1 happens:1 provided:2 gradually:4 describing:1 lead:1 electromagnetic:4 measurements:1 integration:5 per:1 manipulations:1 depletion:22 critical:3 disappears:1 assuming:1 propagating:1 welsch:3 refer:1 expand:2 process:5 denominator:1 obey:1 indicated:1 equivalent:1 l1:8 oscillating:1 agreement:2 wesley:1 abteilung:1 although:1 found:1 imaginary:4 entirely:2 bz:1 chapter:5 about:3 ρˆi:25 extension:2 dˆ:2 a2y:1 generated:1 o:4 essential:1 carries:1 carrier:1 wolf:5 obeys:2 done:1 act:1 blocked:1 backaction:43 introduced:1 consequently:4 other:6 road:1 therein:2 rev:22 markovian:2 h2:1 maxwell:5 image:7 within:1 integral:4 functional:2 three:7 eqs:1 r2:1 hermitian:1 accounts:1 laplacian:1 einstein:11 operator:9 proportional:7 body:3 bosonic:3 often:1 statistics:3 area:1 assumed:2 support:1 approximate:4 gases:4 start:5 anderson:1 much:3 bosons:1 mandel:5 way:4 forward:1 analyze:1 was:2 propagator:1 lowest:2 hospitality:1 medium:9 complete:2 form:3 offer:1 fundamentals:1 forming:1 hp:2 regard:4 agrees:1 but:5 volume:4 illuminates:1 illuminating:2 related:1 hm:3 hc:16 dissipative:4 themselves:1 especially:2 constitute:1 made:2 intuitive:1 2πi:2 characteristic:3 cells:2 up:2 us:17 ur:1 decays:1 limit:3 fluctuations:6 problem:2 define:1 similar:3 called:1 mechanics:1 ac:1 constant:3 addison:1 defined:1 diffraction:3 universal:2 contribute:3 moved:1 general:6 single:5 proves:2 contour:1 ay:3 ax:2 gradients:1 az:1 combining:1 jaksch:2 physical:2 dalfovo:1 again:1 functions:7 compared:2 faithful:1 fellowship:1 no:1 liouvillian:6 edwards:1 percent:1 detail:3 reality:1 field:25 valid:2 role:3 details:1 spatial:7 department:2 you:3 realize:1 optically:1 picture:11 generates:1 kinetic:1 living:2 photon:8 resembles:1 shown:1 variation:1 lens:3 commutator:29 develops:1 important:1 bounded:1 additionally:1 variable:1 transfers:1 range:1 kx:2 coupling:1 assume:6 normally:1 dτ:2 required:2 paraxial:23 equivalently:1 rough:2 mass:1 dot:1 resonances:2 2c:1 n2:1 requires:1 rep:1 oran:1
|
quant-ph9801049.txt |@word consider:1 switched:1 1mhz:1 rev:12 magnetic:10 decays:1 results:1 chaos:1 switches:2 future:1 quadrature:2 consists:2 shot:4 amplified:2 involved:1 reynaud:3 adjust:1 calculate:1 paris:1 γp:2 squeezing:15 present:1 ti:2 cm3:1 cm2:1 sent:1 case:1 supported:1 6p3:5 orthogonal:2 far:3 frequencies:1 brossel:1 wave:7 fall:1 resonant:4 difference:1 exact:1 collett:1 condition:2 common:1 four:1 indicate:1 europhys:1 clouds:1 pbs:2 level:11 transmission:6 t2:1 large:5 solved:1 detected:2 minimal:2 fourier:1 small:1 optics:6 noted:1 heidmann:2 upper:2 smaller:2 compensated:1 direct:1 approximation:2 intricate:1 second:4 video:2 displays:1 pass:3 further:3 dynamics:7 port:1 davis:1 theory:1 blue:1 index:4 appear:2 section:1 cell:2 experiment:4 above:2 new:3 falling:1 piezoelectric:1 method:1 coefficient:4 agreement:2 αin:1 respectively:6 circulator:1 residual:1 atoms:53 behaviour:4 pump:2 operating:1 relaxation:1 based:1 along:1 strong:2 equations:2 change:3 obtained:2 sending:1 100khz:3 spite:1 broken:2 shift:4 study:6 losses:2 round:3 cecchi:1 maximising:1 periodic:1 procedure:1 cesium:5 resonance:17 implement:1 narrow:1 studies:1 diameter:2 via:1 explained:1 ffd:1 highly:2 logarithmic:1 visible:1 decrease:1 total:2 circumvent:1 cloud:8 use:1 takes:2 would:3 commun:2 remains:1 acousto:1 predictions:2 intense:1 stored:1 few:1 harmonics:3 therefore:2 mcclelland:1 taken:3 themselves:1 simpler:1 penna:1 theoretical:6 milliseconds:1 more:5 separated:1 upmc:1 becomes:1 under:2 line:2 emission:1 validity:1 xiao:2 berlin:2 cycles:1 particular:3 raab:1 aligned:2 iii:1 opens:1 escaped:1 account:4 mf:5 work:1 oscillator:11 mk:1 theories:1 reproduce:1 itself:1 values:2 temperatures:1 carefully:2 already:2 making:1 hollberg:1 esprit:1 transition:11 figure:4 scan:3 neglected:1 high:13 indicates:1 performed:3 reconstruct:1 sense:2 times:4 robinson:1 occur:1 working:1 filter:3 end:1 varied:1 decaying:1 optimised:1 rather:2 means:1 chrx:1 located:1 varies:1 ens:1 adapted:3 pure:1 opt:2 instead:1 parameter:6 ensemble:1 information:2 broad:1 aom:1 after:6 derived:1 different:2 hence:2 plane:3 coming:2 date:1 5cm:1 geometrical:2 data:2 parallel:1 constants:1 drop:1 natural:2 waist:1 effective:1 light:7 spectra:1 lines:3 yielding:1 provide:1 so:3 allow:1 jussieu:1 order:10 typical:1 least:1 saturated:1 help:2 modifications:1 developed:1 over:1 displayed:1 soc:1 produced:1 report:1 paper:2 through:7 lasers:1 pbs2:2 mentioned:1 letters:1 cold:19 linewidth:9 its:2 before:3 perfect:1 φnl:1 rapidly:1 lc:1 swann:1 decay:2 chosen:3 interesting:1 temporal:1 vicinity:1 exhibits:1 better:7 absence:5 fig:13 persist:2 covered:1 main:1 photodiodes:4 maximal:2 traversed:1 non:17 good:1 material:1 evolution:1 reflected:4 walls:2 precession:2 detunings:1 asymmetrical:1 they:3 half:3 now:1 term:1 cable:1 fully:1 presented:1 kerr:2 fringes:1 transmitted:8 trap:7 reasonable:1 instabilities:13 found:6 universit:1 quarter:3 traces:1 side:12 mean:2 homogeneous:1 domain:2 differential:1 generation:1 fisk:1 magneto:2 reduce:1 used:7 manifests:1 constitute:2 inhomogeneous:1 frequency:19 expect:1 entering:1 measure:4 quantum:21 our:1 transitions:3 extract:1 out:6 ketterle:1 shown:6 driving:1 display:2 gradient:1 nuovo:1 since:1 interference:1 monitor:1 acting:1 investigation:2 rc:3 induced:2 forth:1 red:1 shows:4 lugiato:2 doppler:2 turning:1 linear:21 spot:1 pumping:13 free:2 quite:3 difficulty:1 recordings:1 complicated:1 york:1 counteracted:1 hand:4 generate:1 interaction:7 created:1 persists:1 confocal:1 motion:1 length:10 produce:2 place:2 exponentially:1 consequence:2 βi:2 first:4 origin:1 initial:2 symmetry:1 variables:1 number:10 comprised:1 done:1 fast:1 mixing:1 ring:1 computed:1 dispersive:1 little:1 checked:1 temperature:1 bistability:15 system:10 approximately:1 response:1 their:7 cooling:1 passed:2 perfectly:1 ranging:1 gives:1 shifted:1 exploring:1 trapped:3 exactly:1 transverse:3 released:2 part:5 authors:1 yurke:1 sublevels:7 joffe:1 than:11 population:2 detection:5 min:2 split:1 bachor:1 cimento:1 rate:4 recording:6 states:2 classes:1 intensities:2 transducer:1 amplitude:1 were:9 vapours:1 powers:8 raman:1 bad:1 turned:4 spectrum:7 curves:3 correspond:3 seen:2 seem:1 clearly:2 angle:1 built:1 depending:1 thoroughly:1 storage:1 able:1 mechanism:1 causing:1 take:2 finding:1 detector:1 switching:3 hyperfine:5 even:2 cnrs:1 added:1 fundamental:2 trace:5 any:1 measures:1 most:1 involving:1 propagate:1 polarisation:1 significant:2 phase:10 marie:1 measured:1 trapping:20 8mm:1 subtracted:1 consist:1 considered:2 calculated:3 later:1 inferred:1 looked:1 curie:1 proceedings:2 reflecting:2 thank:1 velocity:1 left:4 physics:2 fact:2 particularly:1 show:3 pd3:3 probe:27 bring:1 bright:1 participate:1 threshold:1 trivial:1 find:2 ground:11 slot:1 larson:1 ratio:1 parameters:2 writes:1 dynamical:1 distributed:1 enough:2 should:2 jan:1 only:11 going:1 candidates:1 rich:1 φn:1 employed:1 castelli:1 local:11 achieve:1 coherences:1 plate:5 his:1 oscilloscope:1 dependent:2 beams:25 db:2 dc:2 bloomfield:1 beam:38 cannot:1 nearly:2 dv:1 during:3 dt:2 dp:1 layout:1 processes:2 exhibiting:1 densities:1 indicated:1 numerous:1 arxiv:1 bandwidth:7 tuned:1 reid:1 investigate:2 experiments:2 predicted:4 contain:1 including:2 fixed:5 voltage:1 scanning:3 set:3 filters:4 achieved:2 observed:6 intensity:10 result:2 operated:1 close:4 best:2 subject:1 closer:1 detect:1 damping:1 manson:1 resonantly:1 harvey:1 diode:2 pd2:6 pd1:6 state:13 converted:3 various:5 between:7 modulators:1 conditions:6 across:5 recently:2 spectroscopy:1 lange:1 however:4 efficiency:4 windows:1 comparably:1 abruptly:1 both:2 essentially:2 many:1 region:1 la:1 escape:2 equal:2 zeeman:3 called:1 sensitive:1 involve:1 refraction:3 contribution:1 whole:1 experimental:12 otherwise:2 among:1 relevant:2 fields:3 point:1 simple:4 excess:5 homodyne:4 pritchard:2 brecha:1 loaded:1 photocurrents:1 conference:1 destroyed:1 sine:1 described:3 prentiss:1 due:8 been:8 pc:1 detuning:7 much:3 pbs1:2 combined:1 pj:1 ph:1 empty:1 systems:1 describe:1 corresponding:1 given:2 gas:1 coherent:1 understand:2 input:16 standard:2 hmc:1 applied:1 laser:14 pacs:1 straight:2 aip:2 value:4 spontaneously:1 will:5 while:9 ar:1 abrupt:1 promising:2 squeezed:4 situation:2 20ms:1 khz:1 ix:1 larger:4 5mhz:4 orientation:5 coupled:3 thus:4 them:1 ii:1 bias:1 contract:2 interacts:2 disappear:3 increased:1 containing:8 anymore:1 propagation:1 circularly:4 media:1 lett:6 same:6 linked:1 reconstructed:2 complex:1 quant:1 virtually:2 accumulating:1 units:2 filtered:4 finite:1 φl:2 start:1 prerequisite:1 higher:3 investigated:1 eds:3 optic:1 laboratoire:1 numerical:4 effect:4 hysteresis:1 usually:3 compared:2 uses:1 supposing:1 changing:1 anticipated:1 totally:1 cycle:2 centred:1 lower:2 motionless:2 off:7 largely:1 changes:2 lambrecht:4 well:3 roughly:1 analysis:1 without:1 components:2 very:4 model:6 usual:2 6s1:3 less:1 being:3 generally:1 obtain:1 effects:3 difficulties:1 shape:1 underlying:1 atomic:20 harrison:1 alternative:1 afterwards:2 absorption:3 supply:1 had:1 except:1 quadratures:2 treatment:2 kastler:1 excited:4 identical:1 saturation:5 around:3 showing:3 possible:7 dark:1 increases:3 know:1 background:1 vacuum:1 press:1 using:6 qwp:4 bistable:5 imposed:1 like:2 semi:2 sincerely:1 sublevel:2 obvious:1 signal:10 raizen:2 manifest:1 alkali:1 imposes:1 mhz:2 either:2 martin:1 output:6 conclusion:1 orozco:2 essential:2 cooled:3 accessible:1 satisfactory:1 right:2 classical:2 refocusing:1 some:2 pierre:1 competition:2 understood:2 towards:1 mirror:6 oscillations:9 giacobino:7 matching:4 electric:1 specific:1 scale:1 lead:1 cavity:63 resonances:1 avoid:3 measurements:2 recorded:3 intracavity:5 instantaneous:1 mlynek:1 behave:1 bra:1 provides:1 tends:2 ct:1 demonstrated:3 mode:4 measuring:1 varying:1 noise:33 coated:1 detuned:5 equivalent:1 analysed:2 expansion:1 pressure:1 step:1 although:2 analyser:4 bx:1 properties:3 analysing:2 about:7 carried:1 am:1 compatible:1 range:5 larmor:1 mixed:1 gallagher:1 consequently:2 equally:1 beamsplitter:5 chu:1 presence:9 into:13 within:3 numerically:3 three:1 appropriate:1 because:1 arecchi:2 balanced:1 valuable:1 next:1 theoretically:1 eg:1 acknowledgements:1 additional:2 polarising:4 interacted:1 normalised:1 assumed:1 springer:3 there:1 reduction:3 long:2 width:1 low:10 way:3 perform:1 valley:1 was:19 energy:1 1khz:2 record:3 function:6 medium:9 complete:2 boyd:1 constantly:1 but:6 back:4 placing:1 expected:1 ec:2 atom:5 optical:24 highest:2 courty:4 observation:3 directed:1 absent:2 made:1 rejection:1 largest:1 beamsplitters:1 mertz:1 characteristic:2 inside:3 variations:2 up:4 us:1 placed:1 below:2 owing:1 limit:1 sapphire:2 fluctuations:5 problem:1 advantage:2 average:3 polarised:3 ac:1 b60:1 associated:2 pin:2 heidelberg:2 hwp:2 abstract:1 measurement:4 linearity:2 general:1 duration:1 kimble:2 scanned:8 controlled:1 formalism:1 trip:3 dα:1 avoided:2 no:2 whereas:1 populations:2 when:12 slusher:1 power:28 field:15 other:3 electrical:1 branch:3 digital:1 polarisations:1 optically:1 fabre:4 radially:1 variation:1 stay:1 monroe:1 generated:3 important:3 visibility:1 sides:1 structure:1 freely:1 oscillates:1 coupling:3 fluorescence:1 requires:1 space:2 curve:4 interacting:1 original:2 time:9 starting:1 having:4 hope:1
|
quant-ph9801050.txt |@word ungar:1 monte:1 gt:3 consider:9 squared:1 magnetic:1 global:2 results:5 elisabeth:1 acknowledgements:1 leads:5 eds:1 disappears:1 consists:2 expressions:5 contributions:2 xxi:1 reynaud:4 layers:1 inverse:2 calculate:2 paris:1 rayleigh:10 presents:1 finally:2 squeezing:4 under:7 worth:2 sent:1 interacting:1 random:14 advantage:1 orthogonal:1 far:1 frequencies:5 brossel:1 wigner:1 wave:1 fall:10 resonant:1 affect:1 exact:1 electronics:1 condition:1 umn:1 clouds:1 presented:2 transmission:1 positions:4 t4:4 t2:19 ri:5 large:6 progress:1 recall:2 small:6 enhance:1 optics:7 round:1 heidmann:1 smaller:10 estimates:1 approximation:1 second:2 α2t:2 value:10 further:2 dynamics:1 carlo:1 theory:2 even:2 aim:2 rewritten:4 nonlinear:11 plays:1 appear:2 section:22 experiment:5 goes:1 subpoissonian:2 falling:10 consisting:1 dn0:12 devoted:1 explosion:1 deduces:1 respectively:3 here:2 understanding:1 met:1 free:8 excess:3 along:2 standard:1 respect:2 appears:1 change:1 deduced:8 obtained:8 great:1 ref:1 involved:1 study:2 larger:8 commonly:1 ignoring:1 resulting:1 poisson:2 usually:3 resonance:4 fourier:1 studies:1 useful:1 projection:1 family:1 scales:1 hermite:2 castin:1 explained:1 scaled:1 clairon:1 decrease:2 total:2 papoulis:1 cloud:39 readily:2 use:1 haken:1 would:5 remains:3 positive:1 scan:1 france:1 therefore:10 dns:5 taken:1 eiωl:1 themselves:1 theoretical:1 more:7 upmc:1 flying:2 factor:4 curvature:1 stressing:1 degrade:1 particular:8 corresponding:3 cases:6 hold:1 must:2 account:1 room:1 thanks:1 integrating:3 decay:3 equation:10 modified:4 mk:1 remain:1 values:3 thin:7 following:4 example:6 numbers:3 compare:1 give:3 expanding:1 neglected:2 purposes:1 drewsen:2 high:4 effectively:1 assumptions:8 performed:4 want:3 quasistationary:4 times:10 axis:4 cooperativity:2 monitoring:1 provide:2 describes:1 discussion:3 holds:1 write:2 how:2 varies:3 ens:1 instead:1 parameter:12 fv2:3 obeys:1 profile:9 simplicity:2 product:4 description:4 undergoing:1 may:36 after:4 containing:2 connects:1 consequence:6 produce:1 coming:2 society:2 horizontal:1 efficiently:1 stress:1 short:2 waist:5 effective:33 light:2 spectra:2 explicit:2 summing:4 element:1 rather:4 spectral:3 so:5 sn:7 fundamental:1 enter:1 definitions:1 order:14 typical:1 2sm:4 six:1 interpretation:3 help:2 ith:1 developed:2 pointed:1 τr2:16 mainly:6 soon:1 years:1 produced:3 radar:1 thermal:3 experiments:13 through:25 statistical:2 mentioned:1 cold:13 y2:2 ieee:1 its:6 before:1 delay:3 derive:3 longitudinal:2 fit:1 located:1 chosen:4 τg:11 temporal:3 τc:2 scully:1 detected:1 lr:15 τw:20 τr:19 non:3 good:1 focus:1 detectable:1 introduce:1 disregarded:4 effects:2 they:6 half:3 2κc:1 now:7 maxwellian:1 discuss:5 developments:1 easily:1 measures:1 2s:2 always:1 2x:1 applied:2 gt2:8 2g:2 trap:15 l1:1 disregard:1 found:2 universit:1 lorentzian:4 mean:17 weight:5 series:1 magneto:3 gaussian:29 related:2 eiωτ:1 frequency:12 static:1 obtains:2 measurement:6 quantum:9 our:4 out:1 category:1 stands:1 shown:3 opened:1 space:5 furthermore:1 since:8 crucial:2 projected:1 emulate:1 contained:2 exploding:2 socalled:1 formula:1 get:1 evaluation:8 integrated:4 shows:2 exactly:2 lugiato:1 doppler:1 linear:25 fv:4 dealt:1 divergence:10 modelisation:1 quite:2 completely:1 statistics:2 might:1 estimate:2 beginning:1 finite:2 temperature:6 definition:6 interaction:6 r2:1 bistability:1 positiondependent:1 motion:5 length:16 exponentially:1 hence:2 onto:4 first:8 informations:1 already:7 martin:1 polarisability:2 variables:4 number:88 restrict:2 simplified:1 strumia:1 reached:1 precisely:5 evaluations:2 size:19 dispersive:1 passes:3 given:7 publication:1 physique:1 introduction:4 leading:1 least:1 their:4 assumption:3 ballistic:4 too:2 calculations:1 undergoes:1 white:1 recovered:1 scans:1 a37:1 trapped:2 continuous:1 transverse:10 released:5 optical:8 manipulation:1 x2:3 off:1 representing:1 than:20 modes:5 third:1 sections:1 rate:2 limiting:10 a46:1 matter:1 quasistatic:2 determined:4 supposed:1 amplitude:4 iωl:1 gives:2 treated:1 distinguished:1 w2:10 σr2:5 lowest:2 rewrite:1 modern:1 turned:1 spectrum:16 correspond:4 2t4:1 2t2:2 seen:1 santarelli:1 any:7 accounted:1 zero:1 depending:1 latter:3 ryzhik:1 downwards:1 gravity:13 note:3 phillips:1 fitting:1 potential:1 phaseshifts:2 negligible:1 modulus:1 formulas:1 cnrs:1 added:1 multiple:1 sm:4 opposite:2 correlation:12 detect:1 propagate:1 overlapping:1 position:12 phase:25 analytically:1 measured:5 why:2 phaseshift:2 kb:2 deviations:1 laurent:1 especially:1 considered:9 calculated:3 later:2 paragraphs:1 necessary:2 curie:1 part:1 exp:16 velocity:14 serge:1 poissonian:5 sum:1 laws:1 precise:3 particularly:2 show:3 probe:27 relatively:1 relation:2 solutions:1 saturated:2 d0:2 ratio:1 knowledge:1 parameters:3 claude:1 delays:1 dynamical:1 written:7 jan:1 dalibard:1 only:5 ambiguity:1 indeed:3 local:2 over:9 polarizability:4 dn:24 radiated:6 means:1 dependent:4 beams:1 de:11 da:8 beam:63 dz:7 nearly:1 dx:15 dy:7 dv:7 during:2 table:1 interpreted:1 dr:10 becomes:1 holland:1 reveal:1 evolution:3 4πs:5 arxiv:1 αl:8 negligeable:1 investigate:1 paper:11 wish:1 analytical:4 including:1 regarded:1 salomon:1 ignored:1 reference:3 hγ:1 sensitivity:2 correlations:1 σv2:8 detection:13 intensity:3 radius:5 result:2 w0:1 discussions:2 terms:6 uncorrelated:2 acts:1 analog:1 techniques:2 linewidth:1 αt:9 review:4 dipole:2 enough:1 various:5 µk:1 between:4 limit:6 justified:1 conditions:2 across:1 preserve:1 notice:1 recently:1 statistically:1 2σv:2 attention:4 weak:1 however:3 w02:1 spectroscopic:2 incident:3 concentrate:2 key:2 2πx:1 preprint:1 atoms:65 come:3 distribution:16 both:3 essentially:3 instant:1 2k:2 freely:2 density:14 according:1 fulfilled:2 propagation:2 hω:1 σs:7 σr:25 passing:3 expression:18 σv:5 experimental:5 otherwise:2 relevant:1 cn:8 point:3 simple:2 iϕ:1 address:1 cf:1 america:2 semiclassical:1 simply:2 pritchard:1 polynomial:1 associated:5 schleich:1 considering:3 astrid:1 described:2 equations:4 due:6 been:8 detuning:14 much:16 slowly:1 treat:1 interest:1 expected:3 pk:4 ph:2 closed:1 direction:3 flight:12 sufficient:1 releasing:1 precision:3 determination:1 prescription:1 assessments:1 present:16 case:34 laser:13 look:1 exponential:4 variances:3 expanded:1 evaluated:12 excited:1 will:30 while:10 replaced:3 evaluating:3 many:1 situation:3 property:3 hωl:1 elaborate:1 characterizing:1 layer:6 studied:7 coupled:3 vi:2 thus:6 encountered:1 characterize:1 vt:7 rid:1 shift:15 interacts:1 different:6 metrology:1 journal:4 powers:2 cross:1 same:12 unity:1 quant:1 modification:10 products:1 dimensionless:5 gets:1 higher:6 development:1 independent:1 used:8 see:4 laboratoire:1 riis:1 upon:4 effect:16 iδ:1 average:1 v2:1 variance:13 changing:1 expand:1 recent:1 relies:2 lower:1 kept:1 traps:1 whole:3 lambrecht:3 well:4 davis:1 academic:1 quantitative:3 model:2 dimension:1 just:1 generally:1 obtain:6 press:1 shape:2 properties:1 atomic:65 arimondo:1 scattering:1 previous:5 oriented:1 monitored:2 conclusions:2 absorption:1 photons:1 measure:1 character:9 weiss:2 valid:2 treatment:2 theorem:1 kastler:1 transformation:1 momentum:1 divided:1 identical:1 saturation:7 b59:1 depends:2 evaluate:7 possible:3 corresponds:2 confined:1 using:7 characterized:1 dimensional:2 appearing:1 follows:3 signal:2 velocities:2 draw:1 specific:2 mirror:2 mhz:1 either:3 integrals:2 arbitrary:4 multiplicative:2 become:2 stationary:2 essential:1 therein:2 jean:1 representation:1 often:1 classical:1 pierre:1 sφφ:4 b6:1 normalisation:1 giacobino:3 ignore:1 scale:5 describing:1 lead:4 cavity:18 measurements:7 intracavity:2 per:3 instantaneous:2 contributing:1 does:6 unit:2 assuming:2 propagating:1 mode:12 measuring:1 noise:17 obey:1 equivalent:1 processing:2 expansion:3 bt:2 step:1 liouville:1 simpler:1 sub:1 about:1 magnetooptical:1 discussed:4 dependence:6 o:1 simulation:1 sake:1 range:5 greatly:1 introduced:3 consequently:1 other:1 own:1 letters:1 chu:1 keeps:1 previously:1 into:5 gradshteyn:1 integral:10 three:1 down:5 lies:1 because:1 references:3 determine:1 elementary:5 proportional:4 next:1 mere:1 marie:1 area:2 assumed:1 initial:10 long:5 class:1 width:4 conservation:1 low:2 way:1 analyze:2 was:1 interferometry:1 function:30 medium:7 north:1 but:2 back:2 volume:6 properly:1 atom:7 implies:2 courty:1 coupling:2 joffe:1 made:1 drummond:1 qualitative:1 instructive:1 characteristic:5 inside:4 uv:1 characterization:1 up:5 us:1 placed:1 below:2 projecting:1 simplifying:5 ωl:3 spectroscopy:2 fluctuations:54 problem:5 define:1 agree:1 u00:2 regimes:1 detailed:1 khz:1 b60:1 constant:1 labels:1 ln:1 defined:3 focussing:1 abstract:1 describe:1 influence:4 general:13 single:1 wavelength:1 accounting:3 distributions:2 trip:1 physical:4 again:1 functions:6 assessing:1 completeness:1 no:1 allow:2 when:14 detail:1 arctan:1 rewriting:1 field:31 interested:2 role:1 spatial:1 nadir:1 conclusion:3 optically:2 ketterle:1 briefly:1 calculating:2 models:1 fabre:2 center:1 variation:17 covariance:5 important:1 peak:2 variable:10 structure:2 matrix:1 delineate:1 regime:5 longer:4 fluorescence:2 dω:1 assume:1 physics:3 dτ:1 factors:1 covariances:1 equivalently:1 investigated:1 volumes:4 time:56 n0:5 quantity:2 requires:1 normalized:5
|
quant-ph9801051.txt |@word limited:2 caused:1 magnetic:1 results:1 eds:1 quadrature:2 go:1 shot:6 amplified:2 weakly:3 causes:2 reynaud:4 compact:1 b10:1 calculate:2 paris:1 concerned:1 γt:1 supported:1 contract:2 squeezing:27 ti:1 cm3:1 sent:2 random:2 amplitudes:1 6p3:2 very:3 frequencies:2 rise:1 brossel:1 wave:2 fall:1 resonant:3 experimentally:1 difference:1 splitter:1 pbs:1 level:8 transmission:2 t4:1 t2:2 occurs:1 large:6 detected:1 minimal:3 small:1 optics:2 noted:1 still:1 upper:3 smaller:3 consistent:1 prediction:3 sign:1 second:6 video:1 evaluated:2 chen:1 further:2 estimated:1 port:1 linear:2 even:2 index:2 nonlinear:7 trapping:13 apparatus:1 giving:1 sum:1 cell:1 experiment:5 above:3 falling:4 increasing:2 ever:1 method:2 contrast:1 coefficient:3 lee:1 never:1 circulator:1 here:4 atoms:43 explore:1 europhysics:1 represented:1 based:1 strong:1 prentiss:1 appears:1 interpret:1 obtained:6 incoming:1 suitably:1 shift:2 study:2 larger:2 experience:1 amount:1 resulting:2 action:1 resonance:12 raab:1 studies:1 diameter:1 lounis:1 modifying:1 flexibility:1 analyzing:3 total:2 cloud:11 use:1 takes:3 working:1 commun:1 poizat:1 predictions:4 intense:3 few:1 live:1 therefore:3 taken:2 type:2 theoretical:10 more:1 separated:1 upmc:1 becomes:3 under:4 tested:1 particular:1 iii:1 blocking:1 must:1 fly:1 sample:1 account:2 recall:1 averaged:1 oscillator:7 mk:1 values:1 ms:1 making:1 example:2 tat:1 transition:9 figure:6 scan:3 process:2 expanding:2 implementations:1 high:1 indicates:3 minimum:1 performed:2 robinson:1 verlag:1 cooperativity:9 end:2 varied:2 photodiode:3 rather:3 means:1 feature:2 chrx:1 far:2 varies:1 ens:1 monroe:1 parameter:5 ensemble:1 product:1 after:5 derived:2 davis:1 plane:2 designed:1 coming:1 fits:2 horizontal:1 grangier:1 data:4 natural:2 waist:2 light:5 spectra:3 lines:2 correspond:2 provide:1 negligible:2 partly:1 subsequently:1 vapor:1 order:10 instabilities:1 saturated:1 indeed:1 over:1 refractive:2 soon:2 distortion:1 ended:1 thermal:1 paper:1 through:5 lasers:1 affect:1 mentioned:1 beamsplitter:4 cold:16 linewidth:7 its:3 before:1 rapidly:2 lc:1 fit:1 located:1 polarizing:3 expectations:1 decreases:1 absence:1 fig:12 constitutes:1 main:1 τr:1 split:1 maximal:3 non:1 good:3 reflected:1 effects:1 they:1 half:1 now:1 easily:2 cable:1 fully:3 edges:1 presented:1 realistic:1 magnitude:1 transmitted:2 trap:15 each:1 did:1 universit:1 quarter:1 side:5 lorentzian:1 mean:4 significantly:2 generation:1 series:2 magneto:3 gaussian:3 ec:2 constitute:1 frequency:6 measure:1 quantum:15 our:4 transitions:1 eq:1 out:3 ketterle:1 shown:7 furthermore:1 since:1 rev:8 europhys:2 ref:1 correct:1 shows:5 lugiato:2 doppler:3 turning:2 theory:3 spot:1 pumping:6 free:6 standard:1 completely:1 interaction:2 starts:1 could:2 bistability:13 times:2 turn:1 length:3 produce:2 place:2 consequence:1 10ms:1 first:5 origin:1 features:2 symmetry:1 powerful:1 number:11 tektronix:1 electronic:1 size:1 given:3 temperature:3 decrease:1 leading:2 interact:1 system:3 their:5 cooling:1 ballistic:1 too:2 realization:1 compromise:1 a37:1 trapped:2 explanation:1 continuous:1 interesting:1 accurately:1 transverse:3 released:1 optical:13 favorable:1 sublevels:1 representing:1 than:6 dynamical:1 peaked:1 detection:3 kind:1 polarized:2 determines:1 fundamental:1 require:1 cimento:1 intensity:6 correponds:1 recording:1 determined:3 transducer:3 were:6 powers:5 distinguished:1 function:5 avoided:1 nuovo:1 turned:5 spectrum:11 curves:2 departure:1 manner:1 seen:2 any:3 angle:1 built:1 efficient:1 responsible:1 able:2 gravity:1 sinatra:1 ideal:1 potential:1 take:2 so:1 reproducing:1 completed:1 cnrs:1 towards:2 allow:1 trace:2 opposite:1 systems:1 most:1 involving:1 orthogonally:1 position:1 phase:6 marie:1 measured:11 subtracted:1 calculated:1 adopt:1 looked:2 curie:1 reflecting:1 principle:2 exp:1 velocity:3 fact:1 particularly:1 phenomenon:1 rayleigh:1 text:1 probe:21 area:1 threshold:1 find:3 piezoelectric:3 ratio:3 parameters:4 fisk:1 enough:2 should:4 jan:1 failed:1 only:4 going:2 factor:1 castelli:2 local:7 hope:1 plate:4 τr2:3 dominant:1 goes:1 meanwhile:1 dependent:1 beams:17 beam:26 nearly:2 report:1 during:3 interpreted:1 processes:3 bar:3 densities:1 indicated:1 fields:1 arxiv:1 reid:1 bad:2 experiments:9 including:2 fixed:3 salomon:1 scanning:1 set:6 filters:1 swept:1 observed:10 see:1 computer:1 radius:2 result:3 close:2 best:3 subject:1 a46:2 error:3 reproducibly:1 interacting:3 µw:1 diode:1 behind:1 difficulties:1 between:4 conditions:8 across:1 reproduced:1 do:1 initially:1 2σv:1 emitted:1 weak:1 however:4 analyzer:4 efficiency:4 incident:2 enters:1 fluctuations:7 preprint:2 come:1 relying:1 originates:1 both:1 prospects:1 improved:1 swann:1 steep:3 region:1 escape:2 equal:1 against:1 figures:1 τg:1 σr:2 passing:1 expression:1 σv:2 comes:1 adjusted:1 filtering:1 coudreau:1 character:2 excess:6 homodyne:4 pritchard:2 considers:1 ct:1 uncorrected:1 ensures:1 described:4 capable:1 radiative:2 due:9 been:10 pc:1 reduction:8 much:4 pd:1 pj:1 ph:3 empty:1 lett:7 dots:1 corresponding:3 linearity:1 input:2 100khz:1 those:2 hmc:1 case:4 laser:10 exponential:1 pacs:1 solid:2 straight:1 kimble:2 value:11 will:1 while:6 steinberg:1 behavior:1 promising:1 squeezed:1 photodiodes:1 khz:1 studied:2 5mhz:5 characteristics:1 thus:2 xiao:1 discrepancy:1 according:1 itself:2 attributed:1 accounting:1 technology:1 currents:1 containing:1 circularly:1 media:2 same:4 linked:1 parts:2 quant:1 virtually:1 largest:1 several:1 higher:5 development:1 calculation:1 used:6 optic:3 laboratoire:1 numerical:1 effect:5 hand:5 driven:1 cesium:1 levels:1 spurious:1 supposing:1 normalization:1 lower:2 motionless:1 off:6 traps:1 bachor:1 changes:1 lambrecht:6 well:3 edge:2 experimental:12 relied:1 quantitative:1 model:8 1cm:1 left:3 6s1:2 just:1 being:1 grynberg:1 obtain:1 sources:3 bandwidth:2 atomic:23 predicts:1 previous:1 rapid:1 monitored:1 esprit:1 had:3 except:1 exclusively:1 quadratures:2 source:1 unambiguously:1 treatment:1 kastler:1 extensive:1 mod:1 excited:1 opt:2 saturation:7 around:1 possible:1 b55:1 dark:1 increases:1 raizen:1 using:2 part:2 highly:1 qwp:1 insert:2 necessary:1 like:1 flight:1 halfwave:1 signal:6 modulated:1 specific:1 either:1 martin:1 output:4 orozco:1 4mm:1 cooled:2 satisfactory:1 right:4 often:1 some:2 pierre:1 competition:1 accelerate:1 mirror:4 oscillations:1 giacobino:8 provided:1 scale:1 lead:2 cavity:34 resonances:1 avoid:2 measurements:3 recorded:1 does:2 bra:1 provides:1 propagating:1 demonstrated:2 measuring:1 noise:43 detuned:4 broadening:1 processing:1 agreement:3 expansion:1 broken:2 found:1 properties:1 stage:1 about:3 developped:1 substracted:1 dependence:2 recognized:1 range:2 mixed:1 observation:2 slightly:2 letters:1 presence:3 into:4 within:1 bound:1 down:2 references:1 proportional:2 france:1 theoretically:1 additional:3 interacted:2 assumed:1 springer:1 detuning:4 long:1 dispersion:2 width:3 appl:2 low:4 way:1 ed:1 conceivable:1 was:18 energy:1 chu:1 raman:1 medium:4 elsewhere:1 boyd:1 but:2 hu:1 expected:3 gain:2 atom:6 attainable:1 line:4 highest:1 courty:4 longer:1 made:1 wieman:1 inside:1 up:6 placed:1 below:6 limit:1 sapphire:1 demonstrate:1 distribution:1 similar:1 called:1 ac:1 b60:1 constant:4 hwp:1 abstract:1 measurement:6 influence:1 single:1 scanned:6 controlled:1 work:1 check:1 constructed:1 compared:3 no:3 courtois:1 whereas:3 when:6 detail:1 power:4 field:5 points:1 branch:3 spatial:1 calculating:1 models:1 fabre:4 variation:6 prepared:1 generated:2 pumps:1 peak:1 included:1 repumping:2 sides:2 structure:2 coupling:1 fluorescence:1 curve:9 fitted:1 time:13 original:3
|
quant-ph9801052.txt |@word limited:1 consider:7 represent:1 global:1 results:5 elisabeth:1 leads:1 δcf:1 quadrature:1 computation:5 consists:1 follow:1 expressions:14 contributions:13 ballagh:1 reynaud:12 devoted:1 whose:1 depend:2 zone:1 paris:1 iii:3 technique:1 containing:5 finally:2 squeezing:53 present:4 stochastic:4 analogous:1 worth:4 dipoles:5 applied:1 nσ:1 amplitudes:15 g2:4 g1:4 far:3 frequencies:4 rise:1 brossel:1 wave:77 milani:1 interpreting:1 sidebands:2 resonant:7 experimentally:1 emphasized:1 difference:1 matrices:6 expectations:1 condition:9 four:3 differentiated:2 level:4 transmission:3 turns:1 developing:1 solution:4 large:14 solved:1 minimal:1 small:11 inspection:1 round:1 heidmann:4 smaller:3 degrading:3 prediction:1 approximation:1 fold:1 second:4 a41:1 value:9 δeα:7 theory:11 even:2 index:1 nonlinear:5 g22:1 stands:1 gβα:10 section:8 above:1 replaced:7 method:1 contrast:10 coefficient:5 layers:1 deduces:1 respectively:6 component:4 equals:1 here:3 understanding:1 behaviour:2 excess:3 directions:1 based:1 along:3 astrid:1 equations:16 appears:2 deduced:3 obtained:9 incoming:2 study:3 studied:4 leaving:1 strikingly:1 products:1 commutators:1 usually:2 resonance:5 fourier:2 formulated:1 projection:1 passage:2 unit:1 standing:1 use:5 proceed:1 working:2 remains:6 positive:2 predictions:12 france:2 noting:1 call:1 therefore:6 criteria:1 eiωl:1 associated:1 cδ:4 resonator:1 theoretical:2 more:9 separated:1 upmc:1 conclusions:2 factor:1 emission:8 validity:1 normalized:9 particular:7 known:2 cases:1 eα:3 must:1 states:1 account:3 thanks:1 unessential:1 setup:2 work:1 ρm:3 modified:6 theories:2 remain:1 paragraph:1 values:6 thin:3 following:9 spontaneous:7 example:1 performed:1 compare:4 figure:3 give:10 process:2 neglected:1 stressing:2 high:4 assumptions:5 numbers:1 want:1 g3:2 positiondependent:1 axis:6 cooperativity:1 end:2 rather:2 discussion:9 holds:1 regions:1 dependent:3 ens:1 parameter:22 ensemble:1 profile:21 electronics:1 description:5 influenced:1 may:32 after:2 derived:5 treatments:1 wrong:1 plane:56 physik:1 coming:4 g11:3 evaluations:1 da:7 response:5 efficiently:3 diagonal:1 natural:1 waist:2 effective:9 computations:8 light:1 spectra:32 lines:2 summing:2 element:1 perform:2 ones:1 so:9 fundamental:7 correlation:6 definitions:1 words:1 order:39 michel:1 serge:1 2sm:7 saturated:1 closely:1 enter:2 2se:1 over:12 mainly:2 soon:2 ended:1 paper:2 through:10 existence:1 cold:2 y2:1 ieee:1 its:3 before:4 perfect:1 write:3 derive:1 longitudinal:1 reflection:2 chosen:5 sα:2 solving:1 τc:1 writing:2 forms:3 static:2 lr:6 whole:4 rabi:2 main:1 might:1 setting:1 versus:1 non:4 good:3 greater:1 entire:1 planewave:3 fur:1 processes:2 introduce:1 disregarded:3 obeyed:2 p11:1 p12:1 hamilton:1 effects:3 they:12 focus:2 now:15 discuss:2 refering:1 matched:3 susceptibility:21 term:11 2s:5 always:1 kerr:22 identified:1 sufficiently:1 2f:3 magnitude:1 trap:1 2c:6 disregard:3 accounts:1 universit:1 side:2 characterized:1 mean:17 domain:21 differential:2 ei:2 significantly:1 populated:1 fisk:1 magneto:1 gaussian:60 related:4 elementary:1 frequency:26 pβα:1 entering:1 quantum:11 wavelength:1 satisfied:2 out:11 w2:6 reid:4 shown:6 matrix:8 space:2 restricted:2 furthermore:1 since:3 projected:1 denotes:2 contained:1 denoted:1 get:1 evaluation:3 occurs:1 shows:2 lugiato:5 numerical:1 turning:8 linear:17 written:12 favored:1 gardiner:1 divergence:4 given:4 free:1 quite:4 approaches:2 estimate:4 lambropoulos:1 definition:2 interaction:9 derivation:1 via:1 optics:7 could:1 bistability:17 times:2 βe:1 length:8 leading:1 consequence:7 βm:8 onto:5 first:12 already:7 relate:1 variables:3 revealing:1 number:11 reaches:3 enlarged:1 dilute:1 simplified:1 long:2 directly:1 reached:2 ring:1 precisely:5 size:10 dispersive:2 differ:3 grangier:1 checked:1 rewritten:1 tannoudji:1 introduction:2 sm:12 adjoint:1 system:2 relations:5 their:2 assumption:4 calculations:9 susceptibilities:2 perfectly:2 iδ:24 a33:3 a32:2 a30:1 a37:1 becomes:1 a35:1 a34:1 centered:1 transverse:25 released:1 optical:10 authors:1 x2:2 eliminated:1 representing:1 than:10 coefficients:3 population:4 diffusion:1 iωt:1 third:1 cimento:1 rate:4 limiting:3 project:4 matter:1 optimum:8 intensities:8 supposed:1 amplitude:7 represents:2 iωl:1 wiley:1 powers:2 zero:6 result:3 lowest:2 delineates:1 nuovo:1 cohen:1 p22:1 spectrum:8 curves:3 correspond:3 manner:2 recover:1 any:2 strength:1 apparent:1 lies:2 min:2 efficient:1 studying:1 latter:1 responsible:3 physique:3 note:7 square:1 generalized:2 analogy:1 new:2 coincide:9 heisenberg:1 cnrs:1 towards:1 allow:1 gα:2 opposite:1 consistency:2 reach:1 most:1 connected:1 drummond:1 quantitative:4 device:1 marie:1 measured:2 model:33 appear:3 found:3 nonlinearity:3 considered:4 arising:1 clear:3 broadened:1 steady:1 g12:4 curie:1 accounted:6 se:5 exp:3 physics:1 sum:2 lying:3 slope:1 incorporate:2 particularly:2 show:4 timedependent:1 probe:8 rotating:1 relation:1 threshold:2 interpretation:3 degraded:1 find:1 d0:2 ratio:1 criterium:2 parameters:5 claude:1 courty:4 state:6 negligible:4 jan:1 dalibard:1 only:10 going:3 walls:4 postulated:3 constant:3 local:7 hope:3 polarizability:2 do:1 dominant:1 notation:3 means:4 occuring:1 beams:1 de:7 degradation:15 aα:1 beam:34 cannot:3 dz:1 nearly:2 dx:10 dy:3 during:1 averaged:9 dr:5 lossless:1 carmichael:3 adiabatically:1 evolution:1 4πs:7 heaviside:1 fields:19 arxiv:1 bandwidth:1 negligeable:1 bad:1 predicted:3 contain:1 analytical:3 valid:1 transforms:2 ignored:1 computed:6 reference:3 modifications:2 hγ:1 frame:1 detection:2 intensity:19 p21:1 quantitatively:1 w0:1 discussions:2 close:7 forthcoming:1 uncorrelated:1 techniques:1 a46:3 phases:1 interacting:2 manson:1 review:16 uα:4 dipole:8 tend:1 symmetric:1 outside:3 radiated:8 between:5 limit:13 conditions:5 αl:4 multiplied:2 triplet:4 terms:41 a40:1 attention:1 weak:1 however:6 w02:1 hypothesis:1 would:4 key:1 2πx:1 atoms:31 come:4 problem:2 both:1 prescription:1 limits:1 taking:1 decay:7 equal:3 attributed:1 distinguished:1 propagation:1 negative:1 boyd:1 variance:1 contribution:2 estimation:3 adapted:1 generalisation:1 perturbative:1 conclude:2 simple:7 guaranteed:1 each:1 corresponds:3 america:2 coincidence:4 dimensional:1 homogeneously:1 simply:1 brecha:1 respect:3 points:1 considering:3 mcclelland:2 described:9 addition:2 2k:2 three:3 been:8 detuning:9 much:6 damping:5 interest:1 expected:8 ph:1 empty:2 direction:1 modern:1 corresponding:2 linearity:2 sufficient:2 photon:7 covariance:1 coherent:1 ensuring:2 input:16 suspected:1 xxi:1 denote:2 those:7 case:17 laser:19 pacs:1 reliable:10 estimations:2 kimble:5 evaluated:11 transformation:2 will:36 while:5 ain:3 suppose:3 squeezed:1 property:7 hωl:3 region:2 layer:3 larger:6 coupled:6 a28:1 averaging:9 thus:8 xiao:5 according:1 ii:4 characterize:2 eberly:1 trusted:1 different:6 handled:1 multiphoton:1 generic:1 make:1 same:24 clearly:3 shorter:1 unity:5 parts:1 quant:1 modification:9 dimensionless:8 physical:18 grows:1 higher:26 restricting:1 independent:3 used:5 eds:1 imply:3 see:3 laboratoire:1 published:2 upon:7 effect:23 hand:4 driven:2 appreciable:8 supposing:1 passing:1 expand:1 relies:1 lower:2 explains:1 modes:12 bachor:1 expression:8 lambrecht:3 well:7 roughly:1 analysis:3 approached:1 without:1 solve:1 components:8 sets:1 very:1 position:7 jean:1 parametric:3 raizen:2 degrade:2 among:1 vαβ:4 able:1 linearisation:1 obtain:9 shape:1 diagrammatic:1 identify:1 atomic:74 scattering:5 previous:8 inelastic:2 preprint:1 density:5 sopt:6 absorption:5 photons:1 point:12 iϕ:1 iω:21 appeared:1 other:11 treatment:7 unsaturated:3 kastler:1 excited:5 iφ:5 identical:2 iθ:1 saturation:21 fluctuating:1 around:3 depends:3 easily:3 evaluate:6 couple:2 spatial:4 possible:2 cf:3 were:3 provide:1 vacuum:3 using:2 aδ:5 semiclassical:1 bistable:6 appearing:3 iξk:1 systematically:1 follows:3 qualitative:2 adiabatic:1 δs:1 δo:2 either:5 integrals:1 arbitrary:1 output:18 δe:1 orozco:3 δa:3 therein:1 poor:1 right:2 methods:4 classical:1 2x:6 2iδ:1 pierre:1 b4:2 understood:1 deduce:3 added:2 mirror:6 giacobino:5 exists:1 gβ:1 provided:4 describing:2 trace:3 progress:1 communications:5 cavity:32 intracavity:23 2xf:1 does:4 cloud:2 provides:5 assuming:2 demonstrated:1 mode:32 measuring:1 noise:49 forces:1 journal:7 processing:6 expansion:1 restrictive:1 although:2 become:4 drawn:1 relating:1 stage:1 about:1 central:6 carried:1 getting:1 column:1 discussed:3 dependence:6 o:3 collett:2 monomode:1 range:1 important:1 rayleigh:4 introduced:1 bloch:4 enhancement:1 letters:1 δaα:4 presence:1 previously:1 into:9 obtaining:1 due:21 phase:3 because:1 references:5 operator:3 proportional:16 next:3 forget:1 acknowledgements:1 b50:1 log:2 elastic:1 normalised:1 transfer:2 there:3 equation:15 why:1 width:1 describes:2 low:12 lot:1 was:4 naturally:2 function:18 medium:20 complete:2 form:1 enough:1 differences:2 warrington:1 but:5 back:1 properly:1 underestimates:1 atom:7 elimination:1 line:1 true:1 castelli:1 made:2 fluorescence:5 intuitive:1 society:2 proceeds:2 inside:2 up:4 us:2 placed:1 below:1 projecting:2 simplifying:3 ωl:7 fluctuations:42 ωc:2 average:2 recalling:1 detailed:1 b60:1 located:2 defined:14 abstract:1 describe:2 influence:5 general:4 single:2 reliability:4 eigenfrequency:3 our:2 accounting:3 formalism:6 trip:1 regime:9 functions:27 compared:6 when:22 detail:1 nf:2 arctan:1 field:59 priori:2 b10:1 papers:2 ns:8 concerning:2 conclusion:2 optically:2 elements:1 savage:1 models:1 fabre:3 symbol:1 drift:1 variation:1 zeitschrift:1 ξk:4 peak:2 cooper:1 g21:2 structure:16 delineate:3 rosenberger:1 independently:1 implies:3 coupling:8 4x:1 dω:1 assume:2 dτ:1 factors:2 curve:5 fact:5 volumes:1 time:4 requires:1 4c:1 once:1
|
quant-ph9801053.txt |@word represent:1 gs:1 consider:13 gq:8 gp:4 rev:10 results:4 produce:1 leads:6 eds:2 quadrature:9 garching:1 houches:2 mno:1 consists:1 shot:2 expressions:4 zinn:2 contributions:1 reynaud:8 compact:1 whose:1 inverse:1 dα0:9 calculate:4 transferred:1 paris:1 show:5 z1p:3 γt:1 finally:1 critical:1 squeezing:33 c5:1 under:1 analogous:1 presentation:1 worth:1 sent:1 degeneration:1 p2:1 amplitudes:8 g0:1 very:4 rise:2 brossel:1 wave:3 lecture:2 resonant:4 experimentally:1 φnl:2 enter:1 condition:2 milburn:1 four:5 presented:1 transmission:1 turns:1 notes:2 differentiating:3 accidentally:2 culation:1 large:8 solved:1 vector:2 a40:6 science:2 indices:1 enhance:1 ups:1 added:4 degeneracy:2 heidmann:2 upper:5 revolution:1 m4:1 dealing:2 approximation:21 surrounding:1 second:8 value:5 gn:1 manipulating:1 quite:1 linear:57 even:11 index:4 what:1 nonlinear:5 stands:2 iterating:1 brackets:1 section:10 brief:1 expressed:3 current:1 plitude:1 experiment:1 establishes:1 suppose:1 3a:1 increasing:9 method:1 suppress:1 publications:1 coefficient:12 αin:3 q0:2 respectively:2 never:1 spacing:10 here:9 atoms:2 behaviour:2 cylindrical:4 dover:1 possibility:1 excess:5 represented:1 depend:1 along:1 strong:1 equations:2 z1:8 change:1 deduced:1 obtained:6 publisher:2 incoming:7 shift:12 study:4 losses:11 allows:1 experience:1 published:1 resonance:5 had:1 fourier:1 changes:2 plotted:3 uniquely:1 via:1 spatially:1 family:7 scales:1 pling:1 yuen:1 vin:1 mab:5 conditions:1 decrease:1 apply:1 total:2 planck:1 cloud:1 readily:1 eiωt:1 use:6 takes:1 working:8 λpq:2 distinct:1 contains:2 france:1 comparing:1 noting:1 examination:1 therefore:7 m3:1 m2:1 taken:2 eiωl:1 theoretical:1 more:11 introducing:1 vout:1 upmc:1 becomes:5 operators:1 marks:1 validity:1 xiao:3 appendix:8 normalized:11 studied:1 particular:5 known:2 hold:1 iii:2 localizations:1 couples:1 account:7 ma:5 mb:5 recall:1 equation:29 oscillator:6 modified:2 paragraph:1 thin:3 carefully:1 cal:1 following:8 making:1 vary:1 references:1 want:1 figure:11 transmissivity:1 calculation:5 neglected:4 define:1 high:2 performed:3 degenerate:5 arise:3 kχ:1 tions:1 dalibard:1 discussion:3 far:1 ens:1 ent:1 adapted:1 justin:2 simplifies:1 optimal:1 parameter:1 circular:2 profile:1 simplicity:1 de:1 description:2 may:19 max:1 after:3 derived:1 different:23 expectation:1 hence:2 plane:3 designed:1 b6:1 coming:3 φt:14 grangier:1 realized:1 waist:2 multimode:3 ϕl:4 roundtrip:3 light:9 spectra:2 explicit:1 correspond:12 element:1 circularly:1 negligible:4 fundamental:75 jussieu:1 λ2p:2 order:59 michel:1 help:4 produces:3 developed:1 over:2 mainly:1 soon:7 years:1 produced:1 course:1 wiener:1 paper:2 through:11 kopfermann:1 mentioned:3 existence:1 cold:1 still:2 ieee:2 its:13 before:3 perfect:3 derive:5 longitudinal:11 φa:8 ln:1 matrices:3 solving:1 τc:3 coordinates:2 parts:1 lr:6 systems:2 lp:2 might:2 ηm:13 maximal:2 non:60 good:1 affected:1 fig:6 introduce:1 reflected:1 avoids:1 walls:2 quantenoptik:1 dap:2 effects:3 they:7 now:15 discuss:2 dielectric:1 matched:9 susceptibility:2 2v:1 2p:4 always:1 drop:1 kerr:26 realistic:1 b5:1 magnitude:2 transmitted:1 mode:171 instabilities:3 found:4 2i:2 characterized:2 mean:10 domain:2 arxiv:1 significantly:2 generation:1 fisk:1 magneto:1 reduce:1 gaussian:4 solution:1 constitute:1 eiωτ:1 m0:1 frequency:13 ex:1 entering:1 quantum:11 our:2 operation:1 differ:1 standard:1 shown:4 matrix:7 space:10 furthermore:1 since:5 vectorial:1 increase:1 similarly:1 cess:1 perturbatively:3 denoted:2 evaluates:1 illustrate:1 occurs:3 shows:5 lugiato:3 turning:8 approached:1 λpp:6 b3:1 divergence:2 diagonal:1 free:9 treatments:1 small:5 completely:3 threedimensional:1 term:5 estimate:2 beginning:1 generate:1 tudes:1 rewritten:2 interaction:2 r0:9 r2:2 liii:1 could:1 bistability:16 iterative:3 linearized:1 detunings:5 d23:1 length:3 tem00:4 place:1 assumed:2 consequence:2 3a20:1 first:12 origin:2 placing:1 caves:1 symmetry:5 laguerre:7 φ2t:7 number:2 exact:2 smaller:1 simplified:2 least:1 2a0:1 reached:1 noticed:3 appl:1 size:1 given:6 perturbation:4 bracket:2 fluc:2 their:8 introduction:2 chan:1 system:5 relations:5 linearizing:1 obtainable:3 assumption:1 calculations:4 perfectly:8 inserting:1 gives:4 a33:1 a32:1 2ab:2 linearities:1 a35:1 transverse:59 released:1 optical:10 pnl:3 2ap:1 focusing:1 off:1 than:8 coefficients:7 detection:1 kind:1 iω:9 sections:1 depends:1 limiting:1 annihilation:1 matter:1 future:1 intensities:1 supposed:7 amplitude:13 a41:1 iωl:1 perturbative:6 lowest:1 lambrecht:2 iφp:2 close:4 rewrite:1 fluctuation:2 spectrum:1 curves:13 discussions:1 fraction:1 iφa:1 iφb:1 conjugate:1 need:1 seen:3 recover:2 clearly:4 indeed:1 strength:3 boyd:1 zero:7 depending:1 convenient:4 self:2 physique:1 mechanism:2 polarization:2 k2:2 ideal:1 potential:1 generalized:1 so:2 coincide:3 spectral:1 cnrs:1 experienced:1 pqrs:6 electric:2 though:1 a46:2 correlation:9 z2:8 most:2 optimized:2 germany:1 gauss:5 phase:22 measured:3 model:1 appear:1 give:1 especially:1 consequences:1 considered:2 gatti:1 clear:1 adopt:1 steady:3 kl:2 part:2 homodyne:1 lθ:1 exp:6 mechanical:1 sf:1 sum:5 quantity:1 selection:2 particularly:1 phenomenon:1 rayleigh:2 reductions:1 γnl:4 notations:1 x2:2 2g:2 relation:3 solutions:1 superimposed:1 tend:1 find:3 par:3 near:1 based:1 parameters:1 hope:2 written:3 jan:1 analytic:1 only:12 explicitly:1 shelby:1 factor:1 local:6 perturbations:3 do:2 notation:2 dependent:2 ϕt:6 express:1 ϕp:3 2a:6 beam:31 ϕn:1 nearly:2 dx:1 new:2 dv:1 during:3 dt:1 dr:1 lossless:4 carmichael:2 evolution:10 qr:9 ended:1 fields:1 defocusing:1 bandwidth:2 acknowledgments:1 reid:1 experiments:2 contrast:1 contain:1 valid:1 thanks:2 a37:1 shapiro:1 set:1 achieved:1 physically:1 lett:2 dtf:1 relative:9 intensity:19 wiedemann:1 w2:1 w0:1 versus:4 phaseshifts:1 optimum:8 satisfies:1 techniques:1 αq:5 αp:11 αs:1 αr:2 c2:1 manson:1 resonantly:1 nondegenerate:1 review:1 ωk:1 propagates:1 diverge:1 symmetric:1 state:6 determined:1 various:8 chosen:3 between:27 complications:1 mathematical:1 tuations:2 approach:3 quantities:1 notice:2 terms:5 str:1 2αp:1 2αq:1 arises:1 however:11 w02:1 rapidly:2 york:1 concentrate:1 comm:3 pπ:1 modeling:1 come:1 ikm:2 aim:1 both:2 0q:8 last:4 propagator:4 region:1 against:1 propagation:20 les:2 raimond:1 interesting:1 contribution:2 expression:8 experimental:2 point:17 simple:1 iϕ:1 corresponds:7 dimensional:1 z4:2 b60:1 exhibits:1 polynomial:1 respect:1 quadratures:2 pp:2 astrid:1 described:4 transformations:1 cavities:1 suppressed:2 narducci:1 due:15 laplacian:1 pb:1 2a20:3 reduction:10 much:3 slowly:1 treat:2 electr:2 expected:5 transformed:1 ph:1 z3:2 empty:1 ls:1 direction:1 enable:1 corresponding:12 influence:9 sufficient:1 fluctua:1 photon:1 coincides:3 coherent:1 input:22 c3:2 cou:1 c1:1 general:1 present:2 c4:1 case:12 p0:1 laser:3 pacs:1 solid:5 expanded:1 appearance:1 conserved:1 evaluated:1 will:33 while:1 ain:10 encountered:1 evaluating:1 transverses:1 squeezed:1 situation:6 iφ:2 taking:1 a20:5 real:1 larger:2 coupled:2 almost:2 averaging:1 thus:2 them:1 iv:3 ii:3 ik:6 elsevier:2 vanish:1 mcclelland:2 φp:1 containing:3 develop:1 anymore:1 sensitive:3 perform:2 belong:1 cross:2 same:9 undisturbed:1 shorter:1 shifts:4 φb:8 complex:4 quant:3 split:1 modification:8 going:1 dimensionless:5 decreases:1 couple:1 higher:32 laboratoire:1 numerical:1 effect:12 abramovitz:1 appreciable:2 hans:1 robust:3 normalization:1 finesse:1 modes:77 bachor:1 nevertheless:2 whole:1 igp:2 well:9 analysis:2 without:1 reexpressed:1 dashed:5 position:1 jean:1 parametric:4 latter:1 usual:1 λq:8 λp:5 proposed:1 decreasing:1 stegun:1 wagner:1 obtain:1 shape:1 distant:1 atomic:1 aspect:1 integer:1 previous:2 conjugates:1 photons:1 supply:1 seems:1 wavevector:1 add:9 concerns:1 conjugated:4 treatment:6 theorem:1 kastler:1 take:3 identical:2 iλ:1 around:4 evaluate:2 ampli:1 looks:1 possible:9 iη:8 cf:3 αout:2 raizen:1 vacuum:3 using:1 gr:5 loss:3 bistable:4 showing:2 like:1 reduces:2 performing:1 noted:1 specific:1 δl:1 2g0:1 steps:3 either:1 arbitrary:3 resolved:1 output:16 works:1 stationary:4 reduced:2 therein:1 because:2 often:1 exposed:2 2x:1 creation:1 some:3 b4:2 understood:3 deduce:2 aout:4 b1:2 b2:1 mirror:2 multiple:1 little:2 b8:1 kimble:3 savage:1 lead:2 cavity:56 avoid:1 intracavity:17 levenson:1 does:1 provides:1 whereas:1 propagating:2 demonstrated:1 trap:1 limitations:1 noise:32 obey:1 selecting:1 journal:1 expansion:1 step:1 pq:6 although:1 become:1 cα:2 projector:1 session:2 comparison:3 4a20:1 central:1 would:1 simplify:3 orozco:1 am:2 discussed:1 o:4 collett:1 remains:1 range:2 a2:5 recognizes:1 introduced:2 xz:1 soc:1 presence:4 orders:2 into:9 three:1 giacobino:4 device:3 perturbing:5 qrs:6 z2q:2 been:4 proportional:1 institut:1 additional:5 few:1 transfer:9 there:2 detuning:14 amax:3 width:4 pa:1 handbook:1 low:2 way:2 notices:3 m1:1 analyze:4 was:2 energy:5 pφt:2 function:11 considerably:1 medium:38 complete:1 form:3 opt:5 differences:3 but:7 collected:1 cedex:1 cαβ:4 attainable:2 line:10 level:1 courty:3 made:1 drummond:1 differents:1 whether:1 characteristic:1 inside:13 up:8 us:2 ur:1 placed:6 below:1 b7:1 limit:7 ωl:2 autocorrelation:2 fluctuations:53 problem:3 isolating:1 similar:1 calculated:1 expect:1 detailed:2 result:4 ab:2 associated:3 defined:3 curve:9 describe:3 linearity:5 generating:3 denote:2 aq:1 ap:14 single:17 ar:6 exist:1 4p:1 dθ:1 wavelength:1 formalism:2 physical:1 once:1 again:2 functions:11 compared:9 3i:1 na:1 nb:1 when:15 arctan:2 field:40 build:1 other:3 remarks:1 details:2 branch:5 spatial:13 scan:1 out:5 conclusion:1 maxima:1 briefly:1 kinds:3 superposition:2 calculating:1 models:1 fabre:3 polynomials:1 a1:1 a0:20 a3:1 important:8 a4:1 suppression:2 a6:1 structure:11 conclusive:1 algebraic:1 coupling:56 assume:3 dτ:2 rs:1 paraxial:1 rule:1 time:5 n0:1 4g:1 4a:1 having:1 degrade:1
|
quant-ph9801054.txt |@word consider:2 springer:1 switched:1 rev:8 magnetic:12 decays:1 results:3 switches:1 pulsing:2 comments:1 intricate:1 centimeter:1 causes:1 calculate:1 zone:1 paris:2 γp:4 send:1 γt:1 presents:1 those:1 ti:2 cm3:1 cm2:1 supported:1 g2:1 6p3:5 orthogonal:1 very:10 rise:1 brossel:1 wave:1 fall:1 resonant:4 difference:1 four:3 europhys:2 clouds:2 pbs:2 level:6 transmission:8 bonifacio:1 t2:1 large:4 pout:4 small:4 optics:8 round:3 programme:1 upper:1 smaller:4 slower:1 variables:1 aip:1 second:3 evaluated:1 chen:1 further:1 dynamics:3 quite:1 theory:3 even:2 index:4 nonlinear:13 power:18 rate:8 d2:1 section:4 while:3 expressed:1 cell:3 experiment:2 above:1 sup:1 new:2 falling:1 erieure:1 coefficient:7 αin:1 lee:1 larson:1 respectively:1 lange:1 here:1 atoms:48 behaviour:9 separation:1 relaxation:3 along:1 strong:5 equations:3 change:4 obtained:1 great:1 shift:8 study:2 losses:1 completely:1 experience:1 cecchi:3 periodic:1 cesium:5 resonance:11 changes:3 controled:1 diameter:2 via:1 useful:1 lounis:1 explained:2 private:1 highly:1 decrease:2 total:3 cloud:7 takes:2 would:2 clebsch:2 scan:4 france:1 few:1 therefore:1 a29:1 taken:2 start:1 minor:1 more:4 hu:1 ecole:1 brings:2 under:2 validity:1 cycles:1 basically:1 particular:2 known:1 cases:2 iii:1 high:14 keeping:1 mf:9 defines:1 mm:1 work:1 mk:1 reproduce:1 mw:1 values:7 ms:2 following:1 making:1 pritchard:1 vary:1 compare:2 bistability:16 give:3 process:1 suggestions:1 escaped:1 performed:1 want:1 steps:1 times:1 robinson:1 occur:2 end:1 advantage:1 rather:4 get:4 feature:1 chrx:1 write:2 far:1 monroe:1 instead:1 parameter:3 oscillatory:1 narducci:1 may:1 after:4 containing:4 collection:1 plane:2 coming:1 geometrical:2 associ:1 response:2 natural:3 waist:1 effective:2 light:7 deserno:1 βi:3 perform:1 switch:2 cannot:1 so:1 allow:1 jussieu:1 vapor:1 order:7 typical:2 saturated:1 help:1 over:2 eqs:1 dα:1 interpreted:2 raab:1 thermal:1 paper:2 through:4 thesis:1 cold:14 linewidth:5 its:2 before:2 φnl:4 rapidly:1 thank:1 fit:1 decay:1 chosen:1 polarizing:1 vicinity:2 exhibits:1 actually:2 better:1 absence:4 systems:1 persist:1 rabi:1 main:1 easier:1 photodiodes:1 non:9 good:1 evolution:4 introduce:1 reflected:1 mention:1 detunings:2 effects:4 they:6 half:1 accumulate:2 now:3 nor:1 easily:2 term:1 2p:1 hereafter:1 presented:1 kerr:2 mccall:1 transmitted:3 trap:9 instabilities:19 found:5 universit:3 quarter:1 side:5 characterized:2 mean:1 differential:1 magneto:1 ec:2 inhomogeneous:1 frequency:8 entering:1 measure:2 quantum:2 our:4 transitions:4 eq:2 out:4 shown:10 driving:2 solved:1 open:1 since:1 squared:1 chaos:1 investigation:1 formula:1 forth:1 occurs:1 shows:2 lugiato:4 doppler:3 linear:6 normalized:3 pumping:26 free:1 standard:2 recordings:2 complicated:1 hysteresis:2 definition:1 interaction:4 created:1 starts:1 could:2 transition:17 confocal:1 motion:1 turn:1 length:18 place:1 consequence:2 top:1 first:4 origin:3 already:1 features:2 symmetry:1 overshoot:3 number:11 contributions:3 comprised:1 bloomfield:1 enlarged:1 done:1 fast:2 ring:1 quality:1 given:3 checked:1 temperature:1 needed:1 introduction:1 data:1 interact:2 system:13 parallel:1 their:2 cooling:3 intermediate:1 rates:1 too:1 linearities:3 perfectly:1 ranging:2 gives:1 calculations:1 trapped:3 a39:1 transverse:1 released:2 larger:4 optical:41 somewhat:1 authors:1 off:4 sublevels:12 than:8 population:3 wide:1 polarized:6 see:2 submitted:1 recording:5 states:3 classes:2 contrary:2 were:6 enables:1 powers:8 a48:1 result:2 exhibit:2 function:2 turned:1 curves:4 seen:1 clearly:1 angle:1 multistability:1 depending:1 thoroughly:1 self:2 able:2 mechanism:1 note:1 causing:1 square:2 build:1 xi:1 negligible:1 switching:3 unperturbed:1 cnrs:2 towards:2 beyond:1 electric:1 opposite:1 mlynek:1 most:2 involving:3 propagate:1 significant:2 phase:10 marie:2 measured:1 trapping:11 especially:1 windows:2 calculated:5 curie:2 reflecting:1 mechanical:1 velocity:2 left:1 sum:3 fact:4 phenomenon:2 show:5 probe:13 dipole:1 notations:1 bring:1 threshold:2 randomize:1 find:1 ground:14 3k:1 slow:1 parameters:3 tranverse:1 explain:1 dynamical:1 distributed:2 pump:3 jan:1 only:5 going:1 various:4 pointed:1 coherences:1 plate:1 dominant:1 means:1 beams:14 de:2 account:3 necessitate:1 beam:16 ones:1 dt:3 dp:2 processes:2 precession:2 densities:1 fields:4 arxiv:1 tuned:1 twice:1 investigate:3 experiments:3 predicted:2 wieman:1 including:2 fixed:5 cable:1 salomon:1 scanning:1 set:3 computed:1 fair:1 lett:7 operates:1 observed:12 intensity:17 num:1 considered:3 close:5 closer:1 appear:1 interacting:1 resonantly:1 µw:6 diode:1 pd2:3 pd1:3 tend:1 state:20 brambilla:2 invokes:1 between:8 intensities:1 neither:1 conditions:8 across:1 comparable:1 terms:1 spectroscopy:1 however:3 comm:4 recent:1 remaining:1 abruptly:1 swann:1 many:1 region:2 la:1 equal:2 zeeman:4 involve:1 refraction:4 contribution:2 whole:1 experimental:7 among:2 relevant:1 cm:2 simple:4 period:1 simply:1 decreases:2 loaded:1 ct:1 considering:2 destroyed:1 described:3 cavities:1 persists:1 addition:1 prentiss:1 due:18 been:8 pc:1 detuning:11 much:8 slowly:2 interest:1 basic:1 pj:1 ph:1 empty:1 fig:18 describe:1 corresponding:2 quantities:1 gas:1 understand:2 input:15 careful:1 present:2 hmc:1 case:6 laser:16 look:2 pacs:1 kimble:2 value:3 expelled:1 near:1 penna:1 abrupt:2 situation:2 elaborate:1 procedure:1 studied:1 orientation:9 vi:1 thus:5 them:3 iv:1 ii:1 writes:1 contract:2 interacts:1 disappear:3 φp:4 different:5 develop:1 circularly:6 cross:1 same:5 linked:1 shifts:2 complex:1 quant:1 largest:1 units:2 several:4 φl:8 higher:1 development:1 calculation:1 used:1 eds:2 optic:1 laboratoire:2 effect:1 hand:1 action:2 changing:1 cycle:2 normale:1 motionless:1 finesse:1 traps:1 lambrecht:2 well:4 roughly:1 theses:1 without:4 consistency:1 hamilton:1 model:8 latter:1 grossly:1 usual:1 6s1:4 just:1 being:3 grynberg:1 obtain:2 competitive:1 underlying:1 atomic:19 harrison:1 alkali:1 substates:1 enters:1 density:1 absorption:3 photons:1 esprit:1 except:2 other:1 treatment:1 kastler:1 excited:6 take:2 real:1 saturation:9 around:1 susceptibility:1 showing:3 possible:4 cf:1 early:1 increases:5 background:2 press:1 using:3 part:2 vapors:2 usually:1 qwp:2 bistable:6 like:4 sublevel:3 signal:1 velocities:1 shapes:1 communications:1 mhz:4 either:1 output:8 hyperfine:7 orozco:1 cooled:2 accessible:1 satisfactory:1 because:2 some:3 pierre:2 competition:3 understood:1 mirror:5 oscillations:15 giacobino:4 pronounced:1 bottom:1 cavity:52 electromagnetic:2 measurements:2 recorded:1 intracavity:6 per:2 instantaneous:1 bra:1 tends:2 unstable:1 yielded:1 demonstrated:1 mode:1 hsc:1 detuned:5 each:1 agreement:1 expansion:2 pressure:2 although:1 become:1 bx:1 2n:2 simpler:1 about:3 2i:3 range:5 larmor:1 gallagher:1 introduced:1 slightly:1 equally:2 beamsplitter:1 chu:1 diagramme:1 presence:7 communication:1 into:10 within:2 numerically:1 three:1 right:1 arecchi:3 proportional:2 acknowledgements:1 additional:2 prepare:1 area:1 assumed:2 indispensable:1 initial:1 approximate:1 long:2 dispersion:1 width:4 appl:2 low:10 way:3 was:9 record:1 raman:1 medium:2 complete:2 bers:1 enough:2 phenomena:2 analyse:1 warrington:1 but:3 back:4 cedex:1 gain:2 atom:2 highest:2 courty:2 longer:2 directed:1 absent:1 characteristic:2 inside:2 up:1 us:3 placed:2 below:3 owing:1 limit:1 ωl:4 sapphire:2 pumped:1 similar:3 average:1 khz:1 constant:2 pin:2 defined:1 ki:1 escape:1 linearity:4 general:1 duration:1 single:1 scanned:9 au:1 trip:3 fill:1 again:2 gordan:2 no:1 courtois:1 populations:4 when:21 detail:2 field:21 setting:2 conclusion:1 optically:1 explaining:1 keep:1 fabre:2 durations:1 time:12 variation:1 includes:1 generated:1 structure:2 rosenberger:1 regime:1 coupling:4 curve:1 original:1 4n:1 compete:1 broad:1 push:1 starting:3 having:2 once:1
|
quant-ph9801055.txt |@word represent:1 consider:3 rev:7 magnetic:2 reversibility:1 results:2 four:1 eds:2 scalar:1 garching:1 grateful:1 go:1 expressions:1 contributions:9 reynaud:1 layers:1 inverse:1 re:9 paris:3 ıa:1 finally:1 those:2 th:1 stable:1 tb:2 passivity:10 brown:1 amplitudes:27 frequencies:9 brossel:1 induce:1 every:2 infiniteness:1 refractive:1 resonant:4 affect:1 difference:1 exact:1 disturb:1 exponential:1 presented:4 transmission:9 positions:1 developing:1 t2:1 piling:2 vector:1 math:1 dealt:1 small:2 upper:6 smaller:8 force:56 demonstrations:2 approximation:3 imply:1 design:1 evaluated:7 qualitatively:1 spectral:3 will:9 sud:1 phaseshift:1 iterating:1 t2a:1 section:1 t2b:1 dephasing:1 lhomond:1 networks:4 above:1 sup:3 required:1 propre:1 erieure:3 preserved:2 contrast:3 revealing:2 outgoing:1 exchange:4 deduces:1 respectively:4 gathered:1 never:2 here:2 behaviour:1 met:2 possibility:1 ratio:1 astrid:1 equations:1 appears:2 change:2 deduced:1 obtained:9 balance:5 incoming:2 shift:3 elaborate:1 larger:7 approaches:1 suggests:1 amount:1 characterizing:1 resonance:8 narrow:11 raise:1 scales:1 polonica:1 conditions:1 decrease:1 planck:1 unit:2 derivatives:1 use:4 figure:2 would:3 remains:3 positive:5 continuous:2 mirrors:66 negative:4 jaekel:1 france:2 therefore:8 reciprocity:1 typical:1 taken:1 entails:1 more:7 zh:2 ecole:3 operators:1 apparent:1 everywhere:1 particular:13 known:3 cases:1 ρa:3 ma:1 alin:1 science:1 equation:6 when:4 modified:1 values:2 following:4 meet:1 ta:3 example:1 stimulating:1 modulation:1 pushes:1 give:2 haroche:1 high:1 numbers:1 tab:2 absolute:1 provide:2 discussion:3 feature:1 write:1 ρ2a:3 opt:1 acta:1 fp:7 simplicity:1 product:6 may:17 max:1 spot:1 plane:3 designed:3 coming:2 associ:2 efficiently:1 introduced:1 natural:1 ss:1 εa:6 explicit:1 correspond:1 rather:1 so:2 fundamental:2 decreasing:2 sain:1 order:2 frequencydependent:1 neto:1 interpretation:3 help:2 indeed:4 over:2 mainly:1 satisfied:1 stability:1 experiments:2 through:2 kopfermann:1 statistical:1 differs:1 existence:1 still:3 its:6 perfect:6 fis:1 derive:5 outer:1 la:6 interesting:2 trends:1 dispose:1 expectations:3 decreases:3 actually:1 attraction:1 absence:1 complex:4 choose:1 derivative:1 might:3 versus:1 them:3 matches:1 greiner:1 fig:3 introduce:2 disregarded:1 obeyed:5 band:10 quantenoptik:1 repulsive:12 effects:1 they:2 half:3 landau:2 now:8 discuss:2 dielectric:18 easily:1 reflectivities:1 always:4 university:1 realistic:2 magnitude:1 mode:8 each:9 found:1 universit:4 ports:6 mean:1 ee:2 ed:1 energy:13 barnett:1 related:3 constitute:1 frequency:20 expect:1 reached:1 quantum:5 our:1 approximated:3 eq:1 out:5 shown:2 network:3 rr:1 space:2 furthermore:1 since:4 squared:1 imoto:1 attracted:1 contained:1 ra:5 rb:5 denoted:1 formula:1 paola:1 evaluation:3 rj:4 shows:2 slepian:1 theory:1 mechanisms:1 free:4 standard:1 reason:1 besides:1 usual:1 forbids:1 definition:1 r1:12 r2:12 could:2 length:6 place:1 consequence:6 teor:1 onto:2 first:6 already:1 features:1 symmetry:1 relate:1 number:3 reaches:2 huttner:1 restrict:1 least:1 directly:3 stated:3 precisely:1 size:2 πc:4 given:8 siegman:1 rewritten:1 introduction:6 eqs:1 system:2 reflectivity:3 their:3 assumption:1 too:1 calculations:2 airy:3 stora:1 perfectly:4 exerted:1 recovered:1 low:2 back:2 wavelength:1 exactly:2 immediate:1 transverse:2 reflecting:6 representing:1 than:16 coefficients:4 reflection:29 distance:4 holland:2 wet:1 require:1 iteration:1 depends:4 limiting:2 annihilation:1 roundtrip:1 determined:2 str:1 treated:1 a48:1 enhancement:1 rab:1 exert:1 electrodynamics:3 reduction:1 spectrum:1 discussions:1 say:1 manner:4 further:4 controlled:1 slab:14 any:4 built:3 zero:5 depending:2 latter:2 storage:1 able:1 mechanism:1 internal:1 forces:1 new:1 modulus:2 even:1 added:4 multiple:1 allow:2 centre:2 denoting:1 denominator:1 germany:1 letter:3 position:1 pair:1 marie:2 measured:1 why:1 hθ1:2 considered:2 average:1 curie:2 optical:5 tech:1 exp:1 mechanical:1 serge:1 physics:2 sum:1 fact:3 bell:1 particularly:1 show:4 feasibility:1 dependences:2 notations:2 relation:5 expressed:1 thickness:1 fine:2 find:1 causality:5 written:2 should:2 jan:1 analytic:2 only:2 specify:1 factor:1 constant:1 local:1 equilibrium:2 dominant:1 notation:1 means:3 dependent:5 connections:1 de:8 expectation:2 gilson:1 cannot:3 nearly:3 closely:1 despite:1 during:1 dt:1 du:1 net:3 dp:4 processes:2 twice:1 fields:6 arxiv:1 bandwidths:1 paper:2 slabs:8 θab:1 view:3 coefficient:5 set:2 ned:1 lasers:1 undergoes:1 national:2 maximum:1 relative:2 namely:1 result:2 enhanced:1 fail:1 disturbing:1 a46:1 scattering:2 positivity:1 boundaries:2 outside:1 correctly:1 between:29 conceptual:2 ira:1 approach:1 terms:5 amplitude:10 interfaces:1 attention:1 however:4 incident:1 maximilians:1 interface:2 configuration:1 suppressed:2 both:1 recherche:2 mono:1 taking:1 according:1 fulfilled:1 sensitive:3 connection:1 concentrate:3 context:1 casimir:48 exceeds:2 contribution:4 estimation:1 expression:5 experimental:2 arbitrarily:1 mechanics:1 point:4 simple:6 perot:1 thierry:1 corresponds:4 scientifique:2 dimensional:4 simply:1 meixner:4 cancel:1 respect:1 rep:1 considering:1 ensures:1 jetp:1 described:2 tuning:1 cavities:1 marc:1 due:6 been:2 detuning:1 much:5 expected:1 ph:1 systems:3 θj:1 determinant:1 relations:3 flight:3 θb:1 quantities:1 formed:1 input:2 2cτ:1 present:3 case:8 novel:2 reciprocal:4 pacs:1 akad:1 chap:1 value:9 aim:2 while:4 ain:8 abrupt:1 property:7 procedure:1 pertinence:1 vectors:2 coupled:1 ip:32 thus:7 non:3 equal:4 obeying:1 im:1 accounting:1 df:1 confirmed:1 plunien:1 media:2 divergences:1 radiation:2 lett:1 same:5 clearly:1 shifts:2 unity:8 parts:1 quant:1 arguments:1 evaluate:1 modification:1 plates:1 ludwig:1 used:1 peaks:1 see:2 laboratoire:2 upon:2 effect:3 hand:6 sys:1 symmetrical:3 hans:1 b55:1 tighter:1 normale:3 motionless:1 finesse:2 modes:3 largely:1 whole:1 well:2 analysis:1 thought:1 comes:1 components:1 quantitative:3 model:3 left:3 being:1 physique:2 accurate:1 grynberg:1 detail:1 bandwidth:5 stored:1 atomic:1 questions:1 immediately:2 uller:1 macroscopic:1 based:1 density:2 irradiated:1 extra:3 passive:9 reasons:1 valid:1 attractive:14 theorem:2 kastler:1 mod:2 transformation:2 real:8 increased:1 rules:1 bands:1 cf:1 eorique:1 vacuum:14 press:2 using:3 part:1 apart:1 loss:1 appearing:1 alternatively:1 qualitative:1 specific:2 remind:1 loop:1 follows:9 translated:1 output:2 exceed:1 because:4 classical:1 fresnel:1 creation:1 pierre:2 proportionally:1 understood:1 deduce:6 aout:8 choosing:1 mirror:26 giacobino:1 ourselves:1 electric:1 provided:1 lead:1 micro:1 cavity:26 resonances:4 langevin:1 intracavity:2 per:1 causal:1 boyer:1 does:2 provides:1 proc:1 lifshitz:3 minimal:1 noise:1 obey:1 power:1 intimate:1 equivalent:2 arbitrary:6 rue:1 pressure:2 step:1 shifting:1 drawn:1 imaginary:4 onsager:1 properties:20 stage:1 central:1 column:2 discussed:2 dependence:2 side:4 piled:4 range:3 plus:1 obeys:2 connected:1 matrices:1 fabry:1 considerations:1 letters:1 presence:1 pergamon:2 integral:3 bound:2 assess:1 phase:6 right:3 references:1 sov:1 elementary:3 proportional:2 next:1 acknowledgements:1 institut:1 multilayer:17 transfer:1 transform:1 sides:1 dispersion:1 describes:2 inner:1 way:1 was:1 function:10 medium:1 north:2 form:3 analyse:1 but:2 hoped:1 failure:1 cedex:1 gain:1 impedance:2 dissipative:3 paolo:1 whether:2 characteristic:1 inside:7 smooth:1 bounds:3 ur:1 placed:1 below:1 books:1 limit:4 suitable:1 fluctuations:6 similar:2 laplace:1 recalling:1 detailed:1 ab:1 associated:8 up:5 defined:1 diffraction:2 abstract:1 describe:3 general:2 single:6 ar:6 au:1 regularisation:1 relates:1 partly:1 physical:1 functions:2 compared:1 analyticity:1 no:1 index:1 whereas:1 generally:1 vanishes:3 field:16 other:3 electrical:1 polarisations:1 θa:4 separate:1 fabre:1 time:4 variation:1 peak:1 suppression:1 a9:1 ξa:2 reflectors:1 matrix:12 implies:1 longer:1 dω:3 corresponding:9 dτ:1 interval:4 paraxial:1 rule:1 equivalently:1 depth:3 neighbouring:1 lying:1 electromagnetic:4 appl:1 having:3
|
quant-ph9801056.txt |@word concept:3 alien:4 counterfactual:1 reasoning:1 whose:1 certainly:1 depend:3 ac03:1 nonlocal:1 present:1 under:9 circumstances:1 division:1 very:3 confounding:1 choice:7 liability:1 trouble:1 condition:11 obvious:1 level:1 occurs:1 commented:1 disclaimer:1 occurrence:1 imply:1 even:3 established:3 what:7 appear:2 trivial:1 expressed:3 experiment:9 above:2 expresses:2 commercial:1 here:4 berkeley:3 consideration:1 appears:1 knowledge:1 obtained:2 great:3 ahead:1 involved:1 employees:1 suggests:1 products:1 advertising:1 action:1 makes:2 involves:1 inference:1 merely:1 outcomes:10 hardy:1 privately:1 employer:1 use:1 would:10 prove:1 contains:3 chooses:2 examination:1 memory:1 entails:1 more:1 sort:3 tandem:1 particular:4 cases:3 hold:3 effort:1 must:4 high:2 account:1 language:1 rights:1 work:2 paragraph:3 values:6 three:3 henry:2 believed:1 my:10 proof:7 claim:10 stated:1 process:1 attribute:1 purposes:1 states:4 effectively:3 assumptions:1 performed:16 occur:1 information:1 united:4 rather:1 holds:1 feature:1 occasionally:1 endorsement:2 instead:2 lbnl:1 product:1 express:1 may:1 reflect:1 consequence:1 produce:1 fits:2 sr:18 counter:3 explicit:1 so:2 asserts:7 correlation:7 order:1 words:1 office:2 produces:2 indeed:1 argues:1 produced:1 paper:1 mentioned:1 existence:6 still:1 its:3 chosen:4 relativity:1 actually:2 systems:1 hidden:2 factual:4 happened:2 them:3 views:1 thereof:3 now:1 nor:3 dirac:1 name:1 january:1 university:4 faraway:9 l2:6 truth:17 l1:2 found:1 entirely:4 mean:4 challenged:1 energy:4 idea:4 constitute:1 measurement:15 quantum:19 laboratory:2 special:1 research:1 particles:1 gov:2 correct:1 shows:1 theory:10 lawrence:2 structurally:1 free:8 standard:1 completely:1 california:5 conflicts:1 care:3 r1:3 r2:5 hence:1 first:3 already:2 owned:1 inapplicable:1 necessarily:4 service:1 system:25 unruh:11 their:1 attack:1 assumption:7 too:1 statement:29 frame:1 speaking:1 authors:1 believe:1 than:1 kind:2 require:1 second:2 final:1 matter:3 contrary:2 supposed:1 were:1 outcome:13 solely:1 false:1 lbl:1 argument:6 paragraphs:1 seem:1 any:18 agency:3 ideas:1 stapp:3 take:1 responsibility:1 unconstrained:1 accuracy:1 heisenberg:1 normal:1 most:1 regular:1 sponsored:1 unmeasured:2 device:1 measured:5 why:1 give:1 later:12 cover:2 inferred:3 points:1 physics:3 notion:6 fact:6 wording:4 show:1 supported:1 fine:1 causality:2 quoted:1 situations:1 assertion:6 should:6 jan:1 only:1 ambiguity:1 local:1 do:2 his:3 dependent:5 familiar:2 de:1 joint:3 cannot:6 closely:1 import:3 trade:1 justified:1 arxiv:1 fixes:1 irregularities:2 experiments:3 contain:1 fixed:1 favoring:1 reference:1 national:1 correlations:10 observed:1 see:1 result:1 fail:1 fails:2 nuclear:1 justifies:1 state:4 between:14 incompatibility:1 consecutive:1 neither:1 conditions:2 accord:1 nature:6 however:5 tacit:2 premise:1 distinguish:1 amer:1 freely:3 region:15 equal:1 contract:1 σz:1 involve:1 σx:2 context:1 distinction:2 argue:2 expression:1 otherwise:1 comment:1 detailed:1 relevant:2 character:2 non:1 linguistically:1 associated:1 considering:1 described:2 trademark:1 due:2 been:17 linguistic:2 ph:2 define:1 arises:1 xxx:1 assert:1 assigning:1 those:1 case:9 value:19 choices:1 will:2 while:1 shall:1 applies:1 determinism:1 property:3 thus:1 herein:2 ii:1 reads:1 itself:5 claimed:1 capture:1 different:7 perform:1 suggest:1 make:4 same:1 linked:1 html:1 quant:1 document:2 independent:10 used:4 http:2 upon:7 effect:1 hand:1 director:1 experimenter:2 opportunity:1 recent:1 relies:5 locality:6 bohr:1 without:1 position:4 usual:1 opinions:1 proposed:1 being:1 generally:1 lorentz:1 identify:1 human:1 alternative:4 macroscopic:2 thinking:1 had:5 other:5 government:4 read:2 possible:9 using:1 76sf00098:1 necessary:2 like:1 particle:4 follows:3 specific:1 essential:3 specifies:1 pertaining:1 www:1 conditional:1 some:8 recommendation:1 lead:1 measurements:12 recorded:1 legal:1 everything:1 does:12 measuring:1 equivalent:3 stem:1 step:3 manufacturer:1 about:17 asserting:3 actual:7 extension:2 act:1 introduced:1 consequently:1 warranty:1 statements:8 into:3 within:1 predictions:3 appropriate:1 references:1 treated:1 there:9 question:1 physicists:1 way:5 was:7 σ2x:2 assumes:1 naturally:1 quantity:3 but:9 principles:2 failure:1 contradictory:1 line:9 true:7 infers:1 he:2 made:21 whether:1 us:1 below:1 demonstrate:1 mechanics:5 gone:3 lanl:1 proved:5 certain:8 abstract:1 specified:7 influence:2 examine:1 again:1 completeness:1 no:3 when:1 reality:11 regents:3 department:1 draw:1 contradicted:4 prepared:1 william:1 meaning:2 variable:2 observers:1 independently:3 correlated:1 required:4 together:1 implied:1 experimenters:1 time:9 backward:3 original:1
|
quant-ph9801057.txt |@word limited:2 writings:1 magnetic:1 four:3 fortiori:1 consists:9 oldest:1 relationships:1 whose:7 calculate:2 contained:4 edward:1 indicate:1 under:9 lore:1 teaching:1 ontological:1 worth:2 risk:1 rise:1 every:2 affect:1 encounter:1 cause:3 conceive:1 relics:1 particularities:1 entropy:1 force:1 specially:1 concise:2 consistent:13 direct:4 second:4 rigorous:1 even:20 established:6 incompatible:5 specification:2 supplied:2 reconstruction:1 supplies:1 ever:2 consisting:1 told:2 deemed:1 simultaneously:4 notions:2 never:3 here:7 atoms:1 refinement:1 active:1 interpret:1 violate:1 obtained:1 rests:1 study:2 approaches:1 stressed:2 suitable:1 changes:2 mutual:1 appropriately:1 projection:9 explained:2 highly:4 brought:1 total:4 particularity:8 would:16 chooses:2 noting:1 call:4 therefore:10 indiana:2 type:3 tell:7 separated:4 composite:5 brings:2 naive:1 odinger:2 aware:2 backwards:1 eternally:1 hold:1 must:12 me:19 springer:2 word:3 work:3 theories:3 macroscopically:3 itself:9 concepts:2 my:23 example:24 defer:1 fraassen:1 give:6 relativistic:3 distributions:48 stressing:2 degenerate:1 times:1 cushing:2 absolute:3 end:1 thing:3 feature:10 far:4 nontrivial:3 opposite:1 significance:1 answer:9 symposium:1 brassard:1 description:18 undergoing:1 transforming:1 reconciled:1 after:7 wrong:1 meaningful:5 types:1 attempt:2 third:1 acknowledged:1 fictional:2 lasalle:1 complexity:1 fictitious:1 green:1 enter:2 order:2 operations:2 restriction:1 interpretation:31 over:11 before:5 personal:1 better:7 compelling:1 vast:1 roland:1 hidden:5 schmidt:2 interpretive:2 eventually:1 them:11 confuse:1 effects:3 they:16 schools:1 shadows:1 eigenvalue:1 reasonably:1 hamiltonian:2 reasonable:1 each:21 mean:15 prohibit:1 schemes:1 series:2 stronger:1 combining:1 substantially:1 laboratory:4 extract:2 restricted:8 crucial:2 content:9 laid:1 surprise:1 gov:4 forth:1 foundation:2 perception:7 linear:3 written:1 little:2 free:1 standard:3 admits:1 assures:1 necessarily:6 encountering:1 σy2:1 σy1:1 tempting:1 moving:1 onto:2 already:2 features:4 synonymous:1 primary:1 restrict:1 philosophical:4 another:13 electronic:3 illustrate:1 similarly:1 xii:1 too:1 hypothetical:4 john:4 discussion:4 collapse:8 tool:1 albert:1 somewhat:3 kept:1 abandoning:1 peculiar:4 princeton:3 surrogate:1 unmistakable:1 preparation:1 matter:7 enables:2 powers:2 acquisition:1 bridge:1 fashion:1 modern:1 mind:7 mine:1 talking:2 manner:1 emphasizing:1 seen:1 unaffected:2 tells:2 forced:2 traditionally:1 mermin:6 latter:1 isolated:9 subjects:1 correlating:1 grips:1 explanation:3 blue:5 broglie:1 shall:9 object:3 vexing:1 accurately:1 arguing:1 unmeasured:1 coin:5 teller:1 characterizes:1 alarm:1 points:1 principle:2 enterprise:1 notion:8 incomplete:2 probe:1 boojums:1 soluble:1 colors:2 subtle:1 enjoyed:1 resemblance:1 consciousness:35 spite:2 explain:1 pursuing:1 adequate:3 do:24 succinct:1 wide:1 de:1 perceive:7 christopher:3 new:15 represented:1 runs:1 bas:1 covering:1 fields:3 bad:1 contrast:3 aesthetic:1 reference:5 habit:1 clarified:1 depends:3 decided:1 result:7 w1:5 discussions:3 disturbing:1 best:2 clarifies:1 said:3 away:3 artificial:2 continually:1 simplest:2 conceptual:7 encounters:2 terms:22 extend:8 nature:15 component:4 restricting:2 ignorance:9 wi:5 harvard:1 extent:3 suggested:1 received:1 essentially:1 met:1 against:3 logic:1 distinction:3 contribution:1 argue:1 asked:1 suggest:1 presumably:1 had:4 concluding:1 speak:15 σx1:1 σx2:1 basis:5 simplification:1 three:7 been:16 confident:1 much:8 interest:4 life:4 families:1 quantities:6 xxx:5 coherent:1 bohmian:1 child:1 spin:8 applied:3 ahead:1 formalization:1 peculiarity:1 hat:1 air:1 aim:1 asher:1 abrupt:1 viii:2 applies:5 property:3 leaves:1 characterizing:3 ix:14 ir:1 iv:3 ii:2 characterize:5 ramifications:1 ig:1 containing:1 things:4 make:18 complex:2 quant:5 incorrectly:1 several:1 entitled:1 independent:2 everett:14 hand:4 thoughts:1 fourier:2 shortly:1 intrusion:2 epr:3 academic:1 incapable:3 possesses:1 stringent:1 just:12 ideas:1 assigned:2 human:6 facts:1 yet:2 enters:2 infinitely:1 cornell:1 regarded:2 character:8 transformed:1 occurring:1 interprets:1 posed:3 possible:19 possibly:1 whichever:1 unique:5 apart:3 desire:1 appearing:1 alice:5 niels:2 specific:6 follows:2 notorious:1 right:3 old:1 deal:4 people:8 sends:1 underly:2 born:2 insistence:4 critique:1 indistinguishability:1 guess:1 unavoidable:1 comments:2 everything:7 imposes:2 unit:1 arbitrary:6 illustration:1 losing:1 post:3 super:1 properties:11 takes:10 limitation:1 acquire:1 probabilities:18 ensure:1 terminology:1 restate:1 efforts:7 nerve:1 primitive:3 statements:5 presence:1 pays:2 puzzle:10 sketch:1 intellectual:1 negative:2 down:10 lies:1 beings:1 doctrine:1 refined:1 reducing:1 methods:1 initial:5 available:1 class:4 squires:1 physicists:3 way:21 was:18 medium:1 steers:1 irreversibility:1 form:18 offer:2 attempted:1 differences:1 encodes:1 taken:4 satisfactorily:2 encoded:3 removed:1 true:2 versions:1 maximum:2 until:1 considered:2 cosmos:1 adopt:1 proved:1 toss:5 peres:1 exist:4 commuting:2 archive:4 constructed:5 discriminate:1 locality:9 redwood:1 wavefunction:1 when:28 vanishes:1 reality:71 ny:1 setting:1 role:7 holding:1 digital:1 tie:1 picture:3 superposition:1 conditioned:1 a12:3 models:1 preceding:1 felt:1 describe:5 update:1 trouble:1 ballentine:1 assume:2 interval:1 together:7 correspondingly:1 χi:2 remarked:3 serious:2 concept:1 managed:2 remarkable:7 reviewers:1 rob:2 global:8 focus:1 leads:2 tripartite:1 remarkably:1 21st:1 depend:4 environment:3 answered:1 asking:3 circumstances:1 abundance:1 protective:1 orthogonal:11 choice:6 anonymous:1 emphasized:1 exact:1 perceived:12 presented:1 did:4 irreducible:2 leave:2 irreducibly:1 tenths:1 says:1 dealing:5 prediction:1 spectral:1 appear:5 pleased:1 current:1 suspect:1 goes:4 relational:4 appeal:2 paradoxical:1 supporting:1 henry:3 understanding:17 contemplate:4 address:1 alone:1 along:4 teaches:1 appears:1 change:1 ref:1 cuckoo:1 shift:2 commonly:1 simultaneous:6 usually:2 bob:7 pearle:2 emerge:2 regardless:2 griffiths:3 problematic:3 merely:5 prefer:1 logical:1 histories:6 flexibility:1 rarely:1 working:1 predictions:3 explicitly:1 scope:3 theoretical:3 today:8 introducing:1 sharing:1 disconcerting:1 validity:2 visual:2 appendix:10 ignorant:5 cases:5 effort:1 fly:1 ibi:1 thousands:1 values:24 following:1 making:2 claim:1 want:1 predict:1 expanding:1 sense:23 confused:2 heard:2 performed:5 sharp:1 counting:1 hydrogen:2 occur:4 verlag:2 σz2:1 s2:28 s1:42 σz1:1 innumerable:1 pure:30 pins:1 plus:1 type2:1 product:5 may:8 expectation:1 applications:1 produce:2 designed:4 representations:3 man:1 natural:4 dynamical:5 correlate:4 conscious:21 whenever:1 elicited:2 explicit:1 yielding:1 tale:1 sj:1 si:20 so:16 sn:3 representation:3 arrived:1 talk:13 exclusive:7 s3:3 furnished:1 indeed:13 unacceptable:1 course:4 experiments:7 differs:1 still:3 pointer:1 cited:1 relegate:1 thank:1 how:23 interesting:4 vicinity:1 forms:1 offers:2 constitutes:1 ours:1 deviant:1 happened:1 non:30 views:2 impulses:1 records:1 identically:1 now:16 discuss:1 nor:4 above:5 pps:1 term:5 name:2 january:1 hermitian:4 possibilities:1 realistic:2 shy:1 entirely:12 domain:2 fired:4 ed:3 absurdly:1 approximated:1 es:1 intended:1 shown:2 space:15 furthermore:1 interference:3 looking:2 replacing:1 seriously:2 notre:4 suggesting:2 correct:1 shows:4 earlier:2 reformulation:1 theory:23 possibility:3 quite:4 california:1 yuri:1 besides:1 inevitable:1 care:1 vestige:1 poses:1 derivation:1 language:2 impose:1 catalog:1 turn:3 place:3 think:3 first:15 intuition:2 xi:3 symmetry:2 variables:7 cannata:1 omn:1 directly:8 carry:1 impossible:2 sounds:2 open:1 city:2 given:25 1r:13 iai:1 silent:3 europe:1 stimulation:1 imposing:1 1g:4 national:1 speaking:1 gives:3 phenomenology:2 continuous:2 eliminates:1 specialists:1 copy:2 than:19 connections:1 nathan:1 require:4 future:2 were:11 outcome:1 pre:2 dynamically:4 argument:4 say:6 any:45 subsystems:81 answering:1 aside:5 note:5 equipment:1 emphasis:5 maintain:1 take:10 objective:25 performance:1 channel:1 gleason:3 sure:2 investigations:1 track:3 price:4 correlation:42 molecule:1 pair:5 analytically:1 pages:1 especially:1 surprising:1 dordrecht:1 later:3 implications:1 virtually:1 cortex:2 refining:1 filing:1 precise:2 show:2 discovered:1 spaces:3 inconsistent:4 decompositions:2 ground:1 ensembles:3 enough:10 liberation:1 only:57 going:3 developed:1 awareness:9 closed:1 get:3 straightforwardly:3 cannot:21 symmetrically:1 ssc:7 reveal:1 podolsky:4 yield:2 worried:1 roger:1 discussing:1 formulations:2 vision:2 reveals:1 physically:5 violated:1 gottfried:2 relative:7 namely:1 uncorrelated:3 nonlocality:16 kurt:2 fails:1 satisfying:1 inequalities:2 ways:2 subsequent:2 review:2 definite:1 label:1 behind:3 jth:2 between:45 αi:13 justified:1 αj:1 across:1 august:1 useful:2 come:3 perceptions:7 acquiring:1 many:29 region:1 according:9 comes:2 among:29 historians:4 characterization:2 color:2 insist:5 anti:4 assertions:1 bizarre:2 sensible:1 unusual:1 capable:3 combined:4 linguistic:1 sensibly:1 restrictions:1 readings:2 external:26 encapsulation:2 former:1 those:29 case:12 myself:1 developing:1 boris:1 situation:2 nomenclature:1 embrace:1 everyday:2 different:22 develop:1 insofar:1 granted:3 coexisting:2 same:14 shifts:2 arguments:4 pai:1 paj:1 physical:82 events:1 status:3 jeffrey:1 extended:1 assigns:2 closest:2 trivially:2 devoid:1 delicate:1 unqualified:1 tradition:4 traps:1 macro:1 no:31 without:10 solve:2 components:4 inability:3 model:2 sec:1 manifold:5 being:18 generally:1 rest:3 summed:1 flavor:1 ithaca:8 death:1 sheldon:1 thinking:3 seems:4 except:1 treatment:1 empiricist:1 momentum:3 real:11 psi:2 aspects:7 around:1 rules:1 specimen:47 admitting:2 usefully:1 early:4 world:31 mod:2 particle:1 indisputable:1 goldstein:1 either:7 occasions:1 output:2 inter:1 reduced:3 conditional:17 venerable:1 shortcoming:1 specified:5 complementarity:3 provided:6 critical:1 decomposition:2 provides:2 antisymmetrize:1 refer:2 measuring:1 contingent:2 power:3 resurrection:1 william:1 central:3 origins:1 theorems:5 discussed:2 meaning:4 practical:3 mutually:12 obeys:1 act:1 mixed:22 freeing:1 cambridge:3 communication:1 references:5 determine:9 einstein:6 operator:8 accumulated:1 conceptually:2 your:3 loc:3 her:3 refinements:1 there:31 start:2 assumes:2 survives:1 complete:13 smolin:1 regard:2 cabinet:2 philosophers:1 land:1 elimination:2 trying:8 october:2 eschew:1 agree:1 connect:1 detailed:2 lanl:4 ai:10 certain:7 aj:2 am:12 deep:3 general:10 ap:1 grasped:1 formulation:8 encompass:1 drafts:1 cooked:1 deserve:1 rosen:4 field:4 valid:1 remarks:1 mathematics:1 you:18 relegating:1 polar:1 vocabulary:2 separate:2 time:13 includes:2 a1:8 a2:8 observables:50 building:1 calls:1 impossibility:2 adam:1 resolution:8 original:3 externally:1 consider:8 ceases:1 forbidden:1 lack:2 thoughtful:1 commute:2 talks:1 follow:1 expressions:1 reasoning:4 particles:4 preserves:1 acting:3 nonlocal:4 sound:2 belonging:1 amplitudes:1 straightforward:2 very:12 induce:1 primed:4 puzzles:5 worst:1 interpreting:4 difference:3 condition:4 treating:1 accompanying:3 list:1 insufficiently:2 large:2 glossary:2 undone:1 small:2 pramana:1 neighborhood:1 ten:1 appearance:1 perspectives:1 past:1 zero:7 perspective:7 further:7 canonical:1 what:45 skeptic:1 deeply:2 section:13 brief:2 version:3 subspaces:4 learned:3 acknowledgments:1 multitude:1 revealing:1 schilpp:1 full:6 loose:1 modify:1 answers:2 selective:1 investigating:1 directions:1 strong:2 conviction:2 difficulty:2 introductory:2 allows:3 experience:15 published:1 action:1 narrow:1 options:1 uniquely:2 marginal:6 vii:3 straightened:1 establish:1 readily:2 conventional:9 eye:2 proceed:1 distinct:1 contains:3 cornia:1 ψi:10 a54:1 mysterious:3 undivided:1 more:31 knows:1 operators:5 excuse:1 basically:1 particular:32 known:3 foundations:5 evolves:2 none:2 fatal:1 debates:1 science:9 equation:1 remain:1 examined:1 evolved:3 learn:2 abandon:1 clarendon:1 history:1 beautiful:1 ions:2 stated:2 share:2 states:39 abner:1 minimum:1 arise:3 exclude:3 information:9 court:1 goal:1 rather:10 hugh:1 stemming:1 ensemble:8 acknowledging:1 δij:1 algebra:2 suppose:2 tries:3 coming:1 response:1 contrived:1 imagery:1 spectre:1 generic:1 fundamental:13 pay:1 geographic:1 playing:1 tolstoy:1 help:1 ith:1 essence:4 soon:1 attitude:4 paper:3 through:5 existence:9 excitations:3 its:70 reluctance:2 actually:6 late:3 resort:1 absence:7 parts:4 microscopic:8 systems:20 disagrees:1 founders:1 might:5 alter:2 return:1 propose:2 framework:2 oxford:4 mystery:4 easily:3 2r:4 coping:3 always:6 level:1 evade:1 factorizable:1 micro:4 token:1 2g:10 found:2 2i:2 characterized:5 subsystem:103 reactions:1 formulate:1 hard:9 idea:2 macmillan:1 engaging:1 unprimed:4 expect:2 measurement:77 quantum:146 beyond:17 deals:3 robert:3 since:18 misses:1 print:5 occurs:2 perceives:2 differ:2 lesser:1 extraordinary:2 reason:3 conditioning:2 members:1 put:4 teach:1 beginning:4 definition:1 pairs:3 retained:1 american:2 consequence:3 undergo:1 assign:1 arose:1 indebted:1 major:2 probability:47 encoding:1 relate:1 thereafter:2 number:2 done:2 construct:3 story:3 leading:1 interact:1 least:7 pinned:3 assumption:2 statement:2 hundred:1 option:1 discover:1 part:3 off:2 believe:7 convinced:1 kind:11 wootters:2 determines:2 einsteins:1 fuchs:3 determined:6 contrary:1 toward:4 treated:1 peierls:2 deciding:1 motivation:2 electrodynamics:3 defect:1 karl:1 routledge:1 bohm:2 hopelessly:1 self:1 extracted:1 internal:27 analogy:1 commentary:1 play:3 towards:1 warnings:1 measures:2 singlet:5 most:8 significant:2 nothing:23 probabilistic:6 singled:1 branching:2 orlov:1 clear:1 sometimes:4 unreasonable:1 physica:1 traditional:3 electrons:1 physics:62 particularly:2 phenomenon:1 relation:1 carefully:1 fine:2 find:3 dividing:1 endlessly:1 excessively:1 evoked:1 betray:1 his:5 notation:1 dependent:1 zurek:1 express:5 shared:1 during:1 him:4 arxiv:1 remove:1 common:7 consciously:1 set:28 sep:1 plausible:1 see:19 individual:30 bare:1 descriptions:2 constellation:2 lee:2 currently:3 various:2 probably:4 conditions:7 knowing:1 interpretational:2 recently:3 responses:1 complementary:3 initially:1 attention:1 vanishing:4 gilles:1 distinguish:2 alters:2 both:12 last:2 connection:1 context:9 reply:1 whole:4 finds:2 experimental:3 point:15 simple:5 proton:4 dimensional:6 simply:8 throughout:1 pp:6 described:2 transformations:1 due:1 strategy:2 reduction:2 describes:4 collected:2 ph:5 pi:3 empty:1 lett:2 firm:1 addison:1 understand:13 systematic:1 unnecessarily:1 p2:2 p1:2 look:2 solid:1 fapp:1 while:10 replaced:2 behavior:1 error:1 resolved:2 unitary:2 century:4 vol:1 encountered:2 reads:1 obstacle:1 vanish:2 grant:4 read:1 emphasize:1 widely:1 resulting:2 development:2 used:5 affairs:3 assignment:1 generalizes:1 moment:4 uses:2 purpose:4 recent:5 task:1 older:1 underlies:1 analysis:1 obviously:1 consistency:5 clears:1 stating:1 know:9 abilities:1 quarters:1 atomic:4 questions:2 using:1 inference:1 letting:1 kluwer:2 conclusions:1 surprises:1 guaranteed:1 exclusively:2 signals:2 source:1 stapp:5 describable:2 theorem:18 relevance:1 guarantees:3 transformation:2 measurability:1 big:1 hiley:1 entangled:1 extrapolating:1 formal:3 pertinent:1 excluding:1 admittedly:1 interestingly:1 separately:1 arthur:2 continue:1 yields:1 translated:2 essential:4 spins:2 mathematical:1 lucien:3 often:7 absolutely:3 some:21 back:5 understood:3 experienced:3 pφ:2 examples:2 photomultipliers:4 ourselves:4 scale:4 describing:4 affects:1 though:10 tends:1 gyula:2 run:2 s12:4 bi:3 stem:1 br:4 relating:2 hilbert:2 anything:5 coexist:1 firing:1 range:1 modal:2 consequently:1 block:1 therein:1 computational:1 into:34 within:6 dame:4 appropriate:10 proportional:1 criticisms:1 statistics:1 measured:2 apparently:1 question:7 specifically:1 conceivable:1 sections:2 perplexing:1 elsewhere:1 retina:1 deductions:1 atom:4 line:4 collapses:2 consist:4 characteristic:3 stumbling:1 up:12 us:28 livi:1 cit:3 continuously:3 similar:5 called:4 purcell:1 associated:11 reconcile:2 defined:1 stripped:1 influence:1 doesn:1 globally:3 single:5 formalism:6 prevail:2 denying:1 paradox:1 application:1 accounted:1 arithmetic:1 explaining:1 elements:4 conventionally:1 problems:7 prepared:1 replace:2 spatially:1 develops:1 fisher:1 structure:4 correlated:11 algorithm:2 liberate:1 required:1 equivalently:3 weights:1 reprinted:2 international:1 requires:7 having:7 once:2 essay:3 results:11 existing:1 eds:2 proposition:1 broader:5 mcmullin:2 go:5 issues:3 seemed:1 compact:1 alamos:4 deterministic:3 send:1 citing:1 include:2 overlaps:1 random:1 outside:2 implicitly:1 wave:14 electron:4 wishes:2 matrices:1 entire:8 notes:3 michael:1 try:3 inspection:1 noted:9 trw:10 sensation:5 demonstrations:1 imply:2 earth:1 carlo:2 plays:3 evokes:1 apparatus:43 expressed:6 consistently:1 19th:2 experiment:2 concisely:1 expresses:1 body:2 justification:1 led:1 measurements:10 respectively:1 jointly:1 explore:4 objects:2 others:3 fifteen:1 implicit:2 great:3 northern:1 photomultiplier:7 wesley:1 technical:1 larger:5 contradiction:1 leaving:1 evading:1 products:11 makes:10 honor:1 involves:1 composed:1 named:2 manage:2 private:1 outcomes:2 hardy:11 formulates:1 apply:5 resolutions:3 cloud:1 use:3 superpositions:1 remains:3 readable:1 pedagogical:1 few:2 totality:1 themselves:5 simpler:2 sort:1 occurred:1 popper:3 hilger:1 iii:3 discontinuously:2 account:4 emperor:1 obvious:3 universe:3 proof:7 process:7 favorite:2 inaccessible:1 purposes:1 lorentz:1 bene:1 something:7 wonderful:1 embodiment:1 decaying:1 distinguishable:3 regions:1 seeds:1 mysteries:3 establishment:1 tension:1 blocks:1 specifications:1 philosophy:3 collection:1 realized:1 submited:1 advocated:1 lines:2 wittgenstein:2 element:1 dispositions:1 subsequently:1 bipartite:1 produces:1 insight:1 produced:6 including:1 perfect:3 decay:1 chosen:1 arrangements:3 willing:1 degrees:4 choses:1 defining:1 greater:1 orthodox:1 wolfgang:1 polarizations:1 mention:1 insisting:2 realize:1 establishes:1 worlds:14 profound:1 university:4 identified:2 slide:1 transmitted:1 constraints:1 subset:1 lie:1 illuminate:1 doing:1 constitute:5 elementary:4 interplay:1 measure:2 separating:1 our:31 eigenstates:6 special:14 out:11 fundamentally:2 rev:5 lecture:1 supports:1 integrated:1 red:3 disclose:3 interactions:10 discontinuity:1 diagonal:2 completely:16 surely:2 york:6 philip:1 interaction:17 deprived:1 could:5 david:7 conversation:2 explored:2 distinctions:1 hence:1 rudolf:3 apparatuses:5 powerful:3 precisely:2 quality:3 swept:1 los:4 unknown:1 system:124 relations:4 their:11 perfectly:5 final:6 painful:1 completed:1 exactly:3 manifestation:1 constituent:1 completes:1 updating:2 achieves:1 holland:1 penrose:1 submitted:2 rarity:1 succinctly:1 defense:1 leslie:1 distinguished:1 w2:1 ingenious:1 spelled:2 comfortable:1 fail:2 need:5 demonstration:2 clearly:1 viewed:9 theoretic:2 able:8 mix:1 sufficiency:2 subject:7 heisenberg:3 unless:5 who:6 quantifiable:1 device:3 intrinsic:1 why:7 deny:2 consequences:4 undeniable:1 atypical:1 metaphysical:2 perceiving:2 mechanical:12 χn:11 shimony:1 fact:16 impression:1 selection:1 violation:1 supported:1 purely:2 trivial:15 agrees:1 based:4 knowledge:14 rovelli:1 mute:1 receptors:1 should:16 bases:1 molecules:1 constituents:1 local:4 inferior:1 meant:1 means:10 familiar:4 overall:1 joint:40 ones:3 added:1 evolution:2 densities:1 approach:4 she:1 contain:2 view:29 predictive:1 requirement:3 constructing:1 exists:1 acquired:2 tossing:1 frame:5 correlations:191 humans:1 packet:4 closer:1 phases:6 interacting:3 missing:1 favor:1 state:126 difficulties:1 correctly:2 confusion:2 invariant:2 neither:2 prevailing:1 ends:1 ability:12 however:3 key:1 problem:38 observable:25 interpretations:2 weeks:1 taking:4 acknowledge:4 equal:2 minds:1 admit:1 manifestations:2 bristol:1 tactical:1 jersey:2 otherwise:1 comment:1 relevant:1 conclude:3 narrower:1 respect:1 copies:1 responds:1 treat:2 proposal:1 arises:3 corresponding:5 route:1 coherence:1 subspace:1 assert:1 present:7 novel:1 survey:1 contexts:1 harder:3 value:17 choices:2 will:13 frameworks:1 nous:1 ve:1 almost:3 vi:2 thus:10 site:1 propensities:1 descriptive:3 orbital:1 capture:1 perhaps:5 radiation:2 cross:2 member:1 propensity:2 unity:1 strange:2 pauli:1 φi:4 φj:3 infer:2 difficult:2 ball:1 upon:3 effect:3 expand:2 destruction:1 schr:2 geroch:1 nevertheless:2 ingredients:1 well:12 bohr:9 thought:3 sets:5 position:10 arising:3 enormously:1 less:2 underlying:8 paul:2 macroscopic:11 density:26 bell:10 reasons:2 combine:3 maintaining:1 unprecedented:1 ought:8 identical:7 tests:1 famously:1 historic:1 whatever:5 presume:1 press:5 immediately:3 necessary:2 like:10 lost:1 extremely:1 james:2 become:2 works:1 conversely:2 accessible:1 because:21 classical:13 sequence:1 phenomena:7 proper:7 recognition:1 revs:2 happens:3 orthonormal:6 lead:1 demonstrates:1 avoid:2 overlap:1 instantaneous:1 does:20 inaccessibility:1 capability:1 noise:1 disentangle:1 selecting:1 journal:4 chromo:1 expansion:2 pressure:1 although:2 worthy:1 stage:3 about:65 actual:12 extension:1 freedom:4 compatible:1 important:8 insufficient:2 introduced:1 equally:3 own:17 letters:1 clifton:2 articulate:1 chemists:1 van:1 noticed:1 restricts:1 specimens:4 function:9 bridgman:1 north:1 insures:1 but:68 plague:1 gain:1 bub:1 he:7 made:2 compute:2 evident:2 whether:21 wish:1 below:2 tosses:1 demonstrate:1 distribution:11 piece:1 minutes:1 display:1 mechanics:91 pin:2 inadequate:1 meaningless:1 interchanged:1 functions:3 variety:1 detail:1 illinois:1 other:30 expositions:1 kinds:7 inescapable:1 ultimately:1 vein:1 matrix:28 coupling:1 starting:1 factors:1 rule:1 determination:1 augmented:1
|
quant-ph9801058.txt |@word consider:7 ron:1 particular:1 results:3 chaos:1 commute:2 entropy:1 edu:1 rop:3 follow:1 preserves:1 inverse:1 calculate:2 preserved:2 under:2 analogous:2 norm:1 returned:1 straightforward:3 orthogonal:1 bφ:1 wave:2 lrs:2 every:1 hannay:1 matrices:2 condition:1 entire:1 immediately:2 presented:3 t2:4 discrete:3 vector:2 fourier:4 small:2 mn:1 consistent:1 direct:4 zero:1 chopping:1 concludes:1 rigorous:1 dynamics:19 odd:11 canonical:1 even:13 what:3 appear:1 section:1 xφ:1 klimek:2 sxy:2 version:1 contributes:1 method:1 satisfy:3 respectively:1 heller:1 here:8 lev:1 others:1 along:1 standard:1 equations:3 hyperbolic:1 digits:1 remark:2 eiπ:5 shift:3 study:1 stretching:1 bv:12 periodic:10 graffi:1 action:1 deg:1 formulated:1 divide:2 extra:1 planck:4 unit:2 readily:1 use:6 takes:2 would:1 remains:2 positive:1 next:4 almost:3 ψi:3 kinematics:1 taken:1 associated:1 type:1 more:3 formally:2 operators:11 ip0:3 basically:1 informally:1 cases:2 hold:1 iii:1 involve:1 keeping:1 isomorphism:3 quantized:5 recall:1 equation:4 work:3 cat:5 quantizes:1 values:2 caveat:1 following:12 example:3 proof:12 give:2 stacking:1 preserving:2 annals:1 ann:4 states:2 claimed:1 sense:2 expandable:1 made:1 dxe:1 string:1 rather:1 holds:1 write:2 maps:7 rubin:4 pure:1 sin:2 map:25 product:7 description:3 algebra:10 derived:1 mapping:1 φ2m:12 plane:1 inst:1 summarize:1 fn:3 sy:1 natural:3 outline:1 sp:6 explicit:3 provide:1 egi:1 so:2 fundamental:2 correlation:1 representation:3 isola:1 order:2 words:1 over:3 insight:1 course:1 surviving:1 including:1 differs:1 its:2 e2πia:1 regions:4 symmetry:5 interesting:2 e2πik:1 e2πij:1 φb:6 coordinates:2 fruitful:1 lu:1 lr:1 choose:1 constitutes:1 lx:1 ly:4 non:1 integral:6 finitedimensional:1 isomorphic:1 scaling:1 they:1 now:14 sφ:4 easily:2 term:5 2p:4 e2πi:5 january:1 university:2 2x:9 appropriate:1 2z:10 orthonormal:2 l2:5 2a:7 each:2 found:2 2n:11 2i:2 characterized:1 2k:4 domain:2 schemes:1 independent:1 series:1 reduce:1 literature:1 ex:45 calculational:1 quantum:30 laboratory:1 ep:24 out:1 ru:3 shown:7 matrix:10 rr:1 space:14 restricted:1 furthermore:2 since:3 rx:1 ry:2 research:1 fellowship:1 acting:2 dxdx:1 reader:1 induced:1 math:3 shows:1 foundation:1 linear:1 voros:6 given:15 quite:1 completely:1 definition:6 r2:4 omit:3 motion:2 hence:2 onto:2 first:2 intuition:1 already:2 xl:1 lesniewski:3 xf:3 number:1 xe:1 restrict:1 multiplying:1 construct:5 xr:3 xs:3 xp:8 open:1 1p:1 guess:1 checked:1 similarly:1 πk:1 noncommutative:1 relations:4 fmn:5 1d:1 calculations:2 πz:1 scheme:2 structures:1 centered:1 exactly:1 part:1 authors:1 x0:50 completes:1 king:1 nathan:1 eip0:2 appealing:1 symmetries:1 correction:5 argument:2 saraceno:4 say:1 conjugate:1 need:1 constrained:1 any:6 liapunov:1 harper:1 lim:2 note:4 instance:1 k1:1 take:3 kaplan:1 interior:1 analogs:1 heisenberg:1 shall:2 chart:1 phase:1 class:1 exponent:1 χr:2 fjm:2 torus:16 kn:1 physica:1 kl:1 ks:1 points:1 principle:1 exp:13 mechanical:1 χl:2 physics:3 fact:10 called:1 show:3 supported:1 spaces:1 substituting:1 d2:2 find:9 giachetti:1 based:1 combs:2 written:2 should:2 jan:1 lemma:7 only:1 explicitly:2 toral:2 continuity:4 do:1 notation:1 de:1 expectation:1 integrality:1 christopher:1 dx:15 dy:1 dye:1 du:2 dp:9 normalizable:1 evolution:4 covering:4 arxiv:1 2πiθ:3 2πi:4 mapped:1 2sx:1 fixed:6 view:1 kernel:1 set:4 constructing:1 achieved:1 national:1 see:26 result:2 discussions:1 dµ:8 quantizing:1 satisfying:1 commutation:3 boundaries:1 state:6 between:2 invariant:1 boundary:2 previous:2 conditions:2 email:1 preserve:4 terms:3 weak:2 however:2 vanishing:1 harvard:3 comm:2 jk:1 comb:3 thank:1 both:1 limits:1 many:1 uncertainty:1 quantization:16 berry:2 expression:1 comes:2 otherwise:4 affine:1 cn:1 cm:2 point:9 harmonic:2 dimensional:7 2nz:2 ab:7 anti:1 quantizations:1 table:1 ps:2 described:2 transformations:1 lyman:1 piecewise:2 px:8 three:2 describes:1 basic:1 ph:1 abstract:1 define:6 esposti:3 ergodic:1 corresponding:2 commutes:1 am:8 grating:1 subspace:3 andrew:1 coherent:3 observe:12 denote:2 present:3 case:7 eip:3 p0:47 subsets:2 eix:1 value:2 remaining:1 will:1 suppose:2 momentum:3 procedure:1 unitary:10 orientation:1 chaotic:2 ip:1 ir:1 thus:10 iv:7 ii:2 middle:1 itself:2 properties:2 balazs:6 ia:1 vanish:1 bargmann:5 binary:1 different:2 author:1 make:2 same:2 unity:1 quant:1 proved:1 finite:2 φm:17 φn:9 fairly:1 calculation:6 used:4 trajectories:1 nj:1 hepp:1 compared:1 uses:1 infinite:1 changing:1 identity:2 eigenvectors:1 weakly:1 center:1 thought:1 likewise:1 position:2 paradigm:1 dimension:1 usual:1 χex:1 just:2 less:1 nd:1 obtain:1 via:2 using:2 projection:3 letting:1 preprint:2 2πia:13 except:2 valid:1 bnm:1 theorem:4 evidenced:1 iπ:6 transformation:5 kick:1 real:1 iθ:1 around:1 eigenvalue:1 decomposed:1 corresponds:1 increases:1 integer:2 like:1 lost:1 follows:7 reduces:1 diffraction:2 automorphisms:3 yields:3 simply:1 reduced:2 parity:4 because:1 classical:28 fresnel:1 b2:1 respect:1 ourselves:1 dense:1 maitra:1 does:2 steps:1 umn:1 demonstrated:1 refer:1 tabor:1 bm:1 journal:1 wavefunctions:1 expansion:1 bt:1 broken:1 step:4 bp:1 2m:26 hilbert:7 science:1 extension:1 commutator:1 basis:5 o:11 ox:42 2x0:2 introduced:1 consequently:1 op:26 conserving:1 h2:5 into:2 numerically:1 bound:1 down:1 hermitian:1 references:1 determine:1 operator:10 shrinking:1 iπm:3 hep:3 log:2 question:1 transform:4 width:1 conservation:1 inner:6 way:1 keating:1 was:9 propagator:19 complete:1 form:1 φx0:2 but:2 construction:1 hb:2 line:1 removed:1 fjn:1 2πb:1 applying:1 nonlinearity:1 whether:1 below:1 un:1 limit:10 2πip:5 demonstrate:1 problem:2 dudv:2 similar:7 2πix:5 poincare:1 mechanics:3 taylor:1 constant:4 af:6 defined:9 certain:1 universal:1 combining:1 linearity:2 general:2 conserved:1 dθ:3 our:5 ax:1 eric:1 functions:7 nk:1 na:8 nc:1 composing:1 vanishes:1 graduate:1 other:3 details:3 picture:1 elements:5 a0:1 generated:6 bounded:1 vectors:3 n2:1 baker:16 packets:1 having:1 2πim:11 lift:1 observables:6 remarkable:1 requires:1 original:2
|
quant-ph9801059.txt |@word monte:8 surrounded:1 consider:8 remarkable:1 illustrates:1 rev:24 keep:1 truncated:2 results:5 quadrature:2 huge:1 entropy:1 expressions:1 research:1 gk:3 issues:1 scr:1 inverse:9 terms:3 calculate:2 kleiner:1 paris:2 concerned:1 technique:3 contained:1 pˆn:7 supported:1 finally:3 does:2 th:1 stochastic:2 dramatically:2 ingredient:1 summarizes:1 applied:6 photocount:4 worse:1 straightforward:1 far:1 frequencies:3 keeping:1 focus:1 electron:1 telling:1 experimentally:6 exact:4 condition:1 states:9 smithey:3 moya:1 level:1 bn:2 turns:1 confirmed:1 large:3 differs:1 small:2 warszawa:1 accumulation:1 measuring:5 approximately:1 compensated:1 version:1 estimates:1 za:1 sign:3 approximation:1 second:2 evaluated:7 pass:1 rigorous:1 further:4 carlo:8 nauki:1 goes:1 even:3 established:1 what:1 errors:16 appear:1 apparatus:1 trivial:1 sum:3 selected:2 analogously:1 experiment:8 a231:1 above:6 increasing:7 method:2 raymer:5 full:1 evaluating:1 multinomial:1 respectively:1 realizations:1 component:1 equals:1 here:4 diagonal:1 behaviour:1 growing:1 nonunit:4 excess:1 active:1 based:5 along:1 strong:1 knowledge:1 obtained:6 convert:1 ref:2 study:6 studied:2 allows:1 completely:1 commonly:2 suggests:1 amount:1 resulting:3 procedure:3 usually:2 fourier:1 studies:1 pathological:1 plotted:2 buˇzek:1 via:7 followed:1 projection:2 family:6 problematic:1 banaszek:4 marked:1 outcomes:2 first:1 herzog:1 reflected:2 summation:3 apply:3 counts:2 total:1 tools:1 unit:1 plot:2 use:5 asymptotic:2 would:1 commun:1 always:3 positive:3 contains:3 negative:1 hilbert:2 process:1 depicted:2 call:1 therefore:7 taken:2 theoretical:4 more:6 smeared:1 introducing:1 ejected:1 becomes:3 operators:3 factor:2 hradil:1 unstable:1 normalized:1 particular:4 known:3 cases:3 off:6 iii:2 must:2 logarithm:1 reconstructed:27 account:3 valued:2 coefficient:2 integrating:1 recall:2 setup:3 oscillator:6 radon:2 affected:2 fock:5 values:12 following:2 root:1 example:9 performed:1 beautiful:1 alternating:1 leonhardt:8 calculation:3 introduces:1 organized:1 sample:3 professor:1 konrad:1 numbers:4 allowed:1 tan:1 counting:12 evidently:1 guarantee:2 information:13 regularization:3 goal:2 rather:2 divided:2 means:1 feature:2 photoelectrons:2 very:3 methodology:1 numerous:1 pair:2 opposite:3 field:4 parameter:6 oscillatory:1 simplicity:1 product:1 mar:1 description:2 cessa:1 singular:2 may:8 derived:2 route:1 povms:3 wallentowitz:1 subtleties:2 representations:7 data:30 convolution:1 negligibly:1 light:10 grant:1 explicit:1 think:1 provide:1 so:1 fundamental:1 correlation:5 representation:6 first:2 order:6 bins:2 restriction:1 wigner:8 help:1 developed:6 over:3 efficiency:7 years:1 stability:2 course:3 thermal:12 paper:5 statistical:65 signs:2 its:15 before:1 find:1 controllable:1 jacobs:1 derive:2 rapidly:2 manuscript:1 how:2 interesting:1 kelley:1 nontrivial:1 exhibits:1 forms:1 detected:1 systems:1 hidden:1 areas:3 might:2 eventually:2 them:1 photodetection:7 noh:1 combination:1 bernoulli:6 material:1 dai:1 framework:2 resolve:1 they:2 singularity:2 now:7 discuss:6 nor:1 easily:4 february:1 fizyki:1 characterizes:1 reasonably:2 presented:7 coefficients:1 events:2 possibilities:1 realistic:2 mode:10 each:7 found:3 uniwersytet:1 characterized:5 mean:6 different:2 preceded:2 schemes:11 retrieve:2 directly:6 instability:1 series:4 gaussian:1 related:10 inverted:1 balanced:1 extended:1 interplay:2 measurement:9 quantum:47 our:6 beyond:1 eq:6 special:1 out:4 try:1 shown:1 converted:1 matrix:13 space:10 restricted:1 furthermore:1 since:1 crucial:1 denotes:2 increase:2 acting:1 exploding:5 formula:6 squares:1 issue:1 integrated:1 shows:3 inevitably:1 linear:4 νth:1 quite:1 approaches:1 orm:1 complicated:1 dx:3 estimate:3 likelihood:1 determining:1 could:1 transition:1 kiss:3 times:1 counterpart:1 pattern:6 πk:2 corrupting:1 exhibited:1 delicate:4 origin:5 indebted:1 t48:1 probability:14 upper:1 vedral:1 assumptions:1 number:49 contributions:2 restrict:2 minimum:2 enlarged:1 quantified:1 another:4 knight:2 impossible:1 fν:3 illustrate:1 given:13 utilization:3 introduction:1 fixed:3 eqs:1 histograms:6 system:5 least:1 their:3 intermediate:1 difference:5 scheme:9 behaved:4 gives:1 back:1 imperfect:4 calculations:1 discussion:1 continuous:3 contribute:1 direct:5 optical:13 somewhat:1 than:1 relative:3 determines:1 showed:1 double:1 depends:2 tomographic:1 reconstructing:5 matter:4 compensation:4 determined:14 amplitude:3 were:1 outcome:3 treated:1 exhibit:1 questionable:1 fig:17 filtering:2 lines:3 beck:3 mind:2 randomly:1 raw:3 substantial:1 variable:3 manner:1 disjoint:1 seen:3 final:3 demonstration:1 any:11 depict:3 zero:1 studying:1 note:1 high:2 absorbed:1 take:2 algorithms:1 detector:5 accuracy:2 added:2 allow:1 though:3 mlynek:3 recalled:1 object:1 dla:1 most:5 regular:1 instytut:1 formulae:2 device:1 sufficient:3 analytically:1 measured:13 deviations:2 acknowledges:1 considered:3 calculated:3 explode:1 detectors:2 kn:21 typeset:1 part:1 principle:5 exp:4 mechanical:1 section:1 incomplete:1 quantity:5 significantly:1 prim:1 intensity:1 show:4 eres:1 random:10 recipe:3 converge:1 odkiewicz:3 relation:2 kbn:1 d2:2 principal:1 photodetector:3 teoretycznej:1 just:4 parameters:6 should:3 only:6 bases:1 subsection:1 indeed:1 employed:1 local:6 do:1 reconstruction:13 get:1 grey:3 simplest:1 expectation:9 da:1 joint:2 cannot:5 closely:1 dv:1 reconstruct:1 toolbox:1 interpreted:1 carmichael:1 runs:19 ˆk:1 settings:7 encounters:1 arxiv:1 yield:1 difficulties:3 processed:1 photodetectors:2 analytical:3 view:3 kernel:6 requirement:1 set:5 computed:1 exists:1 correlations:9 deconvolution:1 ends:1 up:5 detection:22 namely:1 sec:4 result:4 effectively:3 uller:2 discussions:2 close:1 points:1 annihilation:1 phases:2 evaluation:9 ways:1 subsequent:2 fluctuations:1 tend:3 state:54 difficulties:1 various:10 between:11 understood:2 consecutive:7 neither:1 approach:1 available:2 perfect:2 warszawski:1 recently:2 statistically:2 nature:1 fields:1 attention:2 combining:1 however:7 acknowledgements:1 ascribed:1 efficiency:1 tum:1 significant:2 suppressed:1 problem:1 infinity:1 suggested:1 observable:19 enables:1 numerically:1 cov:2 many:4 region:1 uncertainty:12 according:4 revealed:1 figures:1 variance:5 contribution:3 estimation:1 safely:2 experimental:40 arbitrarily:1 relevant:1 exemplary:1 point:8 simple:6 seems:1 homodyne:30 sampling:1 represented:1 moreover:1 schleich:1 described:1 transformations:3 basis:3 addition:2 due:7 been:14 strategy:3 ai:9 much:1 basic:5 collected:1 applying:3 ph:2 pn:15 pl:1 pm:1 ariano:6 generating:8 θi:57 corresponding:3 both:4 quantities:6 photon:48 covariance:3 royer:1 coherent:12 determination:11 external:4 systematic:3 denote:2 present:2 case:10 novel:1 look:1 subsets:1 pacs:1 solid:3 plain:1 value:18 will:15 diverse:1 suppose:1 behavior:1 error:11 squeezed:7 situation:1 property:2 richter:1 characterizing:3 represents:1 opt:9 vogel:4 characteristics:1 refs:2 thus:6 iv:2 ii:3 characterize:2 good:2 aspects:1 author:1 perform:1 suggest:1 radiation:2 lett:6 same:7 clearly:3 quant:2 accumulating:1 2p03b:1 products:1 finite:2 grows:2 higher:1 independent:10 used:13 schiller:3 feasibility:1 numerical:2 possible:4 mandel:1 purpose:2 recent:1 off:2 fully:3 nevertheless:1 expression:6 poland:1 semiclass:1 well:6 analysis:12 dadb:1 components:2 convenient:1 fail:1 comment:1 enormously:1 proposed:1 moments:3 mayr:1 obtain:3 valuable:1 detail:2 integer:1 polish:1 paul:5 briefly:1 macroscopic:1 yet:1 previous:1 cut:8 density:9 photons:2 characterization:1 character:1 transparent:1 conclusions:1 add:1 setting:2 transformed:1 treatment:1 easy:1 guarantees:1 transformation:13 real:2 rescaled:2 iλ:1 explained:1 insensitive:4 around:2 loss:1 quasidistribution:2 evaluate:5 sums:1 inversion:2 corresponds:1 opatrn:1 increases:1 makes:2 vacuum:3 press:1 using:19 mod:4 scaled:1 tail:2 necessary:1 follows:1 signal:2 noted:1 yields:7 either:2 arbitrary:5 multiplicative:2 pereira:2 parity:31 deal:2 sequence:1 absolutely:1 some:8 somehow:1 experiments:2 regularized:2 examples:2 poizat:1 oscillations:1 finite:17 superposition:1 delivered:1 describing:1 demonstrates:2 avoid:2 measurements:9 recorded:4 comments:1 whole:1 specific:10 equal:2 provides:2 tends:1 steps:1 welsch:2 limitations:2 noise:2 run:2 bm:1 equivalent:5 processing:3 step:2 revtex:1 pathologies:4 corr:4 accompanied:1 properties:16 bz:1 about:1 affect:1 macchiavello:2 aˆ:5 discussed:4 probabilities:4 range:1 involving:1 pression:1 πth:1 ow:1 connected:2 introduced:1 consequently:4 automatically:1 soc:2 computational:1 convergent:3 simulated:2 into:5 within:3 obtaining:3 bound:2 three:3 phase:31 appropriate:2 square:2 references:1 determine:1 operator:34 statistics:19 log:3 few:1 assumed:2 there:1 question:1 transform:2 long:2 width:1 anderson:1 low:1 way:1 jex:2 var:15 was:4 function:21 complete:6 form:4 tasche:1 analyse:2 foug:1 but:3 histogram:6 compensating:1 repeated:1 ho:1 circumvent:1 convergence:2 true:2 count:6 compute:1 instructive:1 whether:2 maximum:3 us:11 discretized:1 frequency:1 limit:8 demonstrate:1 distribution:29 defining:1 advantage:1 average:4 expect:1 detailed:1 constant:2 photoelectron:1 povm:1 certain:5 abstract:1 measure:4 am:2 general:9 substantially:1 single:12 ar:1 exist:1 dλ:2 simulations:5 tomography:3 formalism:3 distributions:11 again:2 functions:11 compared:4 completeness:4 no:5 na:1 whereas:1 when:12 defined:2 coefficient:4 application:3 other:1 b12:1 differentiating:1 defines:2 adam:1 picture:2 elements:7 generates:1 provided:2 preceding:1 problems:2 inherently:1 expressing:1 express:1 faridani:2 important:3 bounded:3 included:1 cooper:2 depicting:1 fraction:1 ejecting:1 correlated:1 assume:1 requires:2 interval:2 notion:1 equivalently:2 fact:1 walker:1 observables:18 starting:1
|
quant-ph9801060.txt |@word represent:2 logarithms:1 concept:1 partial:1 consider:2 limited:1 forbidden:1 eckert:2 shor:3 four:1 prefix:1 markers:1 computation:37 edu:1 chair:1 involved:2 contributions:1 children:1 issues:1 auckland:3 equivalence:1 factoring:2 aun:1 environment:1 topic:2 edward:1 case:1 advantage:1 very:9 reversibility:3 pages:2 wave:1 me:1 cellular:1 elena:1 matrices:1 categories:1 timely:1 entire:1 level:1 knight:1 solution:2 prototypes:1 large:3 discrete:2 sand:2 small:1 speculation:1 overview:1 solutions:3 slower:1 measurable:1 tex:1 reflected:1 invariant:1 machines:2 universities:1 index:1 what:6 appear:1 sun:1 idealistic:1 brief:1 abs:1 new:2 order:1 journal:2 contrast:1 full:1 simultaneously:1 respectively:1 even:1 here:4 atoms:1 objects:1 free:4 making:1 represented:1 november:1 equations:1 appears:2 knowledge:1 obtained:1 suitably:1 shift:1 completely:1 amount:1 permutation:3 resonance:1 automaton:1 settled:1 gottlob:1 point:3 golden:1 tasks:2 pops:1 scales:1 private:1 brought:1 herzog:1 austria:1 use:4 dna:5 would:4 remains:1 gibbons:2 scenarios:1 classically:4 automata:2 call:1 therefore:1 memory:1 encode:1 themselves:3 theoretical:4 today:1 more:5 sort:1 pavlov:1 clever:2 furthermore:1 demon:1 inclined:1 about:1 warm:1 foundations:2 subjective:1 high:3 springer:2 ibm:1 pursue:1 science:3 work:1 remain:1 values:2 following:2 strategies:1 my:2 example:2 proof:4 beautiful:1 heart:1 stated:2 process:2 allowed:2 organized:1 states:8 effectively:1 tag:1 degenerate:1 sense:3 times:1 cloning:1 information:10 needs:1 recursive:2 kwiat:1 provide:1 verify:1 feature:1 georg:1 machine:1 far:2 hot:1 gate:1 profiting:1 map:1 product:2 may:7 turing:2 after:1 ball:1 lot:1 fe:2 physik:1 geometrical:1 meaningful:1 attempt:1 splendid:1 computations:2 lines:1 arrow:1 compressing:1 rather:1 switch:1 cannot:1 so:4 fundamental:2 representation:1 cristian:4 playing:1 operations:3 exclusive:1 developed:1 over:1 fredkin:1 reversing:1 course:2 including:1 mentioned:1 still:1 ieee:1 its:4 before:1 group:2 decay:2 personal:1 interesting:3 undecidability:1 differently:1 maxwell:1 mail:1 might:4 kasevich:1 eventually:1 them:5 good:2 copying:2 finish:1 flipping:1 lunch:1 billiard:1 they:3 symposium:1 nov:1 now:1 day:1 term:3 gets:1 january:1 university:2 presented:1 reasonable:1 universit:1 side:1 characterized:1 mean:1 heavy:1 development:1 schemes:1 doing:1 globe:1 hard:1 idea:2 related:1 slowdown:1 challenges:1 society:1 used:1 measurement:2 quantum:28 our:1 operation:2 herbert:1 out:1 rex:1 space:1 restricted:1 confess:1 since:2 interference:2 parallelizing:2 research:4 increase:1 mihalache:1 participants:1 reader:1 print:1 gov:1 issue:1 integrated:1 perception:1 theory:10 upon:1 little:1 possibility:2 standard:1 reason:1 necessarily:1 beginning:2 interaction:4 speedups:2 via:1 could:3 computers:3 linearized:1 silicon:2 technische:1 hertling:1 gordon:1 hence:1 onto:1 first:2 major:2 already:1 number:5 thereof:1 traveled:1 another:3 tomorrow:1 size:1 given:2 management:2 fair:1 authentic:1 night:1 system:3 least:1 their:3 too:1 statement:2 john:3 bits:7 speaking:1 low:1 collapse:1 mostly:1 completed:2 took:1 alan:1 simulate:1 natural:1 believe:1 bennett:3 than:5 population:1 past:1 kind:2 scheme:1 showed:1 princeton:2 future:1 were:3 result:1 bad:2 well:3 topics:1 argument:2 outperforms:1 say:1 need:1 seem:2 weinfurter:1 any:6 ray:1 latter:1 complexity:1 zoo:1 instance:3 emphasis:1 potential:1 harald:1 algorithms:2 encouraged:1 switching:1 santafe:1 surf:1 blue:1 centre:1 price:2 techniques:1 most:1 rigor:1 immediate:1 device:1 coin:1 probabilistic:1 class:1 zealand:1 salomaa:1 forever:1 constructed:1 consequences:2 sometimes:1 unreasonable:1 tph:3 proceedings:3 generation:1 principle:1 deeply:1 physics:5 fact:2 emerging:1 particularly:1 somewhat:1 charles:2 speedup:1 halting:1 attempts:1 lloyd:1 analogue:2 trivial:2 staff:1 copy:1 based:8 just:3 true:1 dynamical:2 distributed:1 state:4 should:2 jan:1 only:3 factor:1 boris:1 mixture:1 means:1 remedy:1 ones:2 christopher:1 international:3 prime:3 evolution:2 continuum:1 progressive:1 convinced:1 outperform:1 arxiv:1 motion:2 factorization:1 reif:1 processed:2 fixed:2 view:1 overheads:1 fascinating:1 reductio:1 trick:1 computer:6 devices:1 cleverly:1 close:1 paul:1 subject:1 hilbert:1 mechanically:1 speed:1 review:5 written:1 difficulties:1 cooperation:1 progress:1 terms:4 nature:1 importance:1 attention:1 key:1 news:3 come:1 embed:1 received:1 protect:1 2n:2 many:3 annual:1 tuwien:3 participating:1 context:1 contribution:2 comes:1 otherwise:1 mechanics:1 co:1 jeff:1 seems:3 improper:1 article:1 cs:1 respect:2 ad:1 conference:9 better:2 pp:2 transformations:1 wien:1 arbitrary:1 due:5 been:2 mark:1 much:2 basic:1 expected:1 ph:2 waste:1 meeting:1 correction:1 calude:5 systems:3 elitzur:1 both:3 theorem:1 zeilinger:1 coherent:3 personally:1 suspected:1 present:3 applied:3 novel:1 exponential:2 wiedner:1 kimble:1 will:6 while:1 error:1 35th:1 landauer:2 unitary:2 anton:1 thus:1 pressing:1 against:1 technology:3 increased:1 binary:1 containing:1 develop:1 author:2 insofar:1 make:4 same:1 html:1 quant:2 deletion:1 finite:4 status:1 extended:1 http:5 unconventional:6 singapore:2 stressed:1 outperformed:1 publ:1 devoid:1 levels:1 necessity:1 infinite:2 thoughts:1 valeria:1 tracking:1 kept:1 scenario:1 framework:1 reprinted:2 modeled:1 seth:1 leff:1 vaidman:1 patterns:2 experimental:2 organization:1 model:2 researchers:1 proposed:1 emerge:1 being:1 stored:1 aspect:1 yes:1 scattering:1 yet:1 halfway:1 contradicting:1 execution:1 headed:2 sky:1 thermodynamics:1 pile:1 versa:1 technological:2 diagonalization:1 input:1 formal:1 gave:3 aspects:1 around:1 read:1 big:1 results:2 february:1 lanl:1 dark:1 matters:1 increases:1 know:1 press:2 using:1 bit:12 unique:2 prominent:1 loss:1 necessary:1 like:2 lost:1 sizes:1 mit:1 informative:3 indication:1 martin:1 amos:1 become:1 alford:1 www:3 right:1 old:1 methods:3 classical:9 phenomena:2 back:2 polynomial:2 sight:1 moreover:1 complementarity:2 peter:3 ourselves:1 conventionally:1 theoretische:1 measurements:1 extensively:1 per:1 electrodynamics:1 hauptstraße:1 steps:1 algorithmic:2 scientific:1 reaching:2 equivalent:1 processing:2 expansion:1 step:2 santa:2 metaphor:1 svozil:4 thomas:2 actual:1 consumption:1 fringe:1 discussed:1 mutually:1 encryption:1 referred:1 stakes:1 letters:1 garbage:3 previously:1 communication:1 into:7 lies:1 appropriate:1 because:3 references:1 determine:1 artur:2 bijective:1 mere:1 physical:2 impressed:1 institut:1 additional:1 possible:3 area:2 there:9 question:3 alleged:1 why:1 does:1 pessimistic:1 physicists:1 way:3 conceivable:1 was:3 energy:1 vienna:1 function:2 complete:1 but:4 delivery:1 heat:3 contradictory:2 encoded:1 technologies:1 irreversible:4 collapses:1 he:1 again:2 applying:1 embedded:1 circuits:1 practically:1 anyway:1 up:5 us:2 ur:1 problem:3 piece:1 strands:1 called:2 strongly:1 ac:4 later:1 associated:1 moore:2 zeno:1 computing:2 universal:1 rephrasing:3 am:1 deep:1 general:1 single:2 exist:1 promised:1 regime:1 incorrect:1 absurdum:1 compared:1 nm:1 no:7 amounts:2 stake:1 when:2 perceiving:1 scaled:1 field:1 nz:1 other:2 department:1 mathematics:1 revision:1 picture:1 xxx:1 superposition:2 models:4 welcome:1 problems:2 miscellaneous:1 variation:1 includes:1 meaning:2 mechanical:1 dissipation:2 irreversibility:1 remote:1 longer:1 algorithm:2 vice:1 assume:2 age:1 factors:2 speculations:1 together:1 reversible:19 parallelism:1 time:3 decoherence:1 having:3 once:2
|
quant-ph9801061.txt |@word secondly:1 consider:6 similarity:1 results:1 leads:6 consists:1 decisions:1 causes:1 excludes:1 depend:7 calculate:1 paris:1 nonlocal:3 nπ:1 behave:1 present:2 under:1 belonging:1 amplitudes:12 far:1 choice:4 interpreting:1 decide:4 experimentally:1 difference:9 condition:6 splitter:3 impressive:1 transmission:1 correct:1 travels:1 coincidences:2 inertial:1 smaller:1 consistent:2 past:3 imply:2 fiber:1 traveling:1 port:1 even:4 appear:2 section:3 consequent:1 experiment:21 issues:1 new:1 contrast:1 led:1 realizations:1 free:1 represented:1 path:32 quite:1 observing:1 box:1 institute:1 contradiction:1 controversy:3 suggests:1 resulting:1 olivier:1 dra:1 studies:1 polarizers:1 outcomes:1 herzog:1 orderings:3 causal:12 scarani:3 conventional:1 impacts:11 working:1 probabilities:15 give:1 predictions:6 next:1 therefore:4 relativistic:4 taken:2 selects:1 more:1 separated:9 occurred:1 aware:1 appendix:4 normalized:3 particular:2 arranging:1 foundations:1 hold:1 must:3 account:6 contradicts:1 setup:7 theories:1 values:4 following:8 stimulating:1 figure:1 stated:1 discussed:1 suggestions:1 accept:2 states:2 indicates:2 lorentz:3 performed:2 distinguishable:2 influenced:2 discussion:2 watching:2 american:1 antoine:1 delay:1 influences:16 answer:2 ordinary:5 speaks:1 ensemble:1 description:1 superluminal:8 may:3 philosophy:1 violates:1 produce:1 demonstrating:1 stress:1 short:4 four:2 joint:2 light:5 lines:1 yielding:1 cannot:6 so:1 allow:2 pleasure:1 order:5 holds:1 interpretation:1 produces:1 developed:1 produced:2 experiments:8 through:3 argued:1 still:3 its:5 before:12 machine:2 thank:1 acknowledge:1 ll:77 relativity:1 subensemble:6 detected:6 fig:2 them:1 interdisciplinary:1 views:1 wolfgang:1 effects:1 they:1 arriving:1 now:2 february:1 always:1 university:2 did:1 transmitted:1 reasonable:1 each:5 2l:2 found:1 side:9 realism:2 referred:1 successively:2 another:1 zurich:1 series:4 principles:1 related:1 interferometer:4 sketched:1 quantum:9 our:1 happen:1 eq:3 event:1 really:2 shown:2 space:2 since:1 rev:1 denotes:1 particles:2 acting:6 wich:1 electronics:1 occurs:1 foundation:1 after:5 theory:4 possibility:3 standard:1 clarify:1 carried:1 conflicts:1 detecting:2 pairs:14 backwards:2 determining:1 could:1 ordering:8 length:7 hence:2 uses:1 first:10 already:2 probability:15 striking:2 traveled:4 done:3 long:4 hugo:1 given:2 necessarily:2 rejects:1 introduction:1 leading:1 behaves:2 unruh:2 their:1 observations:1 john:1 gives:1 geneva:2 tapster:2 regards:1 undoubtedly:1 than:3 reflection:1 observed:1 second:2 rarity:2 matter:1 determined:1 amplitude:3 were:1 outcome:6 distinguished:1 result:1 epr:1 argument:1 say:1 valerio:1 any:7 paths:10 conversion:1 built:1 mermin:2 nonlocality:8 instance:1 stapp:4 build:1 timelike:3 detector:4 simultaneity:1 broglie:1 unless:1 opposite:1 impacting:6 eight:1 successive:1 pair:4 accepting:2 acknowledgements:1 measured:2 considered:1 clear:2 later:1 detectors:7 km:1 principle:13 parenthesis:3 dos:1 usual:3 physics:1 sum:5 quantity:1 show:1 violation:3 text:1 finkelstein:1 relation:1 keywords:1 substituting:3 d2:10 agrees:1 d1:10 impact:9 aσ:5 causality:15 parameters:3 distributed:1 state:1 should:2 jan:1 only:9 local:6 do:1 dl:2 his:1 quantph:2 means:3 de:5 beam:5 ones:4 listed:1 words:2 reply:1 regarding:2 settings:1 suarez:5 arxiv:1 yield:1 paper:1 predicted:2 switzerland:1 qm:45 view:10 available:1 set:2 observer:2 undergoes:2 frame:1 correlations:2 detection:6 see:2 lausanne:1 us:3 discussions:2 arm:6 eman:1 owens:1 label:1 pump:1 future:1 between:9 invariant:1 subscript:1 numerous:1 arrival:1 notice:2 recently:1 nature:2 emitted:1 however:2 physicist:1 distinguish:1 interfere:1 both:2 cos:8 taking:4 according:7 against:1 sensitive:1 admit:1 exceeds:1 experimental:2 otherwise:1 comment:1 splitters:3 ch:2 point:2 reasons:2 character:1 corresponds:1 whatever:1 coincidence:3 non:3 consideration:1 table:6 strong:1 described:1 capable:1 equations:1 three:4 been:6 basic:1 ph:8 contribute:1 corresponding:3 sufficient:2 coherence:2 photon:37 those:3 case:4 laser:1 brendel:1 plain:1 value:3 choices:2 will:4 information:2 while:1 ongoing:1 promising:1 detailed:1 bohr:1 spacelike:1 violating:1 cone:1 different:1 perform:1 make:1 belong:1 shorten:1 same:5 clearly:1 stimulated:1 quant:8 avoids:1 gets:3 events:2 conflict:2 status:1 meets:2 used:4 effect:2 hand:5 moving:1 entanglement:2 invariance:2 costa:4 center:1 largely:1 makes:1 locality:1 well:1 know:4 obviously:1 without:1 position:1 model:4 left:2 unified:1 proposed:5 being:3 distribute:2 actions:1 predicts:2 paul:1 yet:2 nicolas:1 adding:2 enters:2 photons:1 bell:3 had:1 exclusively:2 source:1 other:7 lett:5 real:5 rnl:10 subensembles:2 possible:9 lengthen:1 entangled:2 integer:1 necessary:1 like:8 particle:12 follows:2 specific:2 detections:4 either:2 become:3 works:1 therein:1 because:3 pσ:1 specified:5 indistinguishability:3 counts:6 happens:2 eiγ:4 eiβ:4 highlighting:1 lead:2 demonstrates:1 though:3 does:5 assuming:1 measuring:1 selecting:1 journal:1 agreement:3 step:1 output:2 epfl:1 refers:1 about:1 would:5 getting:4 accepts:1 o:3 ports:1 mutually:2 nothing:1 characterized:1 equally:1 beamsplitter:1 presence:1 into:3 probabilites:2 chooses:2 down:1 lies:1 appropriate:1 right:3 references:2 ei:8 conceptually:1 support:2 fast:1 accordingly:2 influencing:1 way:4 assumes:2 but:5 count:3 made:3 applying:1 whether:4 devices:1 below:1 demonstrate:1 distribution:2 similar:2 gisin:3 mechanics:4 bearing:1 associated:3 abstract:1 measurement:6 influence:1 denote:5 single:16 exist:2 together:1 tittel:2 interferences:4 no:2 whereas:1 application:1 interested:3 out:1 conclusion:2 superposition:4 preceding:1 mechanical:1 allowing:1 zbinden:2 independently:3 implies:2 faster:2 assume:2 odds:1 rule:2 impossibility:4 implied:1 time:29 characterising:1 backward:10 receive:1 once:2
|
quant-ph9801062.txt |@word words:1 show:2 caused:1 results:1 paper:1 hypersurface:1 trivial:1 find:1 gr:8 system:1 true:1 relativity:3 signals:2 relate:1 mail:1 transformation:1 do:1 misinterpretation:2 preferred:1 untenable:1 every:1 they:1 using:1 hxy:1 evolution:1 showed:1 fails:1 transmission:1 follows:1 arxiv:1 michael:1 alice:2 qc:8 transmitted:1 references:1 classical:2 series:1 national:1 some:1 jump:3 used:1 cloning:5 measurement:1 quantum:13 our:1 eq:1 special:1 nonexistence:2 what:5 kiev:1 space:1 measurements:2 state:2 does:2 apc:1 benjamin:1 causally:1 jumps:3 teleportation:3 effect:1 org:1 hilbert:1 ukraine:2 both:1 actual:1 limits:1 institute:1 involved:1 0y:6 allows:1 against:1 schumacher:2 bob:2 argue:1 involves:1 fallacy:2 comment:1 affairs:1 conclude:1 simple:1 communication:3 ca:1 due:1 pair:1 unitary:2 cb:1 frame:1 operator:1 impossible:1 message:1 jan:1 given:2 exists:3 there:5 three:1 specifically:2 describes:1 ψm:6 ph:4 consistent:1 separated:1 complete:1 academy:1 theorem:6 but:1 assert:1 authors:3 hold:1 iii:2 completes:1 ii:2 made:1 vladimir:3 cite:1 westmoreland:2 universe:1 wheeler:1 proof:5 mechanics:3 claim:2 ab:1 abstract:1 argument:3 states:2 contradicts:1 exist:1 ay:3 ax:9 constructed:1 information:1 no:6 whereas:1 holds:1 sciences:1 φb:2 φc:2 quant:4 papers:1 ordinary:1 simultaneity:1 events:1 elements:1 description:1 superluminal:8 shown:1 wrong:1 entanglement:4 reference:1 recent:1 attempt:1 dynamical:1 clear:1 mash:1 equivalently:1 so:1 χb:1 allow:2 time:2 0m:6 physics:1
|
quant-ph9801063.txt |@word represent:1 consider:1 rev:1 results:1 switches:3 research:2 amplification:1 quasi:1 gbit:2 those:1 th:1 stable:2 amplitudes:1 worse:1 very:5 choice:1 electron:1 figs:1 northwestern:1 level:3 transmission:2 turns:1 large:4 small:1 force:1 ten:1 direct:2 rate:3 design:1 notwithstanding:1 further:1 implemented:1 port:4 repeaters:6 telecommunication:1 even:3 employ:1 nonlinear:12 appear:1 iterating:1 expressed:1 ˆb:5 increasing:1 respectively:1 error:5 component:1 here:1 agreement:1 reported:2 address:2 represented:1 along:6 strong:1 wdc:3 shift:4 study:5 losses:1 resulting:3 studies:1 regenerator:6 via:2 digitally:1 regeneration:1 highly:1 pp:6 achievable:1 linearly:1 prem:1 plot:1 working:3 remains:2 arms:2 vol:6 depicted:1 operators:2 under:1 emission:2 degrade:1 kumar:5 reproduce:1 following:4 spontaneous:2 example:1 transition:1 figure:1 mirrors:2 calculation:1 purposes:1 states:3 effectively:2 magnitudes:1 rescaling:1 sagnac:9 information:1 respective:2 end:1 di:1 how:1 instead:1 sin:2 map:4 modulation:3 after:6 derived:1 improving:1 wave:1 data:1 annotation:1 short:1 third:1 switch:5 so:3 representation:1 order:1 wigner:1 over:2 interpreted:1 through:1 volta:1 its:5 perfect:1 ll:6 decreases:1 permanent:1 fig:11 pavia:1 ηn:2 versus:2 non:1 usa:1 splitter:2 investigated:1 effects:1 optimal:3 ρˆin:2 now:2 transparent:1 susceptibility:2 january:1 university:1 kerr:9 magnitude:1 transmitted:3 mode:5 ports:1 mean:3 domain:1 another:1 revised:1 gaussian:1 interferometer:13 frequency:2 quantum:11 our:1 approximated:1 reprints:1 eq:4 out:1 emerges:1 shown:2 optic:3 views:1 since:2 crucial:1 denotes:1 re:3 contained:1 performs:1 forth:1 integrated:1 shows:2 fiber:2 linear:6 fisica:1 free:2 quite:1 nth:2 ρin:2 proportionality:1 milburn:1 insert:1 times:1 length:2 exponentially:1 twenty:1 hence:1 first:2 origin:1 thereon:1 number:6 fast:1 directly:1 given:4 necessarily:1 leading:1 dipartimento:1 approximately:3 their:3 too:1 amplifiers:5 scheme:2 ranging:1 speaking:1 authorized:1 exactly:1 optical:24 authors:1 achieves:1 effective:1 showed:1 depends:4 annihilation:1 compensation:1 amplitude:7 ber:9 toward:1 modulating:1 curves:1 say:1 recover:1 any:1 conversion:1 zero:2 agency:1 polarization:1 high:3 performance:2 switching:6 established:1 defence:1 sponsored:1 letter:1 phase:10 inserted:1 mach:4 considered:1 average:1 exp:2 mechanical:7 fact:1 precise:1 show:1 text:1 nχ:5 relation:1 threshold:1 networks:2 slow:1 based:1 copyright:1 distributed:4 negligible:1 should:3 jan:1 only:5 factor:2 local:6 achieve:1 mixture:2 distance:1 dependent:1 overall:4 beam:2 october:1 bassi:1 arxiv:1 tuned:2 pulses:2 fixed:1 monochromatic:1 set:5 achieved:2 undergoes:1 maximum:1 detection:2 intensity:4 computer:1 result:1 enhanced:1 arm:1 phases:1 capacity:1 state:26 αe:2 between:2 caves:1 αn:1 available:1 darpa:1 however:2 analyzed:1 cos:2 limits:3 propagation:1 figures:1 variance:1 experimental:1 otherwise:1 arbitrarily:1 relevant:1 point:3 poissonian:2 considering:1 finally:1 keying:1 second:1 aˆ:2 due:1 been:2 much:2 slowly:1 compensating:1 ph:1 lett:4 ariano:5 sanders:1 direction:1 corresponding:4 coherence:1 photon:3 coherent:12 demand:1 giacomo:1 present:2 novel:1 laser:6 value:3 air:1 will:1 dephasing:3 policies:1 promising:1 loop:2 almost:1 characteristics:1 herein:1 coupler:1 sudden:1 il:1 technology:1 different:4 italy:1 make:1 government:2 cross:4 quant:1 split:1 schematic:3 electro:1 used:3 see:4 zehnder:4 numerical:2 effect:3 ρˆout:3 levels:2 interferometers:2 off:3 modes:2 analysis:2 rome:2 command:1 recombine:1 just:3 increasingly:2 hybrid:1 distribute:1 sources:1 bandwidth:2 lossy:7 enters:1 conclusions:1 regarded:1 smith:1 ideal:1 evanston:1 governmental:1 valid:1 projects:1 input:20 transformation:1 opt:3 insensitive:1 easily:1 evaluate:1 iγ:2 iβ:2 iη:1 increases:2 vacuum:5 using:2 bit:6 advanced:1 loss:15 exploiting:1 signal:7 steps:4 either:1 output:14 reduced:1 pertaining:1 because:1 sequence:1 creation:1 ellis:1 bottom:1 does:1 unit:1 unavoidably:1 demonstrated:1 refer:1 noise:3 power:3 equivalent:2 processing:2 usaf:1 step:1 yuen:2 limitation:1 would:2 introduces:1 lucek:1 carrier:1 urges:1 soc:1 letters:3 presence:2 previously:1 communication:3 into:1 photodetection:1 preceded:1 three:1 device:1 appropriate:1 references:1 a113:1 span:1 log:2 assumed:1 strictly:1 there:3 long:3 dispersion:1 low:1 function:1 medium:2 repeater:12 form:1 denoting:1 gain:1 encoded:1 line:10 made:1 transmits:2 official:1 up:1 devices:2 fluctuations:2 distribution:2 constant:2 abstract:1 am:1 engineering:1 laboratory:2 operation:1 regime:2 compared:1 no:2 when:6 cˆ:9 field:4 other:1 electrical:1 digital:1 department:1 conclusion:1 peak:1 dephased:1 independently:1 coupling:4 practically:1 photonics:1 curve:1 having:3 equivalently:1 inset:1 implied:1 dϕ:1 original:1
|
quant-ph9801064.txt |@word results:5 leads:1 ginzburg:1 go:1 follow:1 ballagh:1 griffin:1 dimensionality:1 depend:2 critical:1 indicate:2 those:1 under:1 include:3 tc:1 norm:1 sound:1 breathing:3 orthogonal:1 far:2 frequencies:1 wave:4 mixing:1 exact:3 hamiltonian:1 solution:7 damped:1 large:1 indefinitely:1 small:1 khalatnikov:3 inspection:2 reliable:1 programme:1 lˆ:2 dilute:3 zh:1 consistent:1 jump:1 zero:4 lines:2 populating:1 estimated:1 odd:1 theory:3 index:1 interatomic:1 nonlinear:1 appear:2 stoof:1 sun:1 sum:1 evaporative:1 near:3 expressed:1 experiment:4 above:1 lifshitz:2 method:12 3d:1 body:1 condensed:2 simultaneously:1 ms:2 fiz:1 respectively:3 component:3 here:2 analysed:1 behaviour:1 reported:2 andrews:1 relaxation:4 observing:1 change:2 obtained:2 ruprecht:1 broken:1 eigensolution:2 study:2 larger:1 commonly:1 akt:1 amount:1 resulting:1 usually:1 plotted:1 uniquely:1 projection:2 clark:1 integrator:1 flexibility:1 condensates:2 apply:1 total:1 readily:1 plot:3 conventional:1 reflected:1 figure:3 would:2 distinct:1 until:1 contains:1 predictions:1 bi:6 proukakis:1 vol:1 linear:1 noting:1 therefore:3 renormalisation:1 taken:4 theoretical:2 more:3 flat:2 parks:1 started:1 operators:1 everywhere:1 known:3 cases:2 potential:1 must:2 high:2 account:1 dodd:1 equation:9 work:4 oscillator:3 modified:1 theories:3 values:7 indicating:1 morgan:2 burnett:4 growing:1 cond:1 example:1 claim:1 indicated:1 give:2 process:5 lψ:1 states:2 incremental:1 performed:1 want:1 station:1 times:1 wingate:1 absolute:1 preferably:1 needs:1 united:1 end:1 goal:1 rather:2 divided:1 get:1 orthogonality:1 write:2 how:1 parameter:2 ensemble:1 oscillatory:1 description:4 may:12 after:1 derived:2 confirmed:1 epsrc:1 davis:1 4th:1 derives:1 kurn:1 dynamical:1 third:1 explicit:1 chapman:1 so:3 sm:1 enter:1 sc:1 acknowledges:1 order:6 typical:1 displays:1 fetter:1 developed:1 over:7 satisfied:1 produced:1 course:1 thermal:5 experiments:3 including:2 argued:1 kinetic:1 still:1 excitations:8 its:5 rapidly:1 decay:1 chosen:2 boson:1 actually:2 fig:3 pergamon:1 main:2 eventually:1 non:4 runge:2 practice:1 processes:1 landau:3 band:1 effects:1 they:1 half:1 oxford:3 formulating:1 bogoliubov:2 now:2 represents:3 term:1 indeed:2 university:1 level:1 appropriate:1 sin:1 magnitude:1 trap:6 each:1 crossing:1 2m:4 side:1 mean:5 homogeneous:3 profile:2 weighted:2 instability:3 energy:6 sov:2 reduce:1 gaussian:1 related:2 elementary:4 frequency:1 expect:1 quantum:2 laboratory:1 approximated:1 beyond:1 eq:11 out:3 ketterle:1 shown:3 matrix:1 3rd:1 factors:1 since:3 rev:11 denotes:1 particles:3 collisions:1 print:1 ref:1 correct:1 math:1 shows:2 foundation:1 customarily:1 turning:1 approached:1 gardiner:2 standard:3 advantages:1 matthews:2 estimate:3 hand:1 generate:1 incorporates:1 starts:1 could:1 transition:1 noted:1 motion:5 turn:2 length:2 hence:1 teor:1 crossings:1 first:6 origin:1 there:2 features:1 probability:1 quasiparticle:8 number:3 clear:2 smaller:1 done:2 relations:1 size:3 given:5 perturbation:1 temperature:2 needed:1 introduction:1 gpe:13 condensate:27 system:2 approximately:1 their:3 cooling:1 assumption:2 1d:2 final:2 townsend:1 gives:3 trapped:6 kirkpatrick:2 exactly:1 took:1 part:5 simulate:2 corresponded:1 than:2 coefficients:4 population:10 effective:1 exptl:1 bec:5 rate:5 submitted:1 inversely:1 superfluid:1 determined:1 amplitude:1 treated:1 descriptions:1 pre:1 lowest:1 fluctuation:1 ann:1 argument:1 say:1 manner:1 seen:1 any:7 computationally:1 efficient:1 able:1 ideas:1 mechanism:1 note:3 instance:4 k1:2 subjects:1 analogy:1 finding:3 tool:3 stringari:1 accuracy:1 begin:1 towards:2 populate:1 shall:1 correlation:1 viscosity:3 what:2 most:1 involving:1 position:1 phase:4 measured:2 kb:2 takes:1 considered:1 calculated:1 later:1 points:1 exp:1 kt:3 physics:2 fact:7 quantity:1 superfluidity:2 thomas:1 show:1 attempts:1 minimizing:1 rough:2 find:4 ground:6 based:1 conduction:1 situations:1 writes:1 ox1:1 should:3 jan:1 quasiparticles:1 going:1 factor:2 employed:1 constant:2 perturbations:1 equilibrium:9 do:2 means:1 dependent:3 de:1 fluid:2 cannot:2 closely:3 dr:1 routine:2 evolution:8 arxiv:1 summary:1 investigate:1 paper:3 mewes:1 contain:1 pitaevskii:11 coefficient:1 set:2 beliaev:1 phenomenologically:1 physically:1 frame:1 evolving:1 see:2 result:1 close:2 annihilation:1 ways:1 subsequent:1 yet:1 state:11 µn:2 various:4 between:1 fermi:1 approach:1 across:1 available:1 terms:2 initially:3 however:5 sparc:1 fluctuations:1 bose:5 jetp:1 improve:1 hours:1 dorfman:2 prescription:2 desired:2 many:2 taking:1 acknowledge:1 jin:2 context:1 expression:3 experimental:2 druten:1 relevant:1 cn:14 point:4 harmonic:3 dimensional:1 anti:3 normalisation:1 considers:1 expensive:1 considering:1 described:3 second:3 basis:1 addition:1 equations:2 damp:2 due:3 been:3 quickly:1 reduction:1 describes:3 damping:36 expected:3 ph:1 define:1 corresponding:4 sufficient:1 gas:3 2πνt:1 coherent:2 understand:1 present:4 case:5 explicitly:2 handling:1 look:1 solid:3 straight:1 conserved:1 value:2 transformation:1 while:3 quasiequilibrium:1 procedure:2 real:2 coupled:1 phenomenological:6 vi:3 simulations:2 itself:2 confining:1 vanish:1 helium:1 conserve:1 greater:1 different:1 primary:1 acknowledgments:1 same:1 clearly:2 shorter:1 parts:1 quant:1 arguments:1 widely:1 modification:1 dimensionless:1 several:2 start:1 european:1 kutta:2 independent:3 used:6 kinetics:1 numerical:9 effect:1 possible:4 running:3 levels:1 uses:1 potentials:1 expand:1 recent:3 lower:2 off:1 modes:1 variety:2 well:3 roughly:2 analysis:1 components:2 simulated:1 very:1 quantitative:1 model:1 edwards:2 just:1 λt:1 being:2 accurate:3 linearisation:1 obtain:3 sources:1 shape:2 atomic:2 aspect:1 scattering:1 eigenstates:1 previous:1 onset:1 zoller:1 density:1 cornell:2 absorption:1 theoret:1 other:3 corollaries:1 lett:6 excited:6 gave:1 kingdom:1 iλ:2 increased:1 characterise:1 traps:1 3pu:1 period:1 increases:1 grid:1 press:1 using:12 necessary:2 like:1 particle:2 follows:1 collective:1 adiabatic:2 diagonalise:1 mit:2 alkali:1 vortex:1 indication:1 arbitrary:3 simply:2 essential:1 parity:2 satisfactory:1 because:2 methods:1 some:1 back:1 radians:1 deduce:1 b2:3 oscillations:1 transport:1 gross:2 tmr:1 scale:1 describing:3 calculating:1 operation:1 integration:1 per:2 does:5 provides:1 bessel:1 mode:8 bg:5 run:1 obey:1 use:3 expansion:1 clarendon:1 step:5 although:5 found:3 intense:1 proceed:1 about:3 choi:2 dependence:2 o:4 simulation:5 compatible:1 union:1 plus:2 act:1 introduced:1 road:1 computational:1 presence:2 h2:3 h3:1 into:3 numerically:4 functional:1 accommodate:1 hermitian:6 right:1 einstein:3 operator:2 proportional:1 iµt:2 gennes:1 van:1 support:3 initial:3 u0:1 width:5 quadratic:1 way:1 forward:1 was:6 function:6 only:1 complete:3 form:3 phenomena:1 adjusting:1 but:1 convergence:3 eksp:1 dissipative:1 made:1 applying:1 durfee:1 vtrap:4 inhomogeneous:3 wieman:2 mat:1 maximum:1 quantitatively:1 ψg:4 below:1 ui:3 uk:2 demonstrate:1 similar:1 average:1 interplay:1 units:2 associated:1 choosing:1 defined:1 minutes:1 describe:2 linearity:2 general:6 dashed:4 single:2 periods:2 our:3 formalism:2 eigenstate:5 physical:1 functions:1 us:1 dotted:2 no:1 extract:1 populations:2 when:8 field:5 valid:2 giorgini:2 department:1 deviation:2 intend:2 excitation:5 provided:1 problems:1 variation:2 much:1 deriving:1 generated:1 dissipation:1 else:1 network:1 implies:1 faster:2 algorithm:1 typically:1 required:2 curve:1 equivalently:1 4m:1 mass:1 dot:2 time:25 enskog:1 original:1
|
quant-ph9801065.txt |@word limited:1 monte:6 concept:1 saturating:3 consider:11 illustrates:1 caused:2 green:1 varying:1 amplifier:71 focus:1 existing:1 illustrated:2 quadrature:1 generalize:1 york:3 lewenstein:5 go:1 customary:2 amplified:3 involved:1 revealed:1 amplification:10 breached:1 violate:1 4ns:2 paris:3 assumptions:1 equivalence:2 tr:9 γt:6 finally:1 those:3 th:1 under:3 dτ:1 tr0:5 belonging:1 global:1 g2:2 straightforward:1 orthogonal:3 far:2 exception:1 results:11 impinged:1 putting:1 traced:2 2γt:1 affect:1 difference:3 e2γt:2 condition:6 splitter:1 amplifies:2 affirmative:1 swapping:1 level:3 transmission:10 supports:2 broadening:4 mirror:1 solution:7 damped:1 try:1 discrete:3 vector:1 math:1 small:5 entropy:3 unconditioned:1 originally:2 configurations:1 bd:1 averaged:1 aρa:1 occurrence:1 discriminates:1 consistent:1 direct:11 ornstein:3 approximation:6 rate:10 customarily:1 lw:1 insertion:4 dynamics:1 carlo:6 rivera:1 eλa:1 linear:30 even:4 aim:1 turn:1 errors:5 developed:1 2q0:1 apparatus:4 giving:1 contributions:1 sum:1 brief:1 expressed:1 decoding:3 version:1 above:6 capital:1 replaced:1 method:7 sout:1 satisfy:2 creation:1 behavior:2 degree:1 respectively:1 error:13 helstrom:1 here:4 atoms:6 decay:7 inversion:5 ρx:5 alone:2 depend:4 along:11 strong:2 equations:3 change:1 obtained:6 sender:1 nth:3 averages:1 study:4 losses:4 reason:3 lr:1 atom:3 simply:1 procedure:2 usually:7 resonance:1 conveniently:1 specialize:1 changes:1 pathological:2 plotted:1 composed:1 named:2 via:2 projection:1 marginal:2 castin:1 vii:1 plenum:1 unitarity:1 unitary:3 decrease:1 odinger:1 our:1 establish:2 planck:6 unit:2 remaining:1 derivatives:2 conventional:1 takes:2 would:2 prove:1 probabilities:14 positive:2 lasing:8 contains:2 quasi:1 discrepancies:1 comparing:2 sample:1 approach:2 preamplifier:1 therefore:3 expanding:1 taken:1 themselves:1 e2:1 type:1 refs:4 more:4 separated:1 introducing:1 optimizing:1 populations:1 clearly:1 detail:2 operators:7 starting:1 mismatch:1 about:1 validity:6 derivation:1 interaction:2 degrade:1 studied:2 particular:4 cases:3 iv:1 iii:1 must:9 states:13 keeping:1 valued:1 middle:1 recall:1 equation:34 when:11 ρo:1 theories:2 ρp:2 infinitesimal:1 values:4 ρt:8 transparency:1 concepts:4 following:13 making:1 modifies:1 specialized:1 example:3 abram:1 reviewing:1 compare:5 figure:32 give:5 process:1 discussed:2 choice:1 preserving:1 lindblad:4 reconstructed:2 indicates:1 minimum:1 attain:1 arise:1 specific:1 bassi:1 occur:1 guarantee:1 fpe:21 information:47 needs:3 rescaling:3 g1:1 βe:1 rather:1 interacts:1 discussion:1 means:6 range:1 ariano:8 how:2 criterion:1 answer:1 instead:3 ordinary:1 parameter:3 priori:8 trf:2 map:6 description:8 influenced:1 may:4 db:4 laf:6 after:5 derived:5 91a:1 expectation:2 consequence:3 wrong:1 produce:1 snr:4 account:1 dalibard:1 wave:4 data:1 fn:1 times:1 ambiguous:1 convolution:2 physical:3 outline:1 effective:1 joint:1 valid:2 pseudopotential:1 correspond:5 σzj:1 generic:1 cannot:2 so:4 ultimate:3 allow:1 enter:1 representation:6 order:15 nout:1 typical:1 operations:1 xj:4 attenuator:1 wigner:10 subsections:1 reservoir:1 numbers:2 indeed:4 pointed:2 satisfied:1 interpreted:1 symbols:7 resorts:1 thermal:6 paper:4 including:1 discrepancy:1 during:1 numerable:2 spontaneous:3 belavkin:1 volta:1 its:3 before:4 perfect:3 maps:2 ll:1 lj:2 decreases:1 actually:5 better:6 resort:1 detected:2 according:3 degrees:5 systems:2 pavia:1 total:1 might:1 easier:1 correspondence:1 eventually:1 yk:5 factor:2 pauli:1 mølmer:1 outlined:1 practice:1 processes:2 introduce:3 very:5 tails:2 effects:2 they:3 optimal:1 oxford:2 now:12 bigger:1 qt:5 channels:9 transmitter:1 gets:1 transmissivity:1 2q:2 2s:7 always:5 university:1 presented:1 leading:1 sin:3 orthonormal:1 2f:2 2g:2 transmitted:15 mode:22 l0:8 each:1 crossing:1 found:2 macchiavello:5 characterized:3 referred:6 established:1 domain:1 differential:3 significantly:1 ed:1 energy:1 reduce:2 gaussian:24 related:1 attenuation:2 obtains:1 subsec:5 quantum:45 laboratory:1 operation:2 beyond:2 eq:26 out:10 noiseless:2 shown:6 accomplish:1 agreement:2 network:1 driving:1 space:3 open:4 jump:2 since:4 crucial:1 holevo:2 denotes:4 increase:1 replacing:1 acting:1 gaussians:1 performs:1 maximized:1 ref:14 excess:1 shows:2 exactly:1 lugiato:4 fiber:2 log2:8 theory:12 state:29 monotone:1 mechanisms:1 fisica:1 possibility:1 standard:5 clarify:1 completely:4 ρin:3 term:4 trp:2 detecting:1 hand:7 beginning:1 finite:1 log:1 definition:2 fixed:3 regarding:1 fa:1 determining:1 could:4 fb:1 feasible:1 ordering:3 int:1 unknown:2 hence:5 rewrites:3 eqs:4 first:5 origin:1 xi:1 probability:38 encoding:4 variables:7 sn:6 coding:1 number:21 approximate:1 peculiarity:2 clear:2 xx:1 smaller:2 done:1 relations:1 xs:3 message:5 quality:2 illustrate:1 given:22 histogram:5 temperature:1 their:1 introduction:2 meaningful:2 dipartimento:1 assure:1 system:4 adopted:1 broadened:1 needed:3 intermediate:1 master:18 tune:1 amplifiers:9 realization:1 rates:2 ordered:1 perfectly:2 bits:1 gives:5 amplifying:1 pump:2 centered:1 stinespring:1 continuous:4 zeroth:1 task:1 optical:11 superoperator:3 pna:9 alphabets:1 x0:1 representing:1 than:18 coefficients:3 dynamical:5 diffusion:9 distance:1 kind:4 scheme:1 determines:2 qs:2 sections:1 approximations:1 measured:1 depends:4 limiting:3 probe:2 matter:2 differently:1 contrary:1 amplitude:2 represents:1 ber:41 outcome:1 treated:1 aout:2 result:2 fig:2 false:1 reproduces:1 unchanged:1 measure:3 spectrum:2 latter:1 already:2 idler:11 emission:3 close:1 need:2 seen:1 recover:1 any:5 viewed:1 hypotheses:1 conversion:1 ρout:1 genuine:1 zero:4 min:2 check:1 saturable:13 rout:1 responsible:2 davies:1 mechanism:7 4c:1 polarization:1 instance:1 ideal:38 potential:1 generalized:4 obviously:1 objective:1 performance:5 coincide:1 haake:8 channel:54 specifying:1 towards:2 gγ:1 optimizes:1 trace:6 opposite:2 measures:1 most:1 optimized:4 exploited:1 overlapping:2 significant:4 definitions:1 phase:12 assessed:1 analytically:1 inserted:7 why:1 stands:1 cause:1 considered:7 performances:2 alarm:1 later:1 detectors:1 graphs:1 part:2 principle:5 exp:10 arctanh:1 usual:1 typically:1 section:8 fact:5 quantity:6 probl:1 show:4 random:5 anyway:1 least:1 rotating:1 large:2 relation:3 dum:1 threshold:5 saturated:4 histograms:1 longer:1 d2:4 debate:1 evolved:2 ii:1 q1:19 q0:17 slow:4 ratio:4 knowledge:1 parameters:8 situations:1 explain:1 distributed:2 ox1:1 ox2:1 should:3 jan:1 moments:2 only:8 going:1 subsection:2 ambiguity:1 constituents:1 various:1 constant:2 population:3 over:9 achieve:6 equilibrium:2 do:1 mixture:1 dominant:1 gains:1 di:1 beat:1 semitransparent:1 overall:1 straightforwardly:1 degradation:1 beam:1 ones:1 dz:1 negative:2 dx:4 dy:7 report:1 reconstruct:1 quantifies:2 ds:8 dp:1 adiabatically:1 evolution:15 qu:2 densities:2 upper:1 αm:1 arxiv:1 λa:1 yield:1 appear:1 uu:2 investigate:1 underlying:2 cf:1 though:2 characteristic:2 analytical:1 through:4 qk:9 qj:6 pertains:1 inside:1 view:1 4g2:1 coefficient:2 requirement:1 set:9 computed:1 reference:2 achieved:4 clarified:1 undergoes:2 δjk:1 liouvillian:9 detection:31 mentioned:1 namely:13 sec:13 devices:4 transm:1 suited:1 convenient:1 uncorrelated:2 acts:1 best:3 annihilation:3 αs:2 still:7 capacity:4 interacting:2 resonantly:1 subsequent:1 review:1 definite:1 dipole:2 fano:2 written:2 identification:1 heterodyne:4 cooperation:2 between:27 invariant:2 previous:1 conditions:2 checks:2 wide:1 available:1 lf:7 notice:7 never:1 terms:14 vertical:1 nature:1 initially:3 attention:1 however:9 nilsson:1 efficiency:6 vanishing:3 cut:1 ws:17 ji:1 analyzed:2 configuration:3 distribution:22 improve:4 suggested:1 both:11 essentially:3 toward:1 last:1 limits:3 2αg:1 region:3 density:12 equal:2 against:1 sensitive:2 improves:1 receiver:2 variance:5 contribution:4 estimation:1 comes:2 otherwise:2 karlsson:1 among:1 relevant:1 easy:1 fields:2 characterization:12 simple:1 character:2 tracing:1 corresponds:5 asymmetrically:1 high:4 active:4 exploit:1 pom:9 non:18 consideration:1 leads:1 moreover:3 cp:5 broadens:1 considers:2 fokkerplanck:1 ps:8 described:18 transformations:1 second:7 basis:5 atomic:14 three:4 been:6 nb:5 levenson:1 reduction:4 describes:6 interest:2 basic:3 pj:9 transformed:2 ph:2 pi:4 pn:1 ak:2 partial:3 define:2 traveling:3 generating:1 describe:2 corresponding:10 unavoidable:1 received:2 quantities:4 sufficient:1 photon:10 new:3 coherent:9 external:3 improved:1 careful:3 fokker:6 spirit:1 present:4 case:36 p0:3 p1:1 laser:35 turns:1 expanded:1 value:9 choices:1 will:15 while:1 ain:3 suppose:1 theoretical:1 evaluating:2 applies:1 situation:2 drives:1 leaves:2 characterizing:2 london:1 iy:2 versus:2 sizeable:1 vi:1 n2a:1 vk:3 thus:2 tests:2 surface:1 conditioned:1 rin:1 characterize:3 itself:3 la:9 baths:1 ready:1 technology:1 increased:1 binary:12 different:12 italy:1 σz:3 perform:2 alphabet:5 make:1 radiation:15 lett:8 same:17 linked:1 complex:2 quant:1 schematic:1 proved:2 electro:1 lacks:1 couple:1 higher:3 development:1 independent:3 used:5 see:11 numerical:7 upon:1 functions:2 possible:8 average:5 levels:2 purpose:1 symmetrical:2 invariance:1 ab:2 six:1 normalization:1 lower:1 fourier:1 schr:1 modes:6 makes:1 underlies:1 analysis:4 evolves:2 electrical:1 concrete:2 off:1 without:3 sets:3 become:1 quantitative:1 ae:1 eγt:2 parametric:3 dimension:1 left:7 remember:1 stringent:1 just:11 less:1 being:4 generally:8 2c:2 obtain:3 rest:2 reviewed:1 sources:1 bandwidth:1 lossy:2 transforms:1 moroni:1 poizat:1 alternative:2 λn:1 based:2 note:1 disturbance:4 mirrors:1 zoller:1 conclusions:2 photons:11 point:1 guaranteed:1 improvement:5 signals:6 parts:3 lets:2 other:10 extends:1 treatment:1 versa:1 2nb:1 2nth:1 input:35 extensive:1 guarantees:1 transformation:5 iφ:1 identical:1 rescaled:2 saturation:11 explained:1 insensitive:8 around:2 easily:4 showing:1 psa:1 sums:1 3pu:1 homodyne:6 increases:1 rescales:1 vacuum:12 press:3 using:6 bit:19 detector:5 mod:2 loss:7 tail:4 necessary:1 like:1 lost:1 follows:8 signal:16 adiabatic:13 shapes:1 communications:4 steps:1 either:3 integrals:1 output:34 el0:1 stationary:3 reduced:2 grangier:1 specifies:1 pertaining:1 2qt:6 because:7 classical:1 truncated:1 perturbation:1 conditional:4 some:3 2ns:3 added:2 examples:1 b2:1 respect:1 proper:1 kinds:1 little:1 matching:1 recognition:1 provided:1 gradually:1 scale:3 describing:1 lead:1 cavity:8 positivity:2 measurements:1 integration:3 overlap:4 does:7 exit:1 eliminate:1 provides:1 tends:1 ensemble:1 d2s:3 o2:3 minimal:1 measuring:1 slower:1 noise:61 power:5 2q1:1 performed:1 equivalent:3 processing:1 use:3 expansion:9 clarendon:1 step:2 although:4 yuen:7 casagrande:2 approximating:1 super:1 hilbert:3 asymptotic:1 comparison:3 limitation:1 actual:1 pt:2 bars:1 constraint:3 freedom:5 commun:1 introduces:4 o:7 simulation:10 practical:1 remains:3 carries:2 greatly:4 act:1 uhlenbeck:3 urges:1 mean:4 denote:1 electromagnetic:2 soc:2 rev:10 real:1 letter:1 presence:2 communication:15 into:10 within:1 numerically:1 bound:1 due:1 device:13 right:7 references:1 operator:10 proportional:1 notion:1 fast:4 additional:4 area:2 intrinsic:1 strictly:1 there:7 question:1 transform:1 long:2 u2:1 start:1 much:4 low:3 way:6 analyze:5 was:4 function:12 academic:2 medium:3 complete:5 form:15 opt:2 criteria:4 denoting:1 but:8 encoder:3 gain:19 solved:2 decoder:6 elimination:1 encoded:8 line:16 working:1 irreversible:3 partially:2 made:1 whether:1 ut:6 transmits:1 maximum:3 us:4 duu:5 placed:1 below:2 limit:6 uk:1 fluctuations:1 problem:4 called:11 detailed:2 model:2 adopt:1 associated:1 ad:1 defined:10 pia:32 abstract:1 measurement:6 am:3 meaningless:1 general:5 globally:3 separating:1 single:1 initial:3 rule:2 goodness:3 simulations:5 lifetime:2 inf:1 hamiltonian:1 distributions:12 proceeds:1 worse:2 regime:12 again:1 mutual:31 completeness:1 2ds:2 no:5 na:6 whereas:17 encodings:1 hybrid:1 vanishes:3 nf:1 arctan:1 field:17 shaded:1 unambiguously:1 role:1 normal:1 test:4 coupling:1 ns:11 observable:3 conclude:1 picture:2 briefly:2 elements:2 reconsider:1 models:1 symbol:10 time:14 drift:5 includes:4 meaning:1 a2:1 bounded:1 suppression:1 sql:8 variable:8 sides:1 matrix:10 independently:2 implies:2 anticommutator:1 vice:1 restores:1 proposed:2 ozawa:2 dπ:7 having:1 equivalently:1 correspondingly:1 presenting:1 leak:1 reached:1 observables:1 n2:1 ritsch:1 expands:1 original:1
|
quant-ph9801066.txt |@word logarithms:1 allowed:1 consider:1 desirable:1 results:5 generalize:1 computation:4 consists:1 follow:1 depend:1 finally:2 helps:1 include:1 dramatically:1 amplitudes:25 straightforward:1 corollary:1 difference:7 exact:5 condition:1 entire:1 presented:1 solution:10 large:3 solved:4 convenience:1 minimal:1 shows:2 averaged:1 sign:1 query:2 further:1 dynamics:5 obey:1 even:1 index:1 unavailable:1 section:1 expressed:1 uniform:7 concisely:1 fortschritte:1 above:1 new:2 method:1 satisfy:2 edited:1 full:1 respectively:1 never:1 berkeley:1 represented:1 along:1 equations:10 box:1 search:10 institute:2 items:1 larger:1 allows:1 resulting:1 published:1 followed:1 bounds:1 marked:28 macro:1 apply:2 total:3 eiωt:1 use:2 would:2 toffoli:1 next:1 classically:1 therefore:1 theoretical:2 more:3 israel:2 formally:1 initiated:1 becomes:1 operators:1 benchmark:1 known:3 cases:2 grassl:2 science:1 der:1 work:3 modified:4 grover:24 following:4 averages:3 example:1 proof:2 unmarked:15 calculation:1 bennett:2 organized:1 generically:2 states:22 collision:2 minimum:2 acm:1 arise:1 tan:1 times:6 needs:1 end:1 advantage:1 means:1 fourth:1 optimal:8 sin:4 brassard:3 algebra:1 may:3 package:1 after:5 derived:3 designed:1 physik:1 summarize:1 eighth:1 σl2:5 element:1 so:5 order:3 holds:1 over:3 paper:3 omitting:1 satisfies:3 still:1 its:1 before:1 style:1 systeme:1 interesting:1 lj:3 decreases:1 li:17 systems:1 annual:1 ours:1 maximal:3 non:2 powerful:1 they:1 symposium:1 now:2 developments:1 inversion:2 2r:2 university:2 2x:2 radians:2 theory:1 found:4 universit:1 2i:2 weighted:1 england:1 directly:2 independent:3 reduce:1 related:1 frequency:1 yield:1 measurement:5 quantum:21 our:2 eq:10 special:1 biham:4 matrix:2 discrete:1 since:4 rev:2 research:1 daniel:1 denoted:1 formula:1 rk:1 foundation:1 weaknesses:1 log2:1 linear:3 standard:2 vazirani:1 completely:1 california:1 york:1 initialize:1 ofer:1 definition:2 created:1 could:1 computers:3 david:1 motion:1 terhal:1 arccos:1 first:4 initial:22 probability:4 timeindependent:1 number:6 done:1 another:1 σk2:2 reached:2 zalka:1 evaluations:1 size:1 given:4 1r:1 publication:1 introduction:1 twenty:1 eqs:3 system:1 confirming:1 constants:1 siam:2 final:1 pmax:6 too:1 eigenvectors:1 hoyer:3 exactly:3 than:1 intrinsically:1 iωt:1 subroutine:1 require:1 see:1 determined:1 amplitude:10 markus:1 minus:1 collecting:1 generality:1 boston:1 any:5 relatively:1 efficient:1 converges:1 note:2 high:1 generalized:7 bailey:1 algorithms:4 strengths:1 needle:1 most:2 germany:1 formulae:1 phase:4 class:1 manifested:1 appear:1 latex:1 technion:1 observation:2 considered:1 kj:4 ki:19 later:1 proceedings:2 mechanical:1 physics:2 fact:5 quantity:2 shor:3 show:1 random:1 keywords:1 find:3 subtracting:2 tapp:2 spite:1 situations:1 written:1 only:4 black:1 factor:1 bernstein:1 columns:1 do:2 quantph:1 di:1 ones:1 during:2 prime:1 evolution:8 querying:1 approach:1 arxiv:1 median:1 factorization:3 summary:2 qc:1 racah:1 processed:1 queries:1 set:1 ωt:7 depends:1 computer:3 sec:4 result:2 enhanced:1 satisfying:1 state:8 closed:1 between:2 conditions:4 recently:1 importance:1 however:1 efficiency:4 derive:2 key:1 analyzed:1 article:1 distribution:11 both:2 essentially:2 bution:1 flipped:1 und:1 context:1 variance:1 whole:1 finds:2 boyer:3 arbitrarily:1 among:1 relevant:1 simple:1 ca:1 cf:1 simply:1 iterations:2 polynomial:2 described:2 describes:1 ph:5 meeting:1 define:2 obtained:1 controlled:1 arcsin:1 cos:5 stems:1 denote:2 case:5 unlike:1 variances:3 evaluated:2 will:3 while:1 applies:1 identical:1 unitary:2 coupled:1 averaging:1 thus:5 them:1 hebrew:1 vanish:1 different:1 generic:1 recursion:4 same:2 wherein:1 complex:5 quant:5 several:2 difficult:1 evolve:2 used:3 initialization:1 hand:1 running:1 normalization:1 relies:1 task:1 database:6 expression:3 variety:2 well:1 analysis:2 without:2 solve:3 chemistry:1 being:2 generally:1 immediately:1 eli:1 preprint:5 conclusions:2 iω:1 lett:2 versa:1 theorem:3 diagonalization:2 input:2 haystack:1 real:3 around:1 lanl:5 finding:1 increases:1 know:1 press:1 using:6 loss:1 rotate:2 pertinent:1 success:1 follows:8 steps:9 either:1 arbitrary:9 essential:1 deal:1 some:3 searching:5 elements:2 diagonalizing:2 does:1 provides:1 yields:4 demonstrated:1 measuring:1 process:1 nonuniform:1 power:2 bc:1 uniformly:1 journal:2 expansion:1 step:3 offset:1 dictated:1 properties:2 about:2 usa:1 simplify:1 dependence:2 o:9 reduced:1 important:3 unsorted:1 introduced:1 slightly:1 equally:1 obtaining:1 bound:7 references:1 determine:1 operator:1 jerusalem:1 significantly:1 institut:1 classical:5 there:2 fast:1 lidar:1 workshop:1 analyze:3 was:9 function:1 complete:2 smolin:1 but:1 haifa:1 applying:1 versions:1 flip:2 us:2 ur:1 un:1 limit:2 problem:5 stages:1 average:13 mechanics:1 ab:1 constant:3 ad:2 computing:4 defined:1 abstract:1 measure:2 am:1 general:2 single:3 proves:1 exist:1 accounting:1 distributions:6 durr:1 compared:4 no:2 when:7 arctan:1 tight:2 other:4 department:2 nr:1 karlsruhe:2 conclusion:3 deviation:1 briefly:1 repeat:1 superposition:1 separate:1 databases:1 problems:4 shown:6 includes:1 a2:1 variable:1 algorithm:36 vice:1 assume:1 required:2 together:1 time:21 n1:1 requires:1 original:3
|
quant-ph9801067.txt |@word customary:1 consider:2 rev:13 global:1 results:1 leads:1 consists:1 follow:1 denotes:1 contributions:1 foug:1 whose:2 seno:1 paris:6 tr:3 ts:1 squeezing:15 dramatically:1 random:1 presently:1 advantage:1 dell:2 choice:1 impinged:7 electron:1 fall:1 experimentally:1 difference:1 2rs:4 2rp:4 illustrated:1 presented:2 turns:1 t2:1 haber:1 reg:1 leave:1 a129:1 phase:55 small:2 unsharp:3 setup:3 possibility:1 application:2 sin2:1 cosh:3 zero:1 tana:1 further:1 port:2 even:2 what:1 stands:1 apparatus:9 section:4 ˆa:2 ˆb:5 experiment:3 values:1 method:1 revealing:1 respectively:1 modify:1 here:3 cos2:1 sinh:2 strategies:1 represented:1 appears:2 z2:2 extreme:1 obtained:5 trans:1 suitably:1 institute:1 shift:8 allows:1 contradiction:1 renzi:1 amount:1 resulting:7 usually:1 studi:1 suitable:1 composed:1 via:2 convolution:2 marginal:4 outcomes:1 apply:1 total:8 planck:2 manipulate:2 readily:1 use:1 sharper:2 ψp:1 next:1 a51:2 sample:1 therefore:4 means:3 theoretical:1 more:1 becomes:1 operators:1 apparent:2 berlin:2 particular:1 central:1 cases:1 alexei:1 high:3 ρe:2 quantized:2 indicates:1 der:2 erf:2 obvious:1 making:1 arrive:1 performed:4 photocurrent:7 carrol:1 states:10 unbiased:2 numbers:1 sharp:2 counting:1 information:5 rather:1 s2:1 buzek:1 six:1 opt:4 parameter:2 product:1 blocks:1 max:2 after:1 confirmed:1 plane:4 lay:1 coming:3 data:2 gaussian:4 natural:1 perform:1 maintain:1 so:2 order:9 bins:2 wigner:3 feedback:1 indeed:2 over:2 satisfied:1 produced:1 experiments:1 husimi:2 volta:1 ieee:2 its:2 chosen:2 actually:1 detected:1 parts:1 fig:6 pavia:3 decreased:1 main:1 alter:1 noh:1 scaling:3 tails:1 they:3 now:2 matched:2 represents:2 february:1 always:1 mode:21 2b:1 each:5 universit:2 characterized:1 mean:11 energy:4 displacement:1 interferometer:1 measurement:27 quantum:9 laboratory:1 approximated:1 eq:10 event:2 special:1 out:2 large:2 shown:2 rp:4 matrix:1 space:4 crucial:1 research:1 re:3 ref:1 integrated:1 sinh2:4 working:2 theory:1 fisica:2 physikalische:1 complicated:1 institut:1 dubna:1 definition:1 βp:3 βs:5 optics:1 could:1 bassi:1 unexcited:5 turn:1 produce:1 a115:1 first:9 features:2 probability:4 shapiro:2 valentina:1 powerful:1 number:14 knight:1 xs:6 angular:1 take:1 given:6 introduction:1 leading:2 dipartimento:2 histograms:1 obtainable:1 too:2 scheme:9 killip:1 mandel:2 fraction:4 interferometers:1 moscow:1 accurately:1 modena:3 optical:2 manipulation:1 than:1 relative:5 kind:1 double:2 wodkiewicz:1 matteo:1 namely:2 submitted:1 matter:1 contrary:1 amplitude:3 were:1 distinctive:1 outcome:2 russia:1 a49:1 rad:1 generality:1 faradayweg:1 measure:1 elsevier:1 apparently:1 clearly:1 viewed:2 angle:1 inform:1 latter:2 extracted:4 z1:2 comes:1 generalized:3 bogolubov:1 effectiveness:3 though:2 correct:1 optimized:3 eight:1 remarks:2 histogram:5 intrinsic:1 kb:6 considered:1 average:1 broadened:1 coincides:1 inferred:1 points:1 symmetrically:1 χb:1 χa:1 subsequent:3 redirected:1 physics:1 χi:2 precise:1 intensity:2 show:5 eres:1 probe:25 individuated:1 d2:2 redirect:1 dividing:1 distributed:2 written:1 should:2 jan:1 only:4 going:1 di:6 dependent:1 de:1 2a:1 joint:4 report:1 during:1 dt:1 arxiv:1 summary:1 paper:2 dangerous:1 fixed:2 rms:2 reference:1 sensitivity:5 detection:7 irregularly:1 alessandro:1 radius:1 result:2 techniques:1 closes:1 phases:1 still:2 nuclear:1 review:1 state:8 heterodyne:1 between:1 caves:1 chemie:1 available:1 notice:1 recently:1 wb:2 wa:2 buchler:1 sole:1 however:4 wi:1 continuously:1 comm:1 jointly:1 analyzed:2 phasespace:1 improve:1 suggested:2 both:4 cos:3 according:3 distinguished:1 variance:2 whole:4 experimental:7 among:1 filtering:1 point:4 appeared:1 homodyne:2 semiclassical:1 concluding:1 simply:1 keitel:1 moreover:1 photocurrents:1 considering:1 pq:10 second:6 aˆ:1 due:2 been:6 strategy:4 much:1 basic:1 ph:1 ariano:3 direction:2 offered:1 photon:6 precision:5 fortschr:1 fritz:1 present:5 case:3 variances:1 reliable:3 value:9 error:3 squeezed:16 investigating:1 procedure:4 bin:1 characteristics:1 thus:2 equal:2 reads:1 itself:2 im:3 different:4 italy:2 generic:3 distributions:3 make:1 radiation:4 accomplished:1 same:3 any:1 complex:5 quant:1 independent:1 used:5 numerical:5 upon:1 haus:1 hand:1 uses:1 expand:1 campi:1 fourier:1 modes:3 largely:1 nonetheless:2 well:1 analysis:1 without:1 x2s:2 simulated:5 left:1 just:1 being:5 accurate:1 wagner:1 obtain:2 immediately:1 facts:1 paul:1 enters:1 preprint:2 density:1 photons:4 iϕ:2 improvement:3 valid:1 lett:10 theorem:1 input:1 wiseman:4 excited:9 useless:1 real:2 around:2 loss:1 couple:1 possible:3 vacuum:4 using:3 highly:2 mod:2 insert:1 shaped:1 signal:16 steps:1 setups:1 some:3 ncoh:2 examples:1 choosing:1 respect:1 provided:2 describing:2 lead:1 confirm:1 broad:1 measurements:5 strahlung:1 unit:2 provides:1 refer:1 measuring:3 noise:2 conventional:1 step:25 abteilung:1 yuen:2 imaginary:1 hilbert:1 pζ:2 carried:1 constraint:1 o:1 simulation:1 plus:2 2iψ:1 act:1 germany:2 introduced:2 own:1 into:10 device:3 hermitian:1 references:1 determine:1 operator:3 nsq:1 gerhardt:1 degli:1 measured:1 transform:1 width:1 low:5 way:1 was:1 interferometry:2 function:11 electr:1 denoting:1 but:1 idea:1 squeeze:1 made:1 characteristic:2 up:1 devices:4 placed:1 chizhov:2 fluctuations:7 distribution:19 called:1 gesellschaft:2 defined:3 detectors:3 abstract:1 describe:1 denote:1 single:5 simulations:4 dβ:1 physical:2 functions:1 no:1 whereas:3 when:2 field:10 other:1 details:1 conclusion:1 polar:1 briefly:1 exp:13 symbol:1 a2:1 peak:1 structure:1 factorized:1 rs:5 coherent:5 dρ:2 fact:3 walker:2
|
quant-ph9801068.txt |@word default:1 partial:1 consider:9 maximum:1 helstrom:4 zmin:1 focus:1 leads:4 roy:1 p01:24 bohm:1 francesco:1 follow:1 whose:1 maximally:1 depend:1 integral:1 paris:10 subjected:4 tr:1 finally:1 squeezing:8 under:3 worth:1 applied:3 supported:1 orthogonal:3 very:6 results:3 electron:1 hamiltonian:2 turns:1 notes:1 solution:1 large:6 discrete:1 convenience:1 detected:2 phase:22 small:3 eigenvalues:2 anal:1 optics:2 possibility:1 inserting:1 work:1 force:3 foundation:1 dealing:1 measurable:1 cosh:3 feasibility:1 second:1 value:10 further:1 odd:2 linear:1 spectral:1 l2n:2 plays:1 apparatus:2 trivial:1 section:5 expressed:2 current:1 paying:1 version:1 a231:1 above:3 overcomplete:3 obvious:1 increasing:3 acknowledgments:1 degree:1 respectively:2 here:1 behaviour:7 reported:3 inverse:3 cos2:1 sinh:2 address:2 concluding:1 strong:3 table:1 obtained:4 ref:1 davidovich:1 study:1 larger:1 suggests:1 action:4 adopting:1 rigged:1 examinations:1 via:1 inference:2 projection:1 scales:1 namely:5 yuen:2 outcomes:4 naimark:2 unit:5 positiveness:1 eiωt:1 superpositions:1 would:2 probabilities:1 positive:2 contains:1 negative:1 next:1 a51:1 riv:1 ζa:2 noting:1 examination:1 therefore:3 criteria:1 themselves:1 more:2 becomes:3 operators:3 stable:1 occurred:1 berlin:2 normalized:1 known:1 cases:1 high:2 springer:2 valued:1 equation:4 averaged:2 oscillator:37 modified:2 glauber:1 fock:1 values:4 following:3 strategies:3 arrive:1 example:2 performed:3 figure:5 solved:6 expanding:1 carrol:1 organized:1 haroche:1 states:28 effectively:1 minimum:21 numbers:4 nonnegative:1 conversely:3 information:2 needs:1 end:1 goal:1 e2r:1 rather:2 distinguishable:1 means:2 pure:3 wolf:1 hi:1 parameter:6 sin:1 map:1 product:2 proc:1 description:2 oscillators:1 after:7 containing:1 lab:1 applications:1 wrong:1 inst:1 coming:1 cambridge:1 revealed:1 natural:2 dynamical:1 interpolated:1 sq:8 correspond:1 provide:1 maintain:1 so:1 ultimate:3 order:5 subsections:1 indeed:2 over:1 top:1 soc:2 d19:1 report:4 paper:3 london:1 statistical:3 satisfies:1 volta:1 excitations:1 its:3 derive:2 monitor:1 ln:1 interesting:2 zˆ:1 solving:1 decreases:1 actually:2 lect:1 mπ:1 systems:1 pavia:3 h0:3 weber:1 university:1 numerically:2 evolution:6 introduce:1 scaling:4 framework:3 mismatched:1 they:1 now:3 discuss:1 represents:3 inversion:1 dirac:1 2r:3 reasonably:1 leading:1 realistic:1 mode:1 each:4 2m:1 universit:1 referred:1 osaki:1 schemes:1 independent:4 ed:2 energy:10 reduce:1 displacement:6 related:1 constitute:2 frequency:1 measure:2 quantum:30 our:5 operation:1 eq:7 special:1 out:2 maximizes:2 shown:1 driving:7 space:6 res:1 nuovo:1 crucial:1 holevo:3 denotes:4 increase:1 conclusions:1 izv:1 formula:4 induced:1 cause:1 shows:4 sinh2:1 wiley:2 theory:10 mω:2 fisica:1 free:4 quart:1 assures:2 perturbation:41 proportionality:1 york:2 detecting:1 axioms:1 log:4 definition:1 interaction:1 regarding:1 determining:1 could:10 bassi:1 unknown:2 lax:1 eqs:1 first:4 informations:1 xn:1 features:2 probability:36 laguerre:1 valentina:1 number:18 restrict:2 utilized:1 ihi:1 relations:1 sssr:1 trans:2 electronic:1 illustrate:1 given:5 necessarily:1 checked:1 indicate:1 introduction:2 data:1 dipartimento:1 amsterdam:1 system:17 least:3 their:1 perturbations:7 calculations:1 scheme:6 final:1 mandel:1 inferring:2 ryzhik:1 akad:1 za:1 optical:2 x2:1 attempt:1 eliminated:1 x1:1 representing:2 than:1 outline:1 relative:2 kind:6 matteo:2 alessandro:1 limiting:1 annihilation:3 matter:5 contrary:3 amplitude:7 toward:1 a48:1 extracting:1 false:16 well:1 ann:1 spectrum:2 curves:1 analysis:1 seen:1 null:2 any:5 viewed:1 relatively:1 lie:1 quadrature:1 strength:9 genuine:1 zero:2 depending:3 pvm:4 latter:3 able:1 nonstandard:1 new:2 detector:1 modulus:1 rate:1 unperturbed:2 even:3 multiple:1 trace:2 closes:1 price:1 evaluation:1 most:1 optimized:6 gradshteyn:1 device:2 analytically:4 probabilistic:2 class:1 considered:3 mean:5 alarm:16 adopt:2 coincides:1 fluctuations:5 regards:1 tech:1 principle:1 exp:31 mechanical:3 camb:1 physics:1 fact:1 quantity:4 intensity:22 show:1 random:7 spaces:1 relation:1 threshold:1 d4:1 d2:1 find:2 d1:1 based:1 implementation:1 written:2 zα:1 jan:1 only:10 going:2 constant:1 araki:1 represent:1 ser:1 do:2 di:3 dependent:3 lehmann:1 de:4 cannot:1 dz:1 preparing:1 dx:1 devising:1 combinations:1 during:3 dt:1 lahti:1 dp:3 reveal:2 processes:1 pearson:7 fields:1 arxiv:1 circuits:1 nauk:1 contain:1 ban:1 fixed:10 guessing:1 set:10 questions:1 testing:5 j0:2 up:1 detection:25 depends:3 us:3 enhanced:1 arg:1 discussions:1 optimum:2 contour:1 best:2 concern:1 preparation:13 phases:2 still:1 mechanically:1 commutation:1 ieee:1 αa:1 state:32 various:1 between:6 intensities:1 approach:1 brune:1 available:1 notice:1 terms:3 initially:6 attention:3 weak:2 however:5 regime:1 hypothesis:10 multiplier:2 problem:8 thank:1 observable:2 cos:3 outcome:4 eigenvalue:1 many:2 region:2 uncertainty:2 equal:2 propagation:1 raimond:1 comm:1 estimation:4 whole:3 fix:1 comes:1 otherwise:1 arbitrarily:1 strongly:1 relevant:3 shapiro:1 simple:1 seems:2 asymptotically:1 harmonic:22 dimensional:2 pom:6 d30:1 lagrange:2 ae:1 selfadjoint:3 described:3 capable:1 due:1 been:20 strategy:6 int:2 describes:1 interest:1 electr:1 expected:1 ph:1 algebras:2 topics:1 fig:8 ariano:2 contribute:1 corresponding:2 both:3 coherence:1 subspace:1 coherent:14 external:4 denote:3 present:3 case:10 evaluated:4 excited:1 will:2 optimization:2 error:1 squeezed:11 cats:1 procedure:1 stoler:1 opt:3 almost:1 averaging:1 renzi:1 thus:14 ii:1 reads:2 examined:1 im:2 busch:1 binary:11 different:13 italy:1 sensitive:1 perform:3 appreciable:1 radiation:2 indistinguishable:1 same:2 clearly:1 complex:2 quant:1 widely:1 louisell:1 defines:1 infer:6 difficult:2 evolve:2 used:1 see:1 singapore:1 i0:4 numerical:1 upon:2 effect:3 nonorthogonal:3 driven:3 usually:1 levels:1 purpose:1 infinite:1 identity:1 eigenvectors:1 lower:3 weakly:1 schr:1 p11:10 nevertheless:1 expression:1 modeled:1 x0:1 roughly:2 operatorial:1 thought:1 academic:3 displacing:1 without:1 solve:1 experimental:1 components:1 sets:1 model:1 paradigm:1 left:2 just:3 being:3 observed:1 obtain:4 properties:1 ozawa:1 aspect:2 eigenstates:4 kluwer:1 density:4 iϕ:1 transparent:1 signals:1 belongs:1 conjugated:2 lett:2 easy:1 theorem:1 guarantees:1 solvable:1 tolerable:1 real:4 usable:1 insensitive:1 easily:2 evaluate:1 possible:9 rnd:1 possibly:1 increases:2 vacuum:11 press:2 world:1 mod:1 displaced:1 δz:1 excluding:1 kennedy:3 follows:3 signal:4 specific:2 detections:1 become:2 reduced:1 mathematical:1 satisfactory:1 dordrecht:1 often:1 deal:2 simplicity:2 creation:2 some:10 born:2 choosing:1 convex:1 oscillations:1 matching:3 provided:2 describing:1 a13:1 lead:1 bottom:1 decision:11 measurements:3 overlap:25 does:2 linearly:3 provides:4 prog:1 bessel:3 measuring:1 eiϕ:2 scientific:1 plot:3 equivalent:1 oscillating:3 stenholm:1 found:1 pv:1 hilbert:6 asymptotic:2 about:1 carried:1 dˆ:11 freedom:1 basis:1 dependence:1 o:8 mutually:1 plus:1 act:1 introduced:1 projectors:1 perturbed:9 rev:11 into:1 h1:4 obtaining:1 bound:4 a54:1 three:2 remarks:1 square:2 references:1 determine:1 operator:17 nsq:12 span:1 classical:1 initial:26 a53:1 borel:1 quanta:1 low:1 way:1 series:1 analyze:1 was:1 neyman:7 m0:1 function:12 project:1 complete:1 form:1 fundamentals:1 denoting:1 preparations:1 properly:1 true:6 partially:1 infn:1 wise:1 mat:1 whether:3 characteristic:1 gravitational:1 detectability:1 bounds:2 devices:1 record:1 below:1 limit:5 ωa:1 detectable:18 distribution:2 cahill:1 mechanics:2 phil:2 proved:1 defined:3 abstract:1 measurement:28 general:8 proper:1 single:1 formulation:1 inf:1 check:1 physical:6 again:1 discriminate:5 cim:1 antenna:1 no:2 whereas:2 when:9 field:1 role:1 theor:2 acceptable:1 picture:1 apparent:2 kinds:1 superposition:4 excitation:8 hirota:1 polynomials:1 prepared:10 bounded:2 variable:1 structure:1 independently:1 dϕ:1 implies:2 starting:1 interval:3 rule:2 mass:3 northholland:1 time:7 walker:2 2mω:4 resolution:2 rep:1 once:2
|
quant-ph9801069.txt |@word represent:2 concept:1 managed:1 consider:4 remarkable:1 desirable:1 four:1 lahti:1 partial:18 gk:1 preserves:2 depend:1 violate:5 tr:2 send:1 environment:1 summarised:1 those:5 tb:11 worth:1 case:5 conjecture:4 g2:1 g1:1 very:2 every:1 matrices:4 condition:7 quantitatively:1 presented:1 transmission:2 knight:2 trb:1 large:2 solved:1 convenience:1 vector:1 small:1 eigenvalues:2 ree:4 vincenzo:1 rohrlich:1 says:2 direct:1 fold:1 second:2 infimum:1 qualitatively:2 canonical:1 intimately:1 what:1 pawel:2 suspect:1 above:4 consisting:1 satisfy:1 ibid:1 exchange:1 respectively:1 component:2 teleportation:3 here:3 ryszard:1 plenio:2 address:3 active:2 consideration:1 standard:1 appears:1 ensembles:1 obtained:1 sending:2 convert:1 institute:2 vectors:3 contradiction:1 amount:3 products:1 schumacher:2 action:4 bob:3 via:5 useful:2 fµ:1 namely:2 private:1 first:4 limn:1 nonlocal:4 univ:2 use:3 additive:1 asymptotic:1 would:9 remains:1 positive:6 negative:4 definition:2 properties:1 ψi:5 ψb:3 ψa:3 type:3 theoretical:2 more:2 formally:1 successful:1 operators:2 odinger:2 effort:1 particular:3 cases:1 hold:1 producing:2 must:11 equation:1 work:3 remain:1 three:1 following:3 example:1 define:1 f1:1 f2:1 links:1 process:1 bennett:6 distillation:9 purposes:1 states:29 identified:1 numbers:1 sense:1 spanning:1 story:2 conversely:1 simple:1 information:8 needs:1 end:1 discussion:1 get:1 rippin:1 write:1 how:1 criterion:17 pure:8 field:1 ensemble:1 brassard:2 map:1 product:5 teleport:1 after:1 collection:1 applications:1 wrong:1 produce:2 faculty:1 fi:1 fj:1 data:1 types:2 natural:2 imply:1 joint:1 explicit:1 summing:1 purification:1 perhaps:1 ones:1 so:4 fundamental:1 pay:1 subsequently:1 operations:2 indeed:5 over:2 fν:1 years:1 produced:2 cambridge:1 including:1 twoqubit:1 mentioned:1 converting:1 still:2 its:2 tending:1 thank:1 systems:2 mail:3 main:1 than:2 practice:1 h2q:1 mention:1 they:13 now:11 discuss:1 represents:1 vidal:1 2q:4 always:1 university:3 level:2 orthonormal:2 each:4 found:2 entirely:1 cliffs:1 referred:1 em:1 different:1 en:1 ei:1 needless:1 energy:2 ef:4 constitute:1 quantum:22 our:2 operation:3 eq:1 shown:6 matrix:5 space:3 rep:1 since:4 rev:15 m2q:5 particles:5 similarly:1 acting:1 investigation:1 hill:1 absorb:1 mν:1 specifically:1 math:1 shows:1 log2:1 theory:2 8a:1 little:1 free:4 quite:1 reason:1 formation:2 beginning:1 pairs:10 distilled:15 could:3 omit:1 nonnegative:1 counterpart:2 turn:1 hence:4 onto:1 exhibited:1 separable:6 initial:3 striking:1 vedral:2 coming:1 number:3 channels:1 open:1 effects:1 given:6 necessarily:1 their:1 revealed:1 system:5 least:2 needed:1 wootters:3 bits:1 store:1 acquire:1 supplemented:1 shortly:2 separability:8 kind:4 showed:5 wiesner:1 zero:2 distill:1 project:1 matter:1 crepeau:1 supposed:1 were:5 projections:1 collecting:1 filtering:1 correction:2 say:2 need:1 exhibit:1 recover:1 any:14 bohm:1 subsystems:2 latter:7 able:3 nonlocality:1 note:1 internal:3 generalized:1 analogy:4 finding:1 channel:3 twodimensional:2 price:1 singlet:15 most:3 connected:2 letter:4 nothing:1 considered:2 satisfied:2 implications:1 usual:1 physics:3 satisfies:1 fact:3 laws:1 show:2 spaces:2 subtle:1 certainly:1 finally:1 popescu:6 true:1 written:4 peculiar:1 jan:1 only:3 bases:1 factor:2 circle:1 bernstein:1 local:3 do:5 his:1 subspaces:1 quantph:1 means:6 familiar:1 famous:1 cannot:14 reversal:3 despite:1 report:3 dt:1 interpreted:1 lossless:1 podolsky:2 transposition:20 arxiv:1 protocols:1 nν:1 view:1 correlations:2 depends:1 result:9 violates:3 satisfying:4 capacity:1 tensor:1 positivity:2 state:41 converted:2 prentice:1 recently:3 nature:2 qubits:2 inseparable:23 however:7 succeed:1 unnormalized:3 infinity:1 suggested:1 both:1 similar:1 equal:3 nµ:1 connection:1 context:3 qubit:13 whole:1 among:1 appeared:1 had:1 asymptotically:1 dimensional:1 werner:3 proved:1 singlets:1 described:3 basis:7 locally:1 due:3 been:5 pb:8 extraction:1 pa:8 pg:1 basic:2 ph:3 pi:5 pl:3 faced:1 arises:2 corresponding:1 deeper:1 sufficient:2 formed:1 subspace:1 great:1 observers:1 understand:1 spin:4 present:3 applied:1 multi:2 reciprocal:1 pacs:1 reliable:2 remaining:1 will:3 technical:1 suppose:2 reliably:2 error:2 di:1 property:1 procedure:1 larger:1 thus:5 surprisingly:1 seen:1 busch:1 vanish:1 different:1 jozsa:1 perform:3 things:1 make:1 clearly:1 φa:3 φb:3 quant:3 mixtures:2 constructed:2 higher:1 independent:1 used:4 see:1 i0:4 usually:2 entanglement:33 normalization:1 recent:1 schr:2 poland:3 well:1 thought:1 without:1 position:1 know:1 protocol:3 proposed:1 being:1 when:1 obtain:6 rest:1 gda:9 identify:1 mif:1 bi0:3 density:3 seems:2 hall:1 thermodynamics:2 belongs:1 lett:13 input:1 transformation:1 eigenvalue:2 showing:1 possible:2 spanned:1 possibly:1 philos:1 entangled:3 distillable:7 sanpera:1 using:2 helpful:1 brought:1 englewood:1 necessary:2 like:2 lost:1 follows:6 signal:1 performing:1 alice:3 discarded:1 wooters:1 arbitrary:4 output:1 reduced:2 pertaining:1 because:1 classical:6 some:7 examples:1 affects:1 curious:3 finite:1 nonzero:2 asher:1 dimensions:1 comments:1 defined:2 does:4 decomposition:1 proc:1 equivalent:1 processing:2 bi:12 hilbert:2 bz:1 noisy:2 about:1 discussed:1 woronowicz:1 a2:2 act:1 mixed:9 consequently:4 projectors:2 soc:1 nsk:6 eint:7 communication:4 into:5 bound:5 ai0:3 pair:2 distillability:3 einstein:2 operator:1 deal:1 her:1 strictly:1 there:15 question:4 much:1 way:6 astrophysics:2 was:4 naturally:1 function:1 complete:1 form:16 enough:1 smolin:2 tarrach:1 but:4 taken:1 hb:2 ha:3 irreversible:1 made:1 applying:1 embedded:1 horodecki:12 whether:6 particle:2 us:6 projecting:1 problem:4 piece:1 informational:2 called:2 eigenvector:1 gisin:1 associated:1 ai:7 michal:1 describe:1 general:1 peres:12 exist:2 trit:3 inf:1 formalism:1 check:1 physical:4 no:4 amounts:1 ekert:1 rosen:2 defined:3 other:1 role:1 papers:1 test:1 mathematics:1 elements:5 problems:1 inherently:1 prepared:1 meaning:2 important:2 implies:6 time:7 n1:1 decoherence:1 backward:1 having:1 once:1
|
quant-ph9801070.txt |@word reparametrize:1 measurements:3 consider:9 chain:1 global:2 results:2 know:1 scalar:3 subtle:1 consists:2 follow:1 gk:4 gj:1 forget:1 content:1 preserves:1 inverse:1 depend:2 producing:1 concerned:1 deterministic:1 nonlocal:2 γk:6 does:3 infinitesimally:4 present:1 th:10 under:6 kλ:2 stochastic:1 analogous:4 pilot:1 worth:1 kν:1 u2:3 belonging:5 supported:1 g1:4 evolves:1 very:4 observables:2 implicitly:1 conditions:1 unchen:2 every:2 orientations:1 y1:6 difference:1 continued:1 condition:6 solves:2 level:3 positions:13 solution:1 t0:1 try:1 vector:19 guiding:4 section:4 manifestly:2 div:8 integrand:1 der:1 second:1 evaluated:5 gn:4 further:3 dynamics:17 incompatible:1 belief:1 even:6 what:6 const:3 assured:1 tentative:1 specification:1 interactions:1 analogously:1 expressed:2 δx2:6 current:10 looking:1 version:1 transformed:2 above:3 boundary:3 new:2 order:4 acknowledgments:1 contrast:5 codimension:1 satisfy:2 edited:1 full:1 simultaneously:1 whose:2 component:3 here:7 tangent:13 possibility:1 directions:1 path:18 along:6 equations:7 δp:2 change:1 obtained:3 antisymmetric:1 numerator:1 suitably:1 hbd:14 leaves:6 vectors:1 reason:2 amount:1 simultaneous:1 resulting:1 karin:1 stressed:2 usually:1 suitable:2 makes:2 involves:3 uniquely:1 formulated:2 regardless:3 projection:4 figure:1 requiring:1 explained:1 marked:1 outcomes:1 brought:1 equivariant:10 thought:1 rσ:24 summation:1 differ:2 unit:12 derivatives:1 use:1 synchronized:1 usa:1 covariant:13 positive:4 eφ:1 predictions:11 next:1 definiteness:1 noting:1 call:1 therefore:5 iαk:1 means:2 brunswick:1 more:8 sort:1 flat:2 duality:1 comparison:1 initial:1 factor:2 odinger:1 fixed:1 everywhere:3 normalized:2 particular:4 central:1 hold:2 iii:3 ontological:1 eγ:1 must:4 states:1 crosses:2 defines:1 anything:1 frobenius:1 avoiding:1 equation:22 work:1 mk:2 degrees:3 paragraph:1 values:3 thin:1 universe:1 following:2 making:1 spontaneous:1 example:3 nino:1 proof:2 compare:1 bell:3 give:1 relativistic:4 choice:2 sense:2 pieces:1 involve:4 indicates:1 lorentz:35 dxk:6 hyperplane:2 allowed:1 δxk:15 kluwer:1 cushing:1 axis:1 normalize:1 ones:1 straightforward:1 divergencefree:1 turn:1 rather:3 discussion:1 holds:1 moves:1 formulate:1 write:5 how:4 criterion:1 adapted:2 significance:2 absolute:1 parameter:6 encounters:1 simplicity:2 product:5 description:1 may:29 derived:1 containing:3 hence:4 develop:1 summarize:1 geometrical:5 parallel:2 natural:5 outline:1 joint:2 light:1 counter:1 foliations:3 yielding:1 element:3 sk:7 generic:1 synchronization:3 so:9 specifying:1 insofar:1 subsequently:2 first:3 counted:1 talk:1 breaking:1 interpretation:2 words:2 indeed:3 over:3 eqs:1 displayed:1 choose:1 course:4 experiments:1 through:8 statistical:8 hypersurface:34 argued:1 existence:1 satisfies:7 y2:5 dodecaneso:1 observational:1 regions:1 symmetry:2 maps:1 masses:2 relativity:1 translation:1 coordinates:4 writing:2 forms:1 detected:1 microscopic:1 fig:9 main:2 defining:3 image:2 s1:1 correspondence:2 measurement:5 them:1 good:1 widely:1 thereby:1 orthodox:3 fragment:1 integral:1 amenable:2 processes:2 elementary:1 reflected:1 they:4 now:7 transparent:2 nor:1 establishes:1 easily:3 term:2 φk:1 dirac:42 profound:1 goldstein:6 fully:1 university:2 presented:1 labeling:1 establishing:1 realistic:1 each:5 crossing:10 universit:3 side:8 mean:1 spinor:1 differential:1 transforming:1 splitting:1 ek:2 independent:9 idea:2 related:1 operator:2 measure:5 quantum:36 our:2 beyond:1 eq:1 out:2 emerges:1 ultimately:2 fluxes:1 matrix:2 space:39 restricted:3 furthermore:3 since:7 rev:2 particles:41 replacing:1 ajk:1 dsk:4 formula:1 get:2 unch:1 integrated:1 inevitably:1 theory:26 γk0:2 associate:1 candidate:1 divergence:7 fisica:1 free:5 standard:2 approaches:1 toy:2 straightened:1 generate:1 dfx:1 interaction:2 vˆ:1 v1:4 geometry:1 rule:1 could:2 v2:3 times:2 motion:10 thing:2 length:1 consequence:1 stated:1 view:5 dipartimento:1 βk:2 origin:1 xk:32 note:8 xn:26 probability:21 omitted:1 variables:8 number:1 philosophical:1 undivided:1 directly:2 yk:3 impossible:3 precisely:1 genova:3 given:26 law:12 reference:1 their:1 introduction:1 leading:3 crossings:7 system:10 approximately:1 belongs:1 conservation:2 kµ:1 dfg:1 really:1 tangency:3 tuple:1 helpful:1 serve:1 foliation:55 required:1 assumption:2 part:3 x2:13 x3:5 x0:2 x1:41 than:2 positively:1 dynamical:6 whatsoever:1 distance:2 kind:1 determines:2 coherently:1 pointers:1 higgs:1 measured:1 see:11 hypersurfaces:20 future:8 implication:1 negatively:2 eγk:1 distinguished:13 perspective:1 sees:1 entail:1 explicit:1 dynamically:3 mind:1 say:2 manner:8 need:6 curved:1 seem:1 themselves:1 any:21 accounted:2 routledge:1 paths:17 issue:1 zero:1 normals:3 convenient:1 hyperplanes:4 mechanism:1 primed:3 oriented:11 potential:2 reparametrization:2 neither:1 objective:1 simultaneity:5 begin:1 unless:1 normal:19 denominator:1 systems:1 most:4 said:1 germany:1 gauss:1 occurred:1 position:5 remarks:1 plays:1 speakable:1 intrinsic:1 class:2 observation:1 ψk:1 considered:2 later:3 flow:2 typeset:1 points:11 se:1 urr:5 thank:1 incorporation:2 left:1 physics:2 notion:2 fact:7 laws:2 precise:1 saying:1 show:4 violation:1 random:1 purely:2 xl:2 registers:1 relation:1 twofold:1 αk3:1 αk2:1 αk1:1 determined:5 fine:1 find:3 δx1:17 subtracting:1 q1:4 based:1 just:3 extending:1 assertion:1 should:6 tuples:1 only:9 subsection:2 geometric:1 integrable:2 adequate:1 covariantly:1 local:3 γn:9 theresienstraße:1 equilibrium:10 continuity:8 do:4 αki:1 his:1 handle:1 intersect:2 δxi:1 di:2 dependent:2 between:13 satisfied:1 conceptual:2 cannot:2 dx:2 despite:1 dv:1 dt:2 ds:4 becomes:3 areas:1 evolution:5 increasing:1 densities:1 held:1 fields:4 arxiv:1 comprising:1 sum:2 paper:3 common:5 switzerland:1 london:1 qk:3 paradoxical:1 qn:4 riemannian:1 requirement:1 set:5 exists:1 achieved:1 variations:2 frame:13 correlations:2 respect:3 j1:4 lett:1 relative:1 cattaneo:1 depends:5 computer:1 devices:1 discussions:1 close:1 outward:2 surfaces:5 fails:1 satisfying:5 tensor:1 vˆk:3 its:9 iγk:1 written:2 difficulties:1 various:1 closed:1 simplest:5 αi:2 invariant:15 αk:3 approach:2 counterexample:2 terms:4 statistically:3 extend:1 nature:1 adjoint:1 however:12 samols:1 hypothesis:1 key:1 jk:47 analyzed:1 configuration:7 autonomous:1 recall:1 suggested:2 both:3 σn:6 many:1 taking:1 density:8 according:2 contract:1 agree:6 detlef:1 iv:3 context:1 σs:7 expression:2 lateral:2 σt:9 arbitrarily:1 among:2 relevant:3 point:15 simple:2 character:1 dimensional:2 ii:4 simply:1 maudlin:2 moreover:3 slots:1 appraisal:1 considering:2 described:3 addition:2 trajectory:5 locally:1 orthogonal:1 been:5 describes:2 basic:2 expected:1 compelling:1 ph:1 pn:2 abstract:1 fk:3 define:3 box:2 direction:4 describe:2 corresponding:11 concerning:2 readings:1 bohmian:14 understand:1 external:4 albeverio:1 careful:1 spin:3 those:4 c4:3 case:6 multi:5 p1:3 value:1 transformation:1 will:8 equivariance:4 while:4 rutgers:1 suppose:1 situation:5 region:4 ultralocal:1 detailed:1 vkl:2 coupled:1 metric:3 vk:10 thus:15 non:1 surface:4 equal:6 obeying:1 casati:1 dual:1 seen:1 df:1 wave:20 ink:1 fermion:1 currents:6 around:1 different:4 constrained:1 italy:1 grant:2 perhaps:3 suggest:1 make:1 connection:1 same:6 clearly:1 member:1 another:1 noninteracting:6 quant:1 split:1 coworkers:2 figures:1 constructed:2 difficult:1 evolve:1 extended:1 swiss:1 singapore:1 trivially:1 trajectories:5 upon:8 effect:1 hand:9 parametrized:5 action:1 intersects:1 delicate:1 urich:2 potentials:3 entanglement:1 invariance:9 identity:1 fourier:2 schr:1 charges:2 spacetime:1 nonetheless:4 well:3 roughly:2 analysis:6 obviously:1 bohm:27 academic:1 dubious:1 without:2 sets:1 coordinate:5 claims:1 model:49 arising:2 dimension:2 usual:5 world:3 manifold:1 proposed:3 less:1 being:2 when:4 obtain:8 vanishes:2 via:8 distant:1 immediately:2 yet:1 adding:1 rs:5 sheldon:1 field:32 regarded:5 nonrelativistic:4 had:2 parametrization:2 discuss:1 passive:1 instrument:1 add:1 valid:1 extends:1 location:1 theorem:4 ado:1 violations:1 remaining:1 dqk:1 angewandte:1 timelike:1 lacking:1 iγ:1 papers:2 disagreement:1 possible:4 hiley:1 entangled:4 press:1 using:7 intersection:4 apart:1 theor:1 necessary:2 like:16 particle:43 achieve:2 obvious:3 reduces:1 shaped:1 δs:3 characterization:1 manifest:1 specific:1 flux:1 n1:5 yields:3 either:1 sezione:1 arbitrary:7 completely:2 analyzing:1 works:1 introduce:1 reduced:1 satisfactory:1 right:7 namely:1 smoothly:1 some:10 stat:2 understood:2 examples:2 integrability:1 specified:1 images:1 transport:1 nonzero:1 provided:4 scale:1 leaf:1 electromagnetic:2 tube:1 shall:13 integration:1 per:1 critical:1 decomposition:2 provides:1 innovation:1 prog:1 steps:1 intersections:1 prob:1 refer:1 bd:5 scientific:1 indicated:1 equivalent:1 agreement:2 expansion:1 broken:1 step:1 revtex:1 nowhere:2 drawn:1 vˆµ:4 unpublished:1 properties:1 bz:1 takes:1 stokes:1 about:2 actual:1 would:3 extension:7 zangh:5 freedom:3 discussed:2 label:3 compatible:2 probabilities:2 ensure:1 δxn:9 functions:1 cambridge:2 follows:5 into:5 within:1 year:1 nsf:1 three:1 down:1 lies:1 appropriate:2 because:3 references:1 determine:2 frames:4 strasse:1 vkσ:1 bosonic:1 behind:1 statistics:2 institut:2 additional:12 infinitesimal:2 area:5 extremely:1 there:6 u1:3 why:1 squires:2 way:6 forward:1 ψn:1 analyze:1 was:3 assumes:1 naturally:3 function:22 form:14 regard:2 but:10 displacement:2 volume:2 state:2 aµ:1 pk:4 line:2 true:1 nutshell:1 he:2 infn:2 made:1 applying:1 places:2 whether:3 minkowski:7 smooth:3 maximum:1 signed:2 ur:1 dordrecht:1 below:1 dms:1 uk:4 planes:1 distribution:23 called:3 mechanics:10 partition:1 associated:4 convey:1 defined:15 ak:2 aj:1 general:9 single:3 ingredients:1 formulation:6 formalism:2 distributions:3 check:1 physical:4 nj:1 nk:7 us:1 nn:4 no:6 mathematik:1 generally:2 ascertained:1 nf:1 application:1 other:19 role:1 spatial:1 department:1 mathematics:1 proposal:1 sufficient:1 unobservable:1 conclusion:1 mathematisches:1 picture:1 briefly:1 elements:2 denote:3 generates:3 models:8 symbol:1 setting:1 problems:4 transported:1 generated:1 important:1 allowing:1 velocity:3 variable:2 sides:2 structure:11 nµ:3 assume:2 starting:1 dτ:3 factors:1 resolving:1 δx:26 governed:2 original:3 eαk:1 incomplete:1 time:41 serious:6 n2:4 n3:3 requires:2 having:2 unspeakable:1 once:1
|
quant-ph9801071.txt |@word limited:2 positions:1 concept:1 consider:2 represent:3 rev:10 both:2 brownian:2 results:8 leads:1 eds:5 ginzburg:1 disappears:1 controversial:2 compatibility:1 intricate:1 remarkably:1 involved:1 hole:2 rigidity:1 devoted:2 certainly:4 careful:1 terms:1 paris:3 concerned:2 involve:1 seriously:1 presents:1 charge:1 permanently:1 present:7 th:2 under:3 aux:1 analogous:2 include:1 applied:3 roc:1 outside:1 very:4 frequencies:2 continues:1 brossel:1 resistance:3 electron:3 witten:1 every:1 overbeek:1 mixing:1 verh:1 difference:1 bringing:1 condition:3 school:1 routledge:1 cunningham:1 level:3 opt:2 turns:1 conceive:1 list:1 solution:3 leave:2 solved:2 bypassed:1 form:4 dealt:1 small:3 frolov:1 optics:1 inertial:6 possibility:1 application:1 force:23 pragmatic:2 deutsch:1 oscillator:1 consistent:7 requirements:1 measurable:1 understanding:3 outcomes:1 surrounding:1 second:2 design:1 enhancement:1 plead:2 click:1 quite:1 even:7 will:3 what:2 sud:1 plays:3 appear:6 incompatible:2 giving:1 sum:2 interactions:1 lhomond:1 uniform:18 version:1 establishes:2 sup:2 tranformations:1 falling:1 reynaud:11 ever:1 filled:3 paradoxical:1 body:2 full:3 led:4 notions:2 ibid:4 exchange:1 eksp:1 promising:1 modify:3 answers:1 atoms:2 met:2 objects:4 galilean:3 separation:1 galileo:2 causality:1 dissipated:1 astrid:1 equations:6 appears:1 change:3 deduced:1 obtained:4 processus:1 rigorously:1 technical:2 shift:1 study:2 studied:1 allows:5 approaches:1 experience:1 controversy:1 thoroughly:1 stressed:1 domains:1 opinion:1 changes:3 involves:2 composed:3 emerge:1 named:1 formulated:3 useful:1 lus:1 forbid:1 namely:3 birrell:1 treatment:2 logical:2 emptied:1 brought:2 contradictions:1 frame:6 forefront:1 total:1 planck:5 manipulate:1 use:2 lamoreaux:1 takes:5 would:5 prove:1 positive:2 lying:1 aristotelian:1 uniformly:11 negative:1 jaekel:9 properties:11 nucl:1 therefore:2 usp:2 taken:2 tells:2 associated:8 analysing:1 until:2 today:3 more:13 equivalence:1 ambiguity:1 upmc:1 apparent:1 emission:4 validity:1 ambition:1 grove:2 particular:14 known:6 foundations:1 cases:1 hold:1 must:3 states:1 keeping:1 nauk:1 contradicts:1 der:2 rohrlich:2 eclipse:1 modified:5 london:3 geometry:1 remain:3 deficiencies:1 obvious:1 temperatures:1 concepts:1 following:1 clarendon:1 trans:1 spontaneous:1 example:1 fulton:1 history:1 rosenfeld:1 renormalization:2 mirrors:5 process:1 relativistic:1 choice:3 arise:1 high:3 effectively:1 balibar:1 mixture:1 sense:2 intuitions:1 story:1 calculated:1 absolute:2 lamb:1 compatible:1 end:1 rather:2 discussion:4 feature:3 chemical:1 how:1 numerous:3 criterion:1 adapted:1 answer:1 instead:2 ordinary:1 priori:1 map:1 rise:2 description:17 may:4 after:5 confirmed:1 convincingly:1 consequence:3 produce:2 designed:1 physik:2 coming:1 fits:1 representations:2 law:4 associ:2 response:2 constants:1 atomes:1 realized:1 natural:3 outline:1 effective:1 light:3 attracts:1 explicit:1 correspond:1 provide:1 accelerated:25 so:3 fundamental:5 jussieu:1 representation:8 order:6 serge:1 unsolved:3 interpretation:3 help:2 produces:3 indeed:3 principia:1 mainly:1 soon:3 cohen:1 years:2 stability:1 course:2 pascal:1 experiments:3 through:2 wolf:1 statistical:1 differs:1 existence:5 still:4 its:10 before:3 fis:1 emits:1 group:5 western:1 energies:1 interesting:2 relativity:29 presses:2 writing:1 absence:4 ens:1 microscopic:3 systems:1 constitutes:1 inconsistencies:1 derivative:2 main:3 arguments:2 eventually:1 non:5 ya:1 radi:1 practice:1 impossible:2 introduce:1 primary:1 obeyed:1 framework:6 walls:1 effects:11 they:10 half:1 oxford:1 insisting:1 now:4 discuss:2 association:1 possess:1 finite:2 stated:1 always:2 university:5 presented:1 advent:1 identified:1 realistic:1 transmitted:1 mode:1 each:2 found:4 entirely:1 difficult:1 scattering:1 mean:1 status:1 domain:6 differential:1 vanishingly:1 instability:1 ee:1 ed:2 energy:18 sov:1 reduce:1 principles:3 related:8 frames:10 extended:1 grav:2 measurement:2 quantum:69 our:1 happen:1 enclosure:2 special:2 out:4 shown:3 container:1 generalizations:1 space:33 restricted:1 furthermore:6 since:10 preserve:2 particles:2 acting:1 optical:2 dominated:1 emerged:1 brazilian:1 induced:1 issue:1 originally:1 math:3 shows:4 relativit:1 perception:1 theory:27 localization:2 given:3 free:1 standard:3 difficulty:1 reason:2 ancient:1 besides:2 usual:1 forbids:1 enz:2 definition:6 interaction:2 unwin:1 concerns:1 brown:1 could:4 impose:1 keep:1 motion:61 turn:1 length:1 place:5 fiz:1 a220:1 hence:4 teor:1 approaching:1 onto:1 first:6 origin:1 heidmann:1 mehra:1 already:5 symmetry:4 potentiality:1 number:3 preservation:1 long:3 directly:7 reached:2 precisely:5 electronic:1 george:1 differ:1 necessarily:3 temperature:7 rejects:1 introduction:3 cambridge:3 plagued:1 relations:3 unruh:8 their:12 conservation:1 identity:1 statement:2 realization:1 norton:1 perfectly:3 really:1 sensitivity:1 too:2 noted:2 progr:2 jong:1 distribution:1 exactly:2 stress:1 direct:2 reflecting:5 favorable:1 occurence:1 undoubtedly:1 than:4 reflection:1 distance:2 galil:1 molecular:1 holland:1 showed:1 princeton:1 xxiv:1 favors:1 cimento:1 imply:1 limiting:1 matter:3 historical:1 were:1 identical:1 outcome:1 treated:2 result:1 supplement:1 witt:2 symmetries:6 remained:1 nernst:2 correction:3 modern:4 argument:3 regime:1 say:2 manner:3 curved:3 clearly:3 relatively:1 acceleration:6 generalizes:1 realm:1 built:5 zero:7 depending:2 describe:2 studying:1 ation:1 responsible:1 physique:2 gravity:1 violates:1 instance:1 internal:1 idealization:2 forces:5 spacetime:2 davies:5 detector:2 concern:1 heisenberg:3 cnrs:2 towards:1 altered:2 allow:1 infinitely:1 gunzig:1 object:1 justify:1 most:2 involving:1 propagate:1 but:5 preliminary:2 nothing:1 marie:1 intrinsic:1 class:2 france:2 give:2 observation:1 considered:3 soviet:1 clear:2 later:2 paragraphs:1 physica:2 curie:1 proceedings:1 points:2 electrons:2 principle:16 mechanical:13 velocity:7 abraham:3 physics:16 notion:4 fact:11 laws:7 precise:1 show:1 detection:2 friction:2 discovered:1 developed:2 attempts:1 relation:4 solutions:1 argues:1 subtle:1 scatterer:1 find:1 paradoxes:1 ground:2 based:2 knowledge:1 spite:1 elsevier:1 dissipative:4 explain:1 assertion:1 should:6 jan:1 only:8 black:5 molecules:1 inherited:1 equally:2 over:1 boyle:1 ges:1 do:5 his:3 above:2 meanwhile:1 dekker:1 grynberg:1 de:10 account:2 famous:1 cannot:3 invariant:2 during:1 du:1 learned:1 reveal:1 processes:3 fields:6 arxiv:1 fixes:1 thermal:5 remove:2 roy:1 paper:1 contrast:4 contain:1 including:1 creates:1 movement:14 discussing:1 valid:1 view:4 ignored:1 set:2 amply:1 predicts:3 reference:12 achieved:1 exerted:1 correlations:1 lett:7 espace:1 relative:1 argued:1 depends:3 bare:1 descriptions:4 discussions:3 close:1 uncorrelated:1 particle:6 philosophy:2 subject:3 surfaces:1 gravitation:10 inequalities:2 mentioned:3 macroscopic:3 rindler:5 interpreted:1 motional:5 fulling:4 boundaries:5 favor:2 state:8 difficulties:9 identification:1 radiated:1 between:15 crude:1 progress:2 approach:4 available:1 gives:1 notice:1 recently:1 nature:5 importance:1 emitted:2 however:4 braginsky:1 rapid:1 comm:1 here:2 key:1 interface:2 article:2 configuration:1 come:1 inertia:5 observer:3 improve:1 observable:4 essentially:1 semiclass:1 prescription:2 limits:1 successes:1 freely:1 region:2 uncertainty:1 equal:1 against:3 called:3 fluctuation:2 propagation:2 connection:1 les:1 figures:1 poincar:2 context:2 casimir:7 jh:1 contribution:2 whole:1 experimental:4 otherwise:2 wald:1 onofrio:1 point:11 reasons:2 character:2 thierry:1 tabor:1 khalili:1 distinguish:1 maintained:1 respect:3 objections:1 ether:1 boat:1 considering:2 jetp:1 described:1 raise:2 marc:1 damp:1 exert:1 challenged:1 due:2 been:16 reprinted:1 describes:1 damping:1 hawking:2 electrodynamics:2 expected:1 ph:1 ann:2 empty:8 questioned:1 nuovo:1 addison:1 arises:2 corresponding:1 indeterminacy:1 reaction:11 quantities:1 sufficient:1 formed:1 photon:4 precision:1 new:1 observers:5 understand:1 houches:1 general:8 those:3 case:9 argu:1 novel:1 conception:3 abandoned:1 structures:1 solid:1 akad:1 appearance:1 single:3 value:2 air:2 aim:1 while:1 applies:2 wiley:1 situation:4 property:7 conformal:9 taking:1 procedure:1 pertinence:2 coupled:2 vanishes:2 von:1 drawbacks:1 thus:5 them:2 surface:1 according:1 itself:5 allen:1 vanish:1 interacts:1 attach:1 different:6 russell:1 open:1 sensitive:1 formulations:1 radiation:13 indistinguishable:1 same:7 any:12 zinn:1 another:1 quant:1 emphasize:1 widely:1 proved:1 several:1 composition:2 higher:1 development:2 independent:1 used:3 laboratoire:4 upon:4 effect:8 hand:2 kubo:1 ned:1 moving:8 necessity:1 resonance:1 infinite:5 invariance:5 thoughts:3 normale:2 lower:2 schr:1 modes:1 entre:1 largely:1 nevertheless:1 expression:3 motions:5 lambrecht:1 well:10 thought:1 academic:1 without:1 consistency:1 coordinate:2 position:1 model:1 arising:2 latter:1 bodies:1 charged:2 summer:1 just:1 dover:1 being:1 generally:4 observed:2 newton:4 lorentz:8 obtain:4 rest:5 isolated:1 profoundly:1 identify:1 atomic:2 questions:8 summed:1 speed:3 yet:2 saunders:1 adding:1 renewed:1 density:1 absorption:2 photons:2 had:3 transparent:1 simple:2 spread:1 attractive:1 wet:1 kastler:1 mod:2 transformation:4 momentum:1 take:1 real:5 makes:1 aspects:1 analogy:2 advances:1 possible:3 eorique:1 know:1 birth:2 vacuum:95 press:7 world:1 emergence:1 highly:1 stable:1 europhys:1 disadvantage:1 wesley:1 necessary:2 like:5 lost:1 follows:4 signal:1 velocities:2 manifest:1 ignore:1 imposes:1 arbitrary:3 become:2 accelerations:1 essential:3 depend:2 mathematical:2 reidel:1 satisfactory:3 because:3 often:3 classical:16 absolutely:1 barton:1 some:5 pierre:1 torricelli:1 understood:4 evaluated:1 sight:1 mirror:17 tends:1 soc:5 archetype:1 exists:2 provided:1 describing:2 lead:3 renounce:1 cavity:6 electromagnetic:6 measurements:1 per:1 crisis:1 does:5 eliminate:1 unavoidably:1 prog:1 propagating:3 proc:5 price:1 minimal:2 freed:1 noise:2 obey:1 rep:4 problems:5 coincides:1 oscillating:1 agreement:1 rue:1 pressure:5 step:1 display:1 viewpoints:1 although:6 inherent:1 universit:2 transformations:16 compose:1 about:2 central:3 justin:1 extension:3 entailed:1 universe:2 discussed:3 generated:1 reduced:1 practical:1 mutually:1 ensure:1 obeys:1 introduced:1 raised:4 contains:1 final:1 presence:3 maxwell:4 into:3 within:3 sketch:1 down:1 remarks:1 par:1 references:2 raises:2 einstein:7 elementary:3 proportional:2 lesson:1 next:1 mere:2 dupont:1 detectors:1 logics:1 van:2 deal:1 extremely:2 there:3 question:7 reduction:1 signifies:2 noticed:1 tannoudji:1 anderson:1 much:2 quanta:1 physicists:4 way:5 suit:1 conceivable:1 closed:1 was:18 naturally:2 lowest:1 himself:1 north:1 elsewhere:2 newtonian:1 phenomena:2 causal:2 fore:1 formalisms:1 cedex:2 contradictory:1 satisfactorily:1 fallen:1 atom:4 line:1 true:1 themselves:1 universitaires:2 longer:1 made:2 whether:2 gravitational:2 variations:1 up:3 us:9 theoretical:6 placed:1 faraday:1 exerts:3 limit:2 anew:1 callen:1 continuously:1 fluctuations:40 problem:7 define:1 emit:1 welton:1 mechanics:6 adopt:1 constant:2 play:1 defined:5 certain:1 universal:1 contribute:3 deep:2 evidence:2 dirac:2 conserved:1 erieure:2 au:1 formulation:1 accounting:1 exist:2 formalism:2 commuting:1 physical:13 functions:1 paradox:1 equation:1 no:5 giacobino:3 whereas:3 ecole:2 when:13 detail:1 reality:3 field:28 conceptions:1 other:5 role:4 spatial:1 sciama:2 forcing:1 concerning:2 raine:1 explaining:1 xxx:1 reconsider:2 models:1 fabre:2 berman:1 inescapable:1 odinger:1 a1:1 meaning:2 important:2 curvature:2 a7:1 observables:2 dissipation:3 structure:1 ago:1 implies:3 coupling:2 pointlike:1 bateman:1 equivalently:1 ments:1 mass:5 situations:3 time:11 far:2 serious:4 quantity:1 requires:1 waals:2 once:1
|
quant-ph9801072.txt |@word illustrates:1 induces:1 berman:1 separates:1 brownian:5 results:5 leads:8 eds:1 scalar:7 supplement:1 milonni:1 follow:1 expressions:2 lptens:1 reynaud:5 whose:2 inverse:1 depend:3 violate:1 paris:3 hωc:4 corrections:2 charge:15 those:1 th:2 stable:7 sustain:1 characterised:1 divergent:1 case:9 evolves:1 very:2 frequencies:8 2re:1 induce:1 electron:2 sensitivity:1 affect:1 difference:2 condition:6 arnold:1 transmission:3 positions:1 solution:1 large:5 solved:2 differential:1 decouples:1 small:10 gauge:1 optics:1 der:3 upper:4 smaller:3 force:47 consistent:5 approximation:2 second:1 interval:1 further:1 odd:1 theory:8 even:2 sud:1 identifies:1 appear:3 ere:1 sum:1 selected:1 near:3 lhomond:1 uniform:1 hω:5 poles:1 sup:2 mq:1 propre:1 erieure:2 journal:1 contrast:2 mp:1 coefficient:7 led:1 here:3 objects:1 physikalische:1 eikx:1 dissipated:1 equations:14 deduced:2 obtained:9 incoming:1 wesley:1 leaves:1 vectors:1 allows:1 experience:1 example:1 p2:2 amount:1 resulting:4 explicited:1 domains:1 decouple:1 fourier:2 spacetime:1 involves:1 frictional:3 composed:2 reflectivity:2 shorthand:1 forbid:1 ipk:2 plenum:1 masur:1 causal:10 linearly:5 use:1 haken:1 takes:1 remains:2 positive:13 negative:6 jaekel:5 france:4 few:2 noting:2 examination:1 m0:8 renormalisation:1 expanding:1 taken:4 ψout:2 introducing:2 sharing:1 ecole:2 incident:1 becomes:1 under:2 comoving:2 particular:2 known:3 iv:1 iii:1 must:7 high:13 account:2 defines:1 ibm:1 quartic:1 recall:1 equation:26 rohrlich:1 ik:3 london:1 mt:3 values:2 three:2 transparency:4 following:4 passivity:3 scatter:1 annalen:3 dedicated:1 reflector:4 mirrors:1 relativistic:2 neglected:1 states:2 lorentz:4 unphysical:1 exclude:1 occur:1 charged:1 cours:1 plunien:1 write:2 located:2 ens:2 opt:1 displacements:2 ψin:8 isotropic:1 description:4 oscillators:2 wiley:1 derived:1 φout:2 consequence:3 plane:5 physik:3 fi:1 fj:1 associ:2 response:5 stress:2 introduced:2 natural:1 third:2 light:3 nussenzveig:1 explicit:2 accelerated:1 so:9 ultimate:1 allow:1 jussieu:1 divergences:1 serge:1 belong:1 memory:1 produces:1 kampen:1 developed:2 over:1 satisfied:5 stability:3 thermal:13 paper:1 through:4 motions:15 satisfies:6 still:1 its:9 before:1 perfect:5 regions:1 tending:1 chandrasekhar:1 how:1 2e2:1 decreases:1 forms:1 degrees:6 stochastic:3 derivative:2 main:1 alter:1 non:5 affected:1 greater:3 greiner:1 landau:1 effects:10 half:5 now:1 transparent:1 developments:1 possess:2 2t:2 susceptibility:26 term:1 2p:1 lies:1 ned:1 barton:2 2d:5 sufficiently:1 inequality:3 instabilities:3 instability:3 universit:2 side:2 2k:1 tensor:2 domain:3 ie2:1 ee:2 ed:3 energy:6 ea:2 displacement:3 related:9 frequency:23 static:2 obtains:1 entering:2 amsterdam:2 quantum:20 relates:1 eq:4 out:1 shown:2 matrix:9 space:9 res:1 rep:4 since:1 lagrangian:3 particles:1 re:3 dominated:1 denoted:1 wick:1 induced:6 occurs:1 math:2 shows:2 linear:12 fluctuates:1 interscience:1 gardiner:1 mω:1 differ:1 free:8 standard:2 york:5 besides:2 put:1 statistique:1 e2:8 applications:1 could:1 motion:16 introduction:3 produce:1 place:1 exponentially:1 δij:1 leading:1 hence:3 neglect:1 first:3 there:2 features:1 kernel:1 relate:1 variables:4 number:2 obeying:1 simplified:1 least:1 directly:1 given:5 temperature:8 unitarity:4 πk:2 eqs:1 behaves:1 system:26 relations:7 unruh:1 their:3 regulation:1 white:2 leggett:1 frame:3 recovered:3 gives:1 holomorphic:1 moscou:1 akad:1 took:1 part:6 review:1 occurence:1 translation:2 representing:2 than:6 coefficients:3 modes:2 diffusion:4 iωt:1 molecular:1 holland:2 anticipate:1 regularised:1 see:14 submitted:1 regulator:2 quasistatic:13 determined:3 iωb:1 pre:1 witt:1 exert:1 fluctuation:12 correction:4 connell:1 atomic:1 vilenkin:1 tω:1 seen:1 recover:3 linked:1 indeed:1 acceleration:3 zero:4 depending:1 convenient:1 self:3 responsible:1 physique:4 admittance:7 k3:3 instance:4 emphasis:1 potential:3 forces:3 davies:1 canonical:1 kac:1 spectral:5 cnrs:2 experienced:1 shall:1 correlation:2 viscosity:1 gravitation:1 experiences:2 but:1 remarks:1 marie:1 counterpropagating:1 commutation:1 kb:1 χt:12 consequences:2 considered:5 kj:1 ki:1 neutral:2 physica:1 order:2 χf:1 kq:5 optical:1 reflections:1 mechanical:2 velocity:9 left:2 physics:3 section:1 dot:1 dover:1 premi:1 intensity:1 show:2 lewis:1 scattered:2 friction:4 dipole:1 iǫ:11 relation:14 solutions:8 decompositions:1 scatterer:30 enjoyed:1 ground:1 causality:11 commutators:1 state:21 should:1 jan:1 analytic:4 only:5 explicitly:1 corresponds:2 factor:1 integrable:1 ξai:1 hopf:1 equilibrium:2 dk:16 notation:4 get:1 dependent:3 de:9 remedy:1 ones:2 dx:3 new:5 dt:4 du:2 gen:1 coth:1 processes:2 densities:1 partie:1 conditions:4 arxiv:1 contain:1 including:1 transforms:2 satisfy:2 hθ:1 hξ:2 statistical:1 swept:1 mori:1 exerted:6 correlations:6 depends:6 bare:6 eliminating:2 violates:1 closer:1 caldeira:1 satisfying:2 interacting:1 kubo:1 macroscopic:1 positivity:4 motional:17 fulling:1 symmetric:1 written:8 closed:1 between:5 incompatibility:1 invariant:1 boundary:2 reading:1 approach:1 preserve:1 publishers:1 terms:7 responses:3 nature:2 however:1 vanishing:1 no:2 undetermined:1 reaction:11 brown:1 many:2 region:1 infinitely:2 equal:1 manifestations:1 casimir:3 exceeds:1 contribution:3 expression:3 comes:1 exhibit:1 ch:1 fields:6 point:20 simple:5 thierry:1 harmonic:1 dimensional:5 pole:2 taylor:1 exhibits:1 meixner:2 moreover:1 along:1 runaway:5 considering:2 passive:1 transformations:1 marc:1 radiative:9 due:1 been:5 expressed:1 describes:3 damping:2 interest:1 electrodynamics:1 expected:1 ph:1 lett:2 addison:1 contribute:1 corresponding:3 residue:1 else:1 2in:1 coherent:1 antisymmetric:1 denote:1 present:1 applied:5 k2:1 curie:1 rueda:1 evaluated:2 will:8 while:1 ain:2 iχ:1 behavior:1 freely:1 situation:2 property:1 study:1 loop:1 shortened:2 changed:1 coupled:7 ip:1 zeitschrift:1 them:1 according:2 ii:1 reads:1 examined:1 im:7 anticipating:1 obey:1 vanish:1 φin:13 different:2 develop:1 make:1 cumulative:2 radiation:18 same:1 complex:2 quant:1 units:2 finite:3 used:4 infinity:3 laboratoire:2 retarded:4 upon:2 effect:1 hand:2 average:1 moving:3 infinite:12 invariance:1 normale:2 motionless:1 off:12 reflection:7 acknowledgement:1 changes:1 polarisation:1 well:4 academic:2 boyer:1 components:1 consistency:1 coordinate:1 position:10 model:3 chemistry:1 possesses:2 bodies:2 usual:1 when:5 rest:4 plagued:1 differentiation:1 uller:1 scattering:7 cut:11 preprint:1 density:1 iω:4 source:1 subjects:1 treatment:3 wet:1 input:13 violations:1 scully:1 momentum:5 real:1 comptes:1 fluctuating:8 around:2 easily:1 rules:1 advances:1 showing:1 decomposed:2 measurement:1 cf:8 eorique:2 outcoming:1 vacuum:18 press:2 using:5 mod:1 meaning:1 counterterm:1 mir:1 imposed:2 like:6 particle:13 follows:5 accelerating:2 harmonically:2 specific:2 unstable:4 recalls:1 stationary:4 reduced:1 mathematical:1 because:1 classical:7 some:3 pierre:1 rammal:2 understood:1 examples:1 mirror:4 neglecting:3 provided:3 describing:1 lead:5 realistic:1 cavity:1 electromagnetic:10 measurements:1 langevin:32 does:3 decomposition:3 unit:2 provides:3 tends:1 prog:2 proc:2 noise:7 bold:1 ξt:19 equivalent:1 each:2 aj:3 expansion:1 rue:1 pressure:18 imaginary:1 properties:10 comparison:1 freedom:6 discussed:1 dependence:4 o:3 2i:3 recalling:3 important:1 plus:1 obeys:3 connected:1 mean:7 soc:1 rev:6 letters:1 iπt:2 unbounded:1 into:5 rendus:1 integral:1 bound:2 bath:7 dissipation:12 square:1 determine:1 einstein:3 proportional:6 next:1 van:1 2iθ:2 assumed:1 initial:1 long:2 dispersion:6 conservation:1 low:1 way:3 wax:1 ford:3 propagator:3 function:12 north:2 annals:1 form:5 problems:2 irradiating:1 extended:1 gaussian:1 cedex:2 suffers:1 recoil:7 gain:1 impedance:6 line:1 anticommutator:1 2πc:1 compute:1 versions:1 characteristic:2 experimental:1 below:1 limit:8 2πt:2 fluctuations:16 ωc:3 similar:4 laplace:2 scatters:1 mechanics:1 diverges:1 constant:5 play:1 defined:1 describe:1 am:1 general:4 face:1 identities:1 regime:1 functions:3 compared:1 analyticity:1 variety:1 generally:1 vanishes:6 reality:1 field:56 role:1 appearing:1 papers:1 theor:1 conclusion:1 briefly:1 models:1 hδij:1 4i:1 uniformly:1 subtraction:1 interferometric:1 commutator:15 generated:1 a2:1 dekker:2 renormalised:5 qφ:3 included:1 lifschitz:1 ξf:6 abraham:3 implies:1 coupling:12 coulomb:1 dω:15 assume:1 required:1 original:1 mass:35 time:10 µt:3 meystre:1 requires:2 4c:1 covariant:1
|
quant-ph9801073.txt |@word consider:3 caused:1 results:3 four:1 scalar:9 commute:1 expressions:1 instantaneous:2 reynaud:6 whose:1 depend:1 paris:3 equivalence:2 does:1 th:1 stable:1 tg:1 brown:1 amplitudes:1 frequencies:9 induce:1 electron:3 difference:2 logarithmically:1 leads:1 cmm:6 transmission:1 irreducible:1 henri:1 t2:1 solution:1 large:3 supplement:1 optics:1 equation:6 heidmann:1 smaller:3 force:17 consistent:4 direct:1 approximation:1 zero:4 value:6 greenberger:1 theory:1 even:2 sud:1 identifies:1 stands:1 sum:3 lhomond:1 consistently:1 sup:2 expresses:1 propre:1 erieure:2 annalen:2 exchange:1 maillard:1 component:4 behaviour:1 objects:1 equations:4 appears:3 obtained:4 balance:1 incoming:2 clarendon:1 involved:1 study:1 studied:1 resulting:1 action:1 fourier:1 changes:1 der:2 involves:2 saunders:1 scales:4 reω:1 total:3 planck:1 linearly:2 readily:1 use:3 takes:4 analytic:1 remains:2 positive:6 contains:2 jaekel:6 france:5 process:1 therefore:1 m2:2 taken:1 entails:1 ψout:2 introducing:1 ecole:2 becomes:1 particular:2 known:4 iii:1 must:6 account:3 ma:1 mb:3 inertial:6 rohrlich:1 modified:1 remain:3 mq:2 following:5 modifies:2 conformity:1 f1:1 mirrors:5 imω:1 relativistic:2 neglected:1 high:5 charged:1 lorentz:1 pν:1 axis:1 provide:2 discussion:2 acts:1 delay:9 located:1 ens:2 parameter:1 ψin:4 simplicity:1 description:1 philosophy:1 derived:1 consequence:3 inst:1 physik:2 law:1 associ:2 response:4 types:1 stress:2 short:1 dynamical:1 roundtrip:1 light:2 spectra:5 correspond:1 fluctations:1 so:3 jussieu:1 order:1 serge:1 neto:1 over:1 stability:2 whilst:1 through:6 differs:1 still:1 excitations:1 its:14 perfect:4 derive:1 acknowledge:1 energies:1 exhibits:3 actually:4 h2:2 maia:1 stochastic:1 derivative:2 variables:1 correspondence:1 non:4 remedy:1 auto:2 greiner:1 introduce:3 obeyed:1 effects:7 they:2 now:2 densities:1 easily:1 term:2 always:1 barton:2 2d:4 sufficiently:1 inequality:1 each:1 found:1 universit:2 side:1 lorentzian:1 mean:6 domain:3 square:1 ei:1 significantly:2 ee:2 ed:3 energy:43 gaussian:1 related:1 frequency:13 quantum:20 approximated:1 out:4 respects:1 shown:1 matrix:5 space:5 furthermore:1 since:2 lagrangian:7 particles:1 re:2 acting:1 denoted:1 wick:1 induced:6 evaluation:1 math:4 shows:1 christensen:1 linear:2 fluctuates:3 written:1 contain:1 put:1 additional:1 interaction:2 determining:1 could:1 times:1 motion:9 introduction:1 length:1 relativistically:1 place:1 massive:1 hence:2 first:2 already:1 feel:1 possessing:1 reflectivity:1 fluxes:1 given:8 necessarily:1 rewritten:1 similarly:1 unitarity:3 least:1 unruh:1 their:1 conservation:5 molecular:1 quadratic:3 gives:2 continuous:2 part:1 x2:1 than:4 coefficients:2 iωt:1 accordance:2 depends:3 submitted:1 quasistatic:3 determined:1 treated:1 descriptions:1 exhibit:3 witt:1 entail:1 rewrite:1 fluctuation:1 correction:2 spectrum:5 seen:3 any:1 built:1 latter:1 responsible:1 physique:1 gravity:1 absorbed:1 take:2 cnrs:2 akad:1 correlation:7 gravitation:1 experiences:1 letter:1 phase:1 marie:1 fluctuate:3 appear:2 considered:2 coincides:1 playing:1 curie:1 accounted:1 sciama:1 principle:3 mechanical:1 velocity:4 usual:1 physics:2 section:1 dot:1 laws:1 scattered:3 relation:2 scatterer:16 longer:3 d2:1 causality:4 delays:2 outside:1 should:1 jan:1 transmitting:5 only:7 constant:8 local:5 exchanged:1 do:1 notation:1 means:1 dependent:4 de:7 addison:1 feels:1 cannot:1 during:1 dt:2 du:2 gen:2 heaviside:1 fields:13 arxiv:1 twice:1 divergenceless:1 including:1 wesley:1 gravitational:1 atomic:1 ned:1 computed:1 exerted:3 correlations:7 see:3 bare:1 result:2 discussions:1 uncorrelated:1 satisfying:1 tensor:3 positivity:1 motional:1 propagates:1 state:1 between:7 invariant:2 boundary:1 reading:1 conditions:2 ϕout:2 multiplied:1 comparable:2 terms:5 nature:1 however:5 vanishing:1 distinguish:1 inertia:3 both:4 freely:2 equal:4 hω:3 bristol:1 casimir:5 variance:1 expression:4 point:1 simple:4 thierry:1 cf:8 dimensional:2 simply:1 lagrange:1 respect:1 passive:1 described:2 commutative:1 marc:1 radiative:1 due:2 been:1 much:1 electrodynamics:1 expected:4 ph:1 ann:1 lett:2 box:2 reaction:1 defect:1 those:1 case:3 p0:3 p1:3 single:3 evaluated:2 will:1 while:3 euler:1 situation:1 property:1 real:3 coupled:4 backing:1 ir:1 thus:1 iv:1 ii:1 itself:1 vanish:6 different:2 plunien:1 make:1 radiation:9 same:3 shorter:1 shifts:1 quant:1 units:1 finite:2 higher:1 laboratoire:2 moving:2 necessity:1 infinite:4 normale:2 off:2 reflection:13 pµ:1 whole:1 well:1 academic:1 components:3 position:10 model:10 arising:1 self:1 left:1 less:1 being:2 storage:4 newton:1 rest:10 sources:1 stored:9 transforms:1 uller:1 scattering:15 previous:2 cut:2 density:4 character:1 iω:1 source:7 treatment:2 wet:1 input:3 momentum:18 identical:1 fluctuating:2 around:2 represents:1 rules:1 advances:1 showing:1 corresponds:5 eorique:1 outcoming:1 vacuum:35 press:1 using:2 modifications:1 particle:2 follows:2 δm:1 become:2 dets:1 stationary:2 right:1 classical:2 some:1 pierre:1 scatters:1 mirror:43 neglecting:2 scale:2 describing:1 lead:3 cavity:12 electromagnetic:1 cφ:1 causal:3 behave:1 unit:2 provides:1 propagating:1 proc:1 noise:1 equivalent:4 agreement:1 expansion:1 rue:1 pressure:9 step:1 although:1 properties:1 berman:1 energymomentum:1 dependence:3 ϕin:4 obeys:1 act:1 introduced:1 letters:1 significant:1 previously:1 into:3 within:2 integral:1 included:2 because:2 einstein:4 operator:2 next:1 acknowledgements:1 log:1 measured:1 there:2 generation:1 describes:2 low:5 way:1 xµ:1 function:5 form:9 but:2 cedex:2 recoil:8 optical:1 courty:1 partially:5 compute:1 inside:1 practically:2 up:1 limit:4 continuously:1 fluctuations:39 problem:1 agree:2 diverges:2 associated:3 flat:1 contribute:4 influence:1 general:1 conserved:3 formalism:1 functions:1 no:4 amounts:1 when:6 vanishes:3 reality:1 field:51 role:1 felt:1 variation:2 important:3 dekker:1 variable:4 sides:2 coupling:6 pointlike:6 dω:4 mass:54 time:20 quantity:1 rep:1
|
quant-ph9801074.txt |@word limited:4 dewitt:1 consider:4 remarkable:1 represent:1 gupta:1 results:1 leads:2 eds:1 quadrature:1 commute:1 follow:1 expressions:5 research:1 contributions:4 reynaud:8 whose:1 ihes:1 depend:1 paris:3 disposal:1 braginsky:2 shall:1 does:2 squeezing:2 th:1 stochastic:3 worth:1 kν:2 kσ:2 polnarev:1 kρ:2 random:3 far:1 frequencies:5 implicitly:1 rise:1 wave:1 drever:1 witten:1 putting:1 fall:1 hµν:1 difference:1 four:1 riemann:1 level:1 positions:3 large:1 convenience:1 bypassed:1 small:3 relation:1 optics:3 noted:2 heidmann:1 smaller:6 force:2 consistent:4 kardashev:1 approximation:1 value:2 dynamics:1 remarkably:1 spectral:1 sud:1 adds:1 appear:2 apparatus:3 section:1 near:1 lhomond:1 wolfe:2 annals:1 above:1 sup:2 propre:1 erieure:2 journal:6 contrast:1 publications:1 revealing:1 led:1 mω:1 component:2 here:5 iωτ:1 possibility:1 represented:1 path:2 along:2 equations:3 appears:3 change:1 ascribing:1 obtained:7 property:2 ctp:1 restrictive:1 study:1 larger:3 round:1 action:1 resonance:1 fourier:1 der:2 usp:2 padmanabhan:1 polonica:1 prefer:1 plenum:1 visible:1 total:1 planck:27 linearly:1 derivatives:1 would:4 mirrors:4 jaekel:6 france:2 noting:1 therefore:1 m2:1 taken:1 more:4 separated:1 ecole:2 company:1 pisma:1 curvature:9 normalized:1 particular:7 known:1 cases:1 iv:1 iii:1 must:1 account:2 gql:3 mc:1 equation:1 des:1 reviews:1 lorentz:1 mp:1 following:1 europhysics:1 example:2 control:1 compare:1 cosmological:1 give:2 high:4 assumptions:1 performed:1 feasible:1 ratio:1 feynman:1 end:9 rather:2 discussion:2 rosen:1 american:1 write:1 ens:2 significance:1 acta:1 parameter:3 sin:2 simplicity:1 product:1 description:1 may:11 after:1 derived:3 minkowski:1 designed:1 physik:2 waves:6 cambridge:2 summarize:1 law:3 associ:2 stress:1 short:1 natural:2 effective:1 computations:1 light:3 register:1 explicit:2 correspond:1 thorne:2 105b:1 ones:1 so:2 ultimate:5 fundamental:1 correlation:4 order:9 serge:1 neto:1 reproduced:2 wigner:1 indeed:1 over:2 mainly:2 soon:1 interpreted:1 thermal:1 own:1 through:2 motions:1 experimentally:1 its:1 perfect:1 delay:1 fiz:1 interesting:1 masses:12 affine:1 khalili:2 scully:1 writing:1 forms:2 microscopic:3 lp:2 main:2 might:1 reintroduced:1 emphasize:2 freeman:1 them:2 greater:7 ya:2 universality:1 graviton:1 effects:5 they:6 half:1 now:1 discuss:1 rµ:2 finite:1 stated:2 lp2:5 university:1 barton:2 dominance:1 realistic:1 magnitude:5 irreducible:3 found:5 universit:2 characterized:5 mean:1 domain:4 differential:1 ee:2 ed:4 energy:1 sov:2 idea:1 related:1 constitute:1 interferometer:2 frequency:14 obtains:2 measurement:14 quantum:41 wavelength:6 beyond:2 eq:1 out:1 emerges:1 borderline:2 space:10 restricted:2 nuovo:2 since:2 michelson:1 denoted:1 formula:1 dominate:4 supports:1 math:1 shows:1 commutation:1 wiley:1 theory:6 several:1 mechanisms:2 mmp:1 free:2 standard:7 manifestly:1 put:1 derivation:2 geometry:3 could:1 times:2 motion:3 length:26 place:1 isotropic:1 tempting:1 signature:1 consequence:2 teor:1 undergo:1 first:1 intuition:1 variables:2 geodesic:16 u0:1 relations:1 directly:1 zh:1 angular:1 size:1 given:2 derives:1 introduction:3 eqs:1 least:1 unruh:1 their:8 perturbations:1 compromise:1 too:1 kµ:2 dt2:1 perfectly:1 exerted:1 recovered:1 gives:1 infered:1 transverse:1 part:2 x0:1 than:17 iωt:1 molecular:1 determines:1 require:1 cimento:2 see:8 final:1 a47:2 determined:4 a41:1 supplement:1 lowest:1 fluctuation:1 modern:1 spectrum:8 traceless:1 manner:2 emphasizing:1 null:1 any:1 acceleration:2 angle:2 built:1 latter:1 lp4:1 physique:3 gravity:8 mechanism:2 note:4 instance:3 k0:3 build:1 heisenberg:1 even:2 cnrs:2 added:1 though:1 track:1 jussieu:1 optimized:2 gravitation:6 letter:2 phase:6 marie:1 measured:5 linearized:2 kg:1 considered:4 average:2 focussing:1 physica:1 curie:1 proceedings:1 optical:2 principle:6 mechanical:4 velocity:3 physics:9 show:2 probe:8 registers:2 gauge:3 expressed:3 superimposed:1 d2:1 translation:1 berman:1 current:1 based:2 commutators:1 distributed:1 state:2 jan:1 reactive:1 only:8 geodesics:2 factor:1 rµνρ:1 local:2 ematiques:1 do:2 dominant:1 distance:8 de:8 unimportant:1 cannot:1 nearly:1 words:2 progress:1 dt:2 du:2 falling:1 dq:1 phaseshift:2 fields:4 translating:1 arxiv:1 nauk:2 characteristic:2 including:1 ql:1 ozawa:2 annalen:2 set:2 computed:1 sensitivity:12 detection:2 intensity:5 result:2 enhanced:1 uncorrelated:2 points:9 uν:2 detect:1 tensor:2 subsequent:1 review:9 written:3 various:1 between:12 invariant:1 geometric:1 caves:3 grishchuk:3 terms:2 statistically:1 attention:1 however:5 vanishing:1 jetp:1 emitter:1 uσ:1 concentrated:1 both:1 cos:2 prescription:1 limits:5 freely:1 compton:4 equal:1 propagation:9 receiver:2 variance:1 contribution:1 expression:4 experimental:2 otherwise:1 point:2 simple:1 thierry:1 corresponds:2 coincidence:1 dimensional:4 directions:3 associated:6 cq:1 society:1 considering:3 zimmermann:1 commutative:2 marc:1 atomic:1 due:3 been:1 strategy:3 much:3 electrodynamics:1 expected:2 connes:1 ph:1 deduced:1 empty:1 direction:1 corresponding:3 respectively:1 concerning:1 wheeler:2 wavevectors:2 c3:1 present:4 mashhoon:1 case:4 inadequacies:1 evaluated:2 will:2 pace:1 while:3 φbe:1 squeezed:1 situation:1 endpoints:1 conformal:1 a24:1 characteristics:1 metric:5 thus:3 non:3 according:1 ii:1 itself:1 cone:1 turns:1 different:2 radiation:3 same:5 orders:1 quant:1 arguments:1 advances:1 units:2 dimensionless:3 gets:1 conflict:1 higher:1 independent:6 used:1 laboratoire:2 trajectories:1 upon:5 effect:2 hand:2 domains:1 purpose:1 lightlike:1 normale:2 lower:2 tracking:5 walls:1 analysis:7 components:2 coordinate:1 quantitative:1 model:1 soviet:1 dimension:2 l107:1 braginskii:1 distances:6 able:1 newton:1 aside:1 λc:4 sources:1 bandwidth:2 admittance:2 questions:3 using:3 macroscopic:4 yet:1 monitored:3 character:2 except:1 wavevector:3 rµνρσ:3 valid:1 conjugated:1 treatment:1 momentum:1 take:1 evaluation:1 around:1 depends:1 represents:1 evaluate:1 cf:3 eorique:1 background:2 vacuum:17 press:1 world:1 usually:2 modifications:2 appearing:2 follows:2 signal:3 ignore:1 communications:1 fully:1 reduced:1 accessible:1 often:2 classical:5 a65:1 pierre:1 salecker:1 sight:1 mirror:3 proper:2 giacobino:1 scale:2 describing:3 lead:1 cavity:2 electromagnetic:10 measurements:10 per:1 inequality:1 unit:3 provides:1 assuming:2 limitations:2 noise:11 obey:1 uniformly:1 equivalent:1 rue:1 pressure:7 step:1 although:1 yuen:1 tidal:2 comparison:1 about:1 42a:1 novikov:1 discussed:1 factors:1 o:1 collett:1 range:1 involving:1 wolf:1 unaccessible:1 woronowicz:1 consequently:1 vi:1 mathematical:1 contains:1 letters:8 redshift:2 into:3 integral:2 bound:3 sachs:2 lies:2 appropriate:2 references:6 einstein:1 proportional:1 mere:1 transform:1 misner:1 detectable:1 low:2 way:8 cqq:14 propagator:1 function:8 complete:1 enough:1 regard:1 sketched:1 but:2 back:1 cedex:2 eksp:1 dissipative:1 hg:1 made:1 eiωτ:2 ωp:2 gravitational:26 variations:1 us:2 astrophysical:3 limit:27 fluctuations:66 similar:1 blair:1 detailed:1 constant:2 uspekhi:2 probes:1 defined:3 detectors:1 universal:1 describe:3 general:2 exist:1 our:1 reflecting:1 commuting:1 trip:1 fizika:2 physical:11 functions:5 completeness:1 cosine:1 no:1 uµ:2 hellings:1 when:7 field:5 other:5 details:1 spatial:2 conclusion:2 deviation:3 picture:1 xxx:1 accidental:1 fabre:1 symbol:1 time:20 problems:1 variation:3 commutator:4 generated:1 validity:1 sql:3 dissipation:4 sandberg:1 longer:1 dω:1 d23:1 interval:1 diffraction:1 dσ:1 equivalently:1 neighbouring:1 mass:13 demonstrates:1 push:1 meystre:1
|
quant-ph9801075.txt |@word consider:15 rev:4 results:18 scalar:1 mnl:2 consists:1 r1l:1 gj:1 localized:3 gr:1 inverse:1 depend:1 calculate:1 antiparticles:1 equivalence:5 acting:2 interactions:1 dψ2:1 nπ:1 finally:1 under:2 connecting:1 analogous:7 include:3 hill:1 p2:12 belonging:1 amplitudes:1 g2:17 straightforward:1 orthogonal:1 very:2 iτ2:3 iτ0:1 wave:17 sons:1 experimentally:1 difference:1 exact:2 visualized:1 presented:1 proposals:1 solution:3 ri:7 large:4 solved:1 leninsky:1 math:1 small:7 upper:1 mn:4 compensated:1 tem:1 rcm:1 measurable:1 approximation:1 second:4 substituting:1 further:2 defines:1 generator:1 q1x:1 canonical:6 even:1 aim:1 ˆr:1 ˆs:1 ˆt:1 clock:2 sum:2 associate:1 analogously:4 consequent:1 ˆa:2 experiment:3 gi:1 above:4 new:5 ˆk:2 boost:5 consisting:1 simultaneously:3 ibid:1 kajantie:1 newyork:1 here:11 atoms:1 reported:1 spinless:1 objects:11 smearing:3 galilean:3 q13:2 q12:4 alone:1 path:1 along:2 standard:1 equations:3 change:2 schiff:1 obtained:8 solid:1 generalizing:1 remarks:1 institute:1 study:3 studied:5 completely:2 commonly:1 mx:1 schweber:1 resulting:5 characterizing:1 permit:1 usually:2 opinion:1 suitable:2 studies:3 cˆ1:3 formulated:2 projection:2 sgi:1 coinciding:1 nonlocal:1 apply:1 total:3 unit:1 coester:1 use:7 feb:1 takes:1 kinematics:1 covariant:2 ψs:2 continuous:1 give:1 negative:2 next:1 calculation:1 linear:1 msk:1 g3:10 m3:3 relativistic:21 taken:1 nonpotential:1 associated:2 e2:4 until:1 more:6 separated:1 introducing:1 diamond:1 formally:7 initiated:1 started:1 becomes:5 operators:12 tested:1 needed:1 correspondingly:1 broke:1 particular:5 known:1 physically:1 circle:1 must:6 evolves:2 account:4 ma:2 quantized:1 mb:2 mm:1 equation:22 work:2 mi:2 modified:1 measures:1 mj:2 reproduce:1 lorentz:10 obvious:1 root:1 example:6 point:3 claim:1 compare:1 synchronized:1 do:1 process:1 discussed:3 dτ1:1 dτ0:3 organized:1 purposes:1 xcm:2 states:15 assumptions:2 performed:3 want:1 sense:1 sharp:1 times:1 action:3 absolute:2 needs:1 nary:1 uˆn:1 uˆa:3 holds:3 makes:1 how:1 p212:2 nauka:1 acta:1 weaken:1 parameter:9 ensemble:2 ψin:3 isn:1 simplicity:2 product:3 nonlocalized:4 description:2 copiously:2 algebra:1 relates:1 after:5 uˆj:1 primordial:2 2e12:1 µab:1 compatibility:1 gaussian:2 ambiguous:2 changes:2 natural:1 dynamical:1 effective:1 beam:2 6th:1 spectra:1 su:1 cosmology:1 dilatation:3 spectral:1 synchronization:1 so:14 sn:5 fundamental:2 s2:4 uˆ2:4 m1:12 order:3 talk:1 grossman:1 helv:1 interpretation:3 help:1 produces:2 constituents:5 ϕj:1 choose:2 years:1 paper:2 including:2 statistical:2 hypersurface:1 differs:3 existence:3 peterson:1 its:29 before:1 unruh:1 group:3 decay:1 jacoby:3 masses:2 solving:3 coordinates:11 fruitful:1 quasiparticle:1 complex:2 degrees:3 systems:2 mail:1 main:3 defining:2 distinction:1 correspondence:2 wouldn:1 them:2 return:1 secondarily:1 obtaining:1 iτ1:1 processes:2 introduce:2 framework:3 p12:12 p13:4 effects:4 they:3 hands:1 ρˆin:1 rotation:3 now:9 discuss:2 easily:2 term:2 several:3 january:1 reasonably:1 hamiltonian:18 2x:3 factorizable:1 realistic:2 reasonable:3 each:9 2l:1 found:5 x12:1 d40:1 square:2 ei:2 another:3 ek:2 t2:1 energy:6 journ:2 principles:1 related:5 applicable:2 constitute:2 frames:4 extended:3 poincare:4 vectors:2 measurement:18 quantum:68 our:19 approximated:1 eq:6 event:4 special:3 really:2 pˆ1:1 shown:15 jerusalem:1 khalfin:1 matrix:2 space:19 furthermore:1 interference:1 holevo:1 particles:6 transforming:1 rf:61 vector:11 eprint:1 ra:3 performs:2 rc:4 rl:1 got:1 rn:2 correct:3 rj:5 shows:4 inevitably:1 wiley:1 theory:6 localization:1 given:9 free:9 quite:7 admits:1 analytical:1 reason:1 complicated:3 york:1 members:1 element:1 intermediate:1 beginning:1 spread:2 rewritten:3 definition:3 interaction:1 r1:3 r2:4 r3:3 starts:1 m21:2 m22:5 thus:1 motion:18 ordering:1 length:2 relativistically:1 place:2 gordon:3 arccos:1 corrections:2 measurability:1 neglected:1 qn:2 strictly:1 first:11 origin:3 ability:4 already:1 xn:4 features:1 xb:3 omitted:2 number:2 clear:2 xx:1 done:2 directly:1 carry:1 precisely:1 angular:1 aharonov:5 illustrate:1 differ:2 checked:1 observer:8 width:4 introduction:2 leading:1 interact:2 πn:2 system:17 relations:4 parallel:1 their:15 assumption:2 too:1 calculations:6 realization:1 scheme:1 final:2 gives:1 collapse:9 moscow:3 observable:5 albert:1 amsterdam:1 part:2 x2:2 probably:1 x1:4 reflection:1 distance:2 level:3 john:1 φcl:3 transferred:1 submitted:1 preparation:1 represents:1 were:1 exp:2 russia:1 decompose:1 m2:13 false:1 p23:6 spectrum:1 generalization:4 alike:1 exchanging:3 seen:1 confirms:1 any:20 seminar:1 strength:1 angle:6 zero:1 able:2 gravity:2 mechanism:2 indexes:2 note:4 internal:11 generalized:1 forces:2 objective:1 detector:7 xˆ1:1 nonobservation:1 heisenberg:4 bilinear:2 added:2 multiple:1 established:2 aexp:1 object:7 most:1 connected:4 ht:3 pair:1 measured:2 class:1 es:1 commutation:1 approximates:2 don:6 subtracted:1 considered:3 τi:3 calculated:2 later:1 detectors:4 repeated:1 km:2 points:2 principle:8 lpi:1 axe:1 velocity:4 physics:5 fact:5 laws:2 axes:1 lebedev:1 show:3 violation:1 detection:1 obtains:3 relation:5 solutions:1 wigner:2 find:7 d0:9 principal:1 q1:1 q2:1 resemblance:1 just:2 parameters:6 rovelli:1 situations:1 e13:3 e12:3 written:1 should:6 examples:1 being:1 only:19 ˆc:2 generators:1 factor:3 constant:3 hamiltonians:1 local:1 plate:1 mixture:1 ϕx:1 klein:3 means:13 dependent:1 simplest:3 expectation:4 2jz:1 ϕl:1 unimportant:1 ones:1 preparing:1 dx:1 despite:5 momentums:5 during:2 2mn:1 ϕc:2 secondary:1 rfs:11 reveal:1 evolution:24 approach:5 arxiv:1 2b2:1 factorization:4 aspects:1 cik:1 qc:1 experiments:1 common:1 qi:1 through:3 rfi:1 qm:11 view:2 reveals:1 set:4 reference:4 phenomenologically:1 symmetrical:1 frame:8 omitting:1 packet:10 relative:17 depends:4 p21:4 result:4 arf:38 p22:6 discussions:1 close:1 espagnat:1 analog:1 acquires:3 hilbert:1 rigidly:1 jz:3 crystal:1 ps1:1 s223:1 eigenstates:2 importance:1 state:38 µi:2 between:18 αi:4 invariant:3 conditions:2 statistically:2 extend:1 premises:1 p2l:8 emitted:1 combining:1 ascribed:1 am:1 comm:1 τj:1 both:5 last:1 σn:2 always:2 many:1 taking:1 uncertainty:6 according:2 attributed:1 quantization:1 fulfilled:1 energies:1 σx:2 q11:1 σp:1 schroedinger:5 experimental:1 ansatz:1 arbitrarily:1 presumably:1 relativity:3 cl:6 simple:6 period:1 factorize:1 represented:1 cx:1 d30:1 applicability:1 moreover:1 cq:17 considers:1 pr:1 ps:1 pp:1 described:14 transformations:19 microparticle:1 addition:1 px:6 py:1 due:15 responds:1 r13:3 uct:1 int:1 reduction:4 much:2 treat:1 azimuthal:1 expected:1 transformed:1 ph:1 pi:3 universal:1 define:4 toller:2 decomposed:1 corresponding:4 versa:1 commutes:1 qia:4 occurs:1 m1j:1 m1m:1 coincides:1 observers:3 observe:1 understand:1 external:1 angles:1 demand:1 θr:7 c1:1 general:8 case:15 peres:2 p1:4 uncertain:2 mlj:3 appearance:1 single:2 value:9 eigenstate:2 will:12 euclidean:1 while:1 suppose:3 rotator:3 pˆ:3 property:1 procedure:2 london:1 eimθ:1 unitary:1 blokhintsev:1 ve:4 πi1:2 formulation:1 binding:1 equal:9 cluster:1 ril:2 itself:1 rij:1 demanded:1 ax:2 limit:3 ie:2 orbital:4 different:4 author:1 perform:4 make:1 expect:1 same:5 delocalization:1 parts:1 quant:2 arguments:1 qab:3 finite:5 φl:2 grows:1 development:1 independent:4 used:6 qjl:1 see:3 singapore:2 a2x:1 boosted:1 effect:3 hand:2 v0:4 principally:2 moment:6 moving:2 purpose:1 potentials:1 infinite:2 changing:2 invariance:3 uˆ:1 concluding:1 e1:2 narrow:1 center:1 s212:1 nevertheless:1 cˆ2:3 well:2 analysis:2 s23:2 without:4 components:2 coordinate:12 position:2 model:13 entangled:1 distances:1 manifold:2 proposed:3 less:1 moments:4 newton:2 obtain:5 rest:9 extrapolation:1 clocks:23 transforms:2 alternative:3 ng:5 macroscopic:6 yet:8 previous:2 candidate:1 density:2 absorption:1 regarded:7 nonrelativistic:10 seems:3 except:1 evidences:1 belongs:1 conjugated:1 lett:1 easy:6 role:1 transformation:25 momentum:13 take:7 real:3 psi:1 nuov:1 around:1 demands:2 situation:1 delhi:1 possible:6 corresponds:2 smallness:1 pˆ2:2 bykov:1 know:2 average:3 immediately:1 accepted:2 coincide:1 mod:2 dimensional:1 rotate:1 like:1 particle:19 alternatively:3 performing:4 separately:1 n1:3 follows:8 become:1 accuracy:1 reduced:2 spins:1 parity:3 because:2 classical:15 karmanov:1 some:18 q23:6 b0:1 b1:1 sight:2 specified:1 proper:18 exists:1 c23:1 scale:2 describing:2 dimensions:2 demonstrates:1 measurements:9 comments:1 decomposition:1 assuming:1 proc:2 demonstrated:1 measuring:3 conference:1 2µi:1 bl:1 s12:2 equivalent:1 arbitrary:4 grav:1 neccessary:1 unambiguously:3 references:1 q2x:1 includes:1 properties:6 collides:1 chapter:4 comparison:1 about:3 es1:1 simplify:2 row:1 freedom:3 ρˆf:1 basis:2 introduces:4 dependence:1 o:1 essential:1 practical:1 pz:1 obeys:1 act:2 analogy:1 introduced:1 consequently:3 microscopic:1 considerations:1 own:2 nonequivalent:1 rj1:1 into:7 disentangled:1 phase:3 appropriate:1 accounts:1 operator:40 proportional:3 subm:1 initially:2 positive:1 unambiguous:1 additional:6 inductive:1 probabilistic:1 support:1 initial:5 transform:1 dispersion:12 start:5 ci1:2 describes:5 way:1 resulted:1 ψn:8 decisive:1 θˆr:2 was:10 function:9 uin:1 complete:1 form:5 ator:1 hs:5 regard:9 nonexponential:1 independently:1 but:17 sophisticated:1 pj:1 neutral:1 recoil:1 delta:1 hc:7 rjl:3 true:3 enlarging:1 illustrative:1 absent:1 made:1 dψ:1 joint:3 thanks:1 whether:3 characteristic:1 up:2 devices:2 historically:1 record:2 below:8 ui:7 fluctuations:4 problem:3 similar:1 called:3 connect:2 mechanics:5 qil:2 ab:2 proved:1 conserves:1 classic:1 defined:10 sˆ2:2 abstract:1 measure:5 influence:4 direction:1 doesn:6 denote:2 meanwhile:2 tˆ:2 chap:1 kgr:3 exist:2 laboratory:1 flight:1 formalism:7 physical:2 incorrect:1 functions:4 cim:1 no:1 asymmetry:1 extract:1 when:5 nf:3 reality:1 field:5 other:5 sˆj:2 sˆk:1 sˆi:1 test:3 doplicher:1 theor:1 conclusion:2 polar:2 ll:25 intend:1 superposition:1 models:3 subtraction:1 prepared:3 a1:1 meaning:2 peak:1 ξn:1 fresh:1 variable:1 b2:11 qi1:5 n2:2 structure:1 ago:1 gedankenexperiment:2 correlated:1 factorized:2 pointlike:3 vice:1 assume:5 normally:2 interval:2 packets:2 sˆ3:1 4n:1 passed:1 mass:13 northholland:1 time:63 observables:5 decoherence:1 n3:2 having:2 8th:1
|
quant-ph9801076.txt |@word partial:4 consider:6 particular:1 focus:1 grateful:1 types:2 expressions:1 looking:1 calculate:5 concerned:2 equivalence:2 tr:4 γj:1 finally:2 infinitesimally:1 tk:1 under:10 analogous:1 applied:1 iǫt:1 far:2 continues:1 induce:2 hewlett:1 entries:1 matrices:27 arrange:1 identity:1 leave:1 trx:4 vector:13 generalises:1 indices:2 eigenvalues:2 equation:1 programme:1 ten:1 sign:3 second:2 further:1 rrt:1 linear:3 giving:2 trivial:2 expressed:1 henceforth:1 3n:1 above:2 nine:4 method:3 respectively:1 component:3 here:1 understanding:1 tangent:1 situation:1 represented:1 xα:4 equations:1 change:1 αir:1 institute:2 leaves:1 vectors:1 allows:1 leaving:1 published:1 action:12 der:1 uniquely:1 a21:1 a23:2 total:2 linearly:4 derivatives:4 use:3 would:1 distinct:2 positive:2 γi:2 properties:5 therefore:4 taken:1 tj:1 more:3 linden:2 ti:4 nkm:1 separates:1 hold:1 must:1 grassl:1 mg:2 rβ:2 recall:1 yjj:2 work:2 det:4 infinitesimal:3 values:6 cam:2 following:4 example:2 def:1 give:3 purposes:1 generically:2 states:5 conversely:1 united:3 rather:1 acts:1 write:2 how:4 pure:3 significance:1 sik:1 sij:4 parameter:1 product:5 description:1 algebra:12 may:20 max:1 orbits:18 redundancy:1 otteler:1 physik:1 constants:1 clarkson:1 third:1 mjm:1 explicit:5 su:12 element:10 perform:1 so:12 specifying:1 decreasing:1 representation:4 first:4 order:3 six:2 considerations:1 indeed:1 over:1 move:1 expects:1 stability:1 course:1 paper:2 signs:2 y1:3 y3:3 y2:3 its:2 group:10 fix:3 conjugation:1 forms:2 heslington:1 isaac:1 into:1 non:25 good:1 return:1 greater:2 framework:1 they:5 rotation:1 now:4 eigenvalue:1 january:1 university:1 uρu:1 appropriate:1 each:2 found:3 2n:1 constraints:2 as2:1 financial:1 determine:5 reduce:1 idea:1 gifford:1 contracting:1 begun:1 measure:1 quantum:1 special:1 rt:1 try:1 shown:2 matrix:28 space:12 since:5 induces:2 trusts:1 particles:16 acting:4 trz:1 formula:1 squares:1 ri:1 theory:1 diagonal:8 effect:1 labs:1 complicated:2 york:3 put:1 beginning:1 definition:1 geometry:1 could:1 mahler:1 turn:1 due:1 δij:3 signature:1 hence:1 βm:1 βi:5 βj:1 βk:1 xk:2 xi:2 u1:5 number:16 rank:2 restrict:1 infinite:1 reached:1 ring:2 xt:2 given:7 publication:1 similarly:4 xii:2 adjoint:3 vandermonde:1 system:1 relations:1 πr:1 their:1 1d:1 gives:2 somewhat:1 authors:1 x2:5 x3:5 x1:5 than:3 specify:4 zγ:1 zero:11 lim:1 classes:2 were:1 minus:2 sees:1 mjk:1 any:3 lie:12 mik:1 mij:3 studying:1 lij:3 lik:2 note:11 sciences:1 take:3 finding:5 canonical:23 towards:1 trace:2 eight:1 significant:1 phase:1 beth:1 class:1 αt:5 calculated:2 points:4 exp:1 physics:1 fact:5 particularly:1 show:7 tkj:1 rth:2 spaces:1 relation:4 d2:1 find:7 d1:3 parameters:24 written:2 should:1 jan:1 only:6 explicitly:2 generators:1 coefficients:6 factor:1 local:26 dn:3 do:3 notation:2 means:2 cannot:1 dr:7 differentiating:1 exhibiting:1 fields:10 arxiv:1 summary:1 qi:1 discussing:1 traceless:1 transforms:1 set:14 physically:1 up:1 see:2 individual:1 rmj:1 subject:1 tensor:6 zkk:1 αx:1 representatives:1 state:3 future:1 between:2 αi:11 invariant:14 αk:3 αj:4 αm:1 email:3 terms:1 attention:1 analogues:1 however:4 cijk:3 key:1 jk:1 tensors:2 σk:4 both:2 σi:20 many:1 equal:2 bristol:1 whole:1 very:1 point:22 1dn:1 dimensional:1 polynomial:9 respect:4 considering:3 described:2 transformations:17 basis:6 invert:1 locally:5 copies:1 ph:4 define:1 determinant:1 describe:2 corresponding:4 σj:8 sufficient:2 c9:2 representative:2 systematic:1 spin:13 those:2 case:11 multi:2 value:1 remaining:1 will:10 investigating:1 skj:1 procedure:1 kingdom:3 a22:1 unitary:7 a29:1 ir:4 thus:14 yk:1 ij:1 rij:14 rik:2 orthogonal:4 different:2 generic:29 acknowledgments:1 same:11 clearly:1 complex:2 quant:4 arguments:1 finite:5 showing:1 higher:1 nij:3 independent:14 used:5 iǫijk:1 ri1:3 entanglement:5 a2n:1 expression:1 solve:1 components:22 convenient:4 firstly:2 dimension:12 subgroup:3 popescu:2 newton:5 actions:2 identify:2 λf:2 leverhulme:1 functionally:4 generator:1 density:36 transformed:1 location:2 transformation:5 gave:1 real:6 characterise:6 tik:1 nonpolynomial:1 five:1 using:2 unique:1 particle:8 follows:2 steps:1 invariants:28 works:1 spins:1 mathematical:1 methods:2 namely:1 njk:2 some:4 b1:1 b2:1 b3:1 b9:3 describing:9 dimensions:2 parametrisation:2 rkj:2 expressing:1 assuming:1 demonstrated:1 refer:1 equivalent:8 arbitrary:1 expansion:1 eiφ:1 hilbert:1 analysing:1 detr:1 cb3:1 column:1 discussed:2 range:1 act:1 slightly:1 road:2 22n:3 cambridge:1 letters:1 letter:1 ηm:4 ηk:2 isomorphic:1 ηi:2 three:7 hermitian:4 references:1 5dd:1 ǫijk:2 span:2 additional:1 support:1 there:7 question:1 transform:1 long:2 u2:5 way:4 function:2 complete:1 form:4 but:4 related:1 rjm:1 highest:1 rji:1 compute:1 packard:1 whether:2 maximum:1 us:2 uk:3 similar:2 ac:3 associated:4 qij:1 certain:1 abstract:1 orbit:31 general:4 single:3 constructed:1 functions:1 codes:1 nl:1 no:1 rains:1 d2r:8 when:1 tir:2 field:2 tin:1 other:4 tij:4 d2n:2 department:1 mathematics:1 elements:6 intend:1 separate:5 polynomials:1 a1:4 commutator:1 a3:3 a2:5 a6:1 a9:4 stoke:1 needed:4 structure:1 qijk:10 d21:2 ti1:1 together:1 them:1 characterising:1 requires:1
|
quant-ph9801077.txt |@word consider:5 magnetic:25 cφ:5 leads:2 roy:1 commute:4 grateful:1 go:2 denotes:1 rot:2 centers:1 localized:2 depend:1 charge:3 rashba:1 squeezing:3 petersburg:1 th:5 under:2 pˆy:6 pˆx:8 analogous:1 include:1 applied:1 belonging:3 preserved:2 orthogonal:1 translations:12 wave:14 electron:1 figs:3 immediately:1 presented:3 applicable:2 discrete:1 vector:22 guiding:7 eigenvalues:2 optics:5 degeneracy:2 dilute:1 zh:1 literature:1 sign:2 zero:1 compensates:2 qualitatively:1 dynamics:1 theory:1 even:1 ˆt:1 incompatible:1 section:3 axes:4 xφ:14 zhang:1 current:5 ˆa:4 ˆe:1 above:1 overcomplete:2 new:1 ground:1 method:3 ˆo:6 simultaneously:1 respectively:1 equals:1 here:4 met:1 sinh:1 represented:1 along:2 equations:3 change:4 obtained:2 solid:1 suitably:1 technical:1 studied:2 allows:2 yˆ:13 simultaneous:1 action:1 changes:2 relation:10 plotted:1 useful:1 projection:1 family:2 hermite:2 translational:3 apply:1 should:2 linearly:1 readily:1 standing:1 feb:1 remains:3 positive:2 contains:1 finally:1 next:1 tela:1 definiteness:3 ψn:3 therefore:3 taken:1 theoretical:1 more:4 zeroes:3 pavlov:1 becomes:1 operators:9 apparent:1 odinger:1 berlin:1 appendix:5 virtue:1 eλ:1 varying:1 known:4 iii:2 must:2 evolves:1 springer:1 defines:1 mc:5 science:2 equation:2 work:1 oscillator:3 modified:1 ρn:1 remain:2 anywhere:1 obvious:2 following:6 example:2 lφ:1 council:1 links:1 give:2 calculation:1 december:1 sense:1 organized:1 states:44 minimum:3 numbers:2 degenerate:2 allowed:1 axis:8 swedish:1 soc:1 rather:3 s0:3 feature:3 located:4 instead:1 verlag:1 parameter:6 sin:10 simplicity:1 product:5 mat:1 algebra:1 may:6 ladder:1 after:1 derived:2 orbits:1 expectation:1 plane:10 physik:1 choice:1 meaningful:1 man:5 natural:1 onto:1 explicit:1 st:1 used:1 representation:5 order:1 typical:2 interpretation:1 words:1 produces:1 indeed:2 satisfied:1 paper:3 through:3 statistical:1 signs:1 existence:2 its:2 roots:1 zak:2 derive:1 malkin:3 chosen:5 tˆa:7 vicinity:1 coordinates:5 actually:1 forms:1 parts:1 choose:2 lz:4 into:2 correspondence:1 closure:1 non:12 combination:3 integral:5 vectors:1 evolution:1 landau:17 walls:1 effects:1 they:1 identically:1 rotation:6 now:2 eigenvalue:3 february:1 gets:1 equality:1 always:2 university:1 hamiltonian:18 l2:5 each:1 2l:5 found:6 feldman:2 2i:5 characterized:1 homogeneous:11 vol:1 differential:1 ei:1 density:9 energy:4 revised:1 positioned:1 gaussian:1 related:1 eb:14 books:1 entering:1 amsterdam:1 quantum:16 our:1 eq:49 out:2 shown:1 matrix:2 space:1 ha:1 since:1 rev:4 research:1 re:2 acting:1 denoted:1 ref:2 math:1 linear:5 mω:1 standard:1 reason:3 york:1 besides:1 element:6 put:1 simplifying:1 milburn:1 r0:2 derivation:2 motion:3 turn:2 length:2 consequence:2 teor:2 generalizations:1 first:8 origin:5 reversing:2 features:2 symmetry:23 variables:3 number:3 done:2 relations:1 another:1 angular:3 given:5 cartesian:1 eqs:4 system:6 construct:3 their:5 identity:1 2l2:3 gives:6 shifted:2 centered:1 distribution:3 detail:1 continuous:1 part:1 too:2 manifestation:1 off:1 translation:8 cosh:1 than:4 specify:1 center:14 level:11 holland:1 see:4 collinear:1 sweden:1 represents:1 were:1 bare:1 treated:1 russia:1 fig:4 symmetries:2 pˆφ:2 elongation:1 unchanged:1 modern:1 argument:1 generalization:1 manuscript:1 manner:2 controlled:2 seen:2 yφ:7 any:2 angle:5 built:3 isolated:1 zhukov:1 note:3 potential:15 take:1 so:4 canonical:1 modulus:1 ˆp:1 mˆ:1 multiple:1 electric:1 iφ2:3 probability:3 regular:1 formulae:1 phase:1 subset:1 class:3 commutation:3 physico:1 constructed:1 considered:1 calculated:1 later:1 ko:5 proceedings:1 points:1 principle:1 exp:9 velocity:1 usual:2 physics:3 incomplete:1 lebedev:1 show:3 text:1 supported:1 notations:1 gauge:22 solutions:4 d2:1 find:5 principal:5 cell:2 feng:1 removed:2 parameters:1 written:3 controls:1 reverses:2 only:5 explicitly:1 factor:1 il2:1 circle:7 darwin:2 hope:1 do:1 admissible:1 dependent:2 ˆg:3 overall:1 kind:1 reversal:4 dr:6 gen:1 coth:1 normalizable:3 processes:1 arxiv:1 rotationally:2 prokhorov:1 dodonov:4 london:1 pitaevskii:1 set:2 constructing:1 achieved:1 physically:1 accompanied:1 aragone:2 relative:4 depends:3 radius:1 result:2 cyclotron:1 recently:1 subject:1 preparation:1 said:1 eigenfunctions:11 distinctive:2 review:2 definite:1 sites:1 symmetric:7 state:28 various:2 eksp:1 invariant:7 reading:1 conditions:1 terms:2 attention:1 however:3 analyzed:2 eipx:1 jetp:1 problem:6 thank:1 both:4 cos:9 last:1 2n:1 timereversal:1 uncertainty:11 equal:2 sov:2 fiz:3 variance:1 passing:2 expense:1 expression:6 σv:7 comes:1 σt:5 among:2 conclude:1 simple:3 asymptotically:1 corresponds:1 whatever:1 dimensional:1 directions:2 anti:2 polynomial:2 sees:2 considers:1 transformations:1 aˆ:5 observing:1 been:5 kahn:2 combined:2 basic:1 expected:1 ph:2 derives:1 define:1 direction:4 corresponding:7 sˆ:2 commutes:6 quantities:1 concerning:1 spectrum:1 coherent:11 external:1 denote:1 present:1 case:10 tanh:9 contexts:1 variances:1 value:1 transformation:9 will:1 institute:2 squeezed:35 procedure:2 unitary:1 orientation:2 shelankov:1 them:1 repeating:2 according:1 ii:2 reads:7 im:5 vx:3 vy:2 rammer:1 ie:2 around:4 different:3 suggest:2 belong:2 same:1 complex:8 quant:2 arguments:1 finite:3 solution:1 independent:2 extended:3 infinity:1 upon:1 differing:1 levels:1 moving:3 purpose:1 infinite:1 build:1 invariance:4 normalization:2 lower:2 schr:1 reflection:3 well:2 messiah:1 solve:1 elongated:1 components:3 coordinate:7 position:5 2πl2:5 drawing:1 charged:3 ny:1 being:7 when:3 obtain:1 valuable:1 cˆ:10 transforms:3 vˆy:1 vˆx:1 eigenstates:3 enters:1 generator:6 infinitely:3 point:2 help:1 lattice:3 valid:5 transformed:3 lett:2 constant:2 eigenstate:2 momentum:5 iφ:3 real:5 eigenfunction:6 easily:1 possible:1 harmonic:3 early:1 increases:1 electrodynamics:1 press:2 using:5 moreover:1 mod:1 necessary:1 like:2 particle:7 follows:5 reduces:1 specific:1 flux:2 either:1 arbitrary:6 become:1 stationary:7 reduced:1 terminology:2 therein:1 because:1 often:1 classical:8 some:3 gilmore:1 mirror:5 intact:1 a10:1 δn:1 gradually:1 dense:1 footing:1 extensively:2 overlap:3 ume:2 does:4 unit:2 tends:1 2en:1 proc:1 lifshitz:2 minimal:3 obey:2 equivalent:2 2c:1 perpendicular:1 sandwiching:1 eiχ:1 2m:1 imaginary:1 properties:5 tanh2:2 extension:2 basis:1 discussed:3 generated:1 o:51 covariant:1 larmor:10 recognizes:1 introduced:1 perelomov:2 accessible:1 conserving:1 presence:2 h2:1 pergamon:2 spreading:1 within:1 rotations:8 cylindrically:1 hermitian:8 references:2 strip:4 operator:31 proportional:1 a3:2 uncertainties:1 area:2 periodic:1 there:1 transform:1 nova:1 analyze:2 was:1 efros:1 iˆ:2 function:7 north:1 complete:4 form:6 a9:2 but:4 dξe:1 construction:2 hn:5 ec:5 filed:1 hb:1 hc:5 line:1 squeeze:1 oa:3 applying:2 intuitive:1 up:1 below:4 frequency:1 limit:3 continuously:1 fluctuations:1 ωc:5 similar:1 mechanics:3 gather:1 associated:2 ag:1 defined:5 certain:3 specified:1 strips:1 general:5 single:1 guessed:1 pˆ:1 ay:4 ax:4 commuting:5 check:1 physical:7 again:1 functions:10 oψ:1 generally:3 vanishes:1 field:32 other:4 remarks:1 spatial:1 department:1 conclusion:1 deviation:1 polar:1 elements:4 a11:1 superposition:1 a12:1 ultimately:1 variation:1 a1:1 commutator:1 meaning:2 a2:3 a5:2 a4:1 a7:1 a6:2 variable:2 a8:1 structure:1 building:1 jørgen:1 factorized:1 assume:1 factors:1 packets:2 together:1 equivalently:1 eξ:1 mass:1 presenting:1 time:4 normalized:2
|
quant-ph9802001.txt |@word represent:2 allowed:1 consider:5 limited:1 caused:1 lack:1 desirable:2 results:4 invent:1 overly:1 leads:3 c3:2 scalar:3 selection:1 edu:1 expressions:3 contributions:1 2r2:3 tenable:1 gh:10 devoted:1 whose:3 certainly:1 inverse:1 depend:3 violate:1 deterministic:1 nonlocal:4 simplify:1 must:2 critical:1 preserved:1 excluded:3 under:6 include:1 presentation:1 norm:6 saves:1 virtue:1 far:2 exception:1 wave:15 aware:1 untenable:1 reformulating:1 summarized:1 difference:2 matrices:2 condition:4 entire:1 presented:5 did:1 turns:1 conceive:2 proposals:2 solution:1 integrated:1 large:2 small:1 noted:7 effective:3 strongly:3 alluded:1 2k1:1 2k3:1 construed:1 consistent:3 approximation:1 second:3 castro:2 nonhomogeneous:4 qualitatively:1 chem:1 haag:1 quite:1 linear:27 bilinear:2 what:5 nonlinear:58 const:1 appear:1 d2:2 section:2 celebrated:1 d3:19 pawel:1 version:5 causes:1 δq2:1 new:4 mazur:1 consisting:1 reflecting:1 respectively:2 never:1 component:3 here:3 bi:2 following:2 explore:1 objects:1 galilean:2 address:1 represented:1 based:1 along:2 strong:4 equations:20 logarithmic:1 ordinary:2 obtained:1 derivable:2 inhomogenous:1 gruber:1 drs:1 approaches:2 suggests:1 products:1 usually:2 implement:1 suitable:1 makes:2 uniquely:2 via:1 depart:1 mobility:1 highly:1 first:6 aimed:1 2δr:1 total:6 identifies:1 derivatives:9 use:1 eω:1 would:8 commun:5 sake:3 confounded:1 contains:3 chooses:1 definition:7 next:1 nucl:1 bialynicki:5 call:2 therefore:6 bender:1 taken:1 toy:2 means:1 nonstochastic:1 type:2 theoretical:8 more:12 separated:1 treated:1 preserving:2 stokes:1 composite:5 becomes:1 acceptable:3 odinger:34 surprisingly:1 appendix:3 generically:1 particular:12 known:5 affect:1 cases:5 circumstances:3 involve:1 account:1 valued:1 anything:1 recall:1 equation:57 work:7 oscillator:1 modified:1 theories:1 affected:1 examined:1 values:2 growing:1 example:4 stimulating:1 proof:1 continuity:3 reasonably:1 do:4 discussed:12 sense:4 purposes:1 weinberg:6 states:10 professor:3 identified:1 assumptions:1 numbers:2 want:1 arise:4 occur:2 guarantee:2 counterpart:2 needs:1 end:1 tνµ:2 rather:3 discussion:2 holds:1 feature:5 write:1 how:1 modification:21 pure:2 reject:1 ensure:1 field:8 constraints:1 sin:2 2v:3 stand:1 product:3 description:2 singular:1 may:6 earlier:2 derived:3 mirman:1 ronald:1 corrections:1 produce:1 studies:1 derives:1 response:1 constants:4 contrived:1 realized:1 introduced:1 natural:1 light:1 acknowledged:1 departure:3 element:1 their:10 maintain:1 finds:2 allow:2 sc:2 representation:2 kurt:1 order:6 se:3 lse:4 interpretation:1 mielnik:5 produces:1 indeed:6 pointed:2 lsm:1 mainly:1 unacceptable:1 course:1 concomitants:1 paper:7 frequency:1 elevated:1 statistical:2 mentioned:1 still:3 its:24 fine:1 derive:2 paradoxically:1 render:1 ln:12 interesting:1 relativity:1 encompasses:1 complex:7 lh:3 resolving:1 resorting:1 resort:1 absence:2 parts:3 compelling:1 systems:5 constitutes:2 radical:1 derivative:3 main:4 might:3 into:1 emphasize:1 correspondence:3 them:4 good:1 motivated:1 greater:1 than:2 wolfgang:1 spell:1 processes:1 b2:8 obeyed:1 framework:7 effects:1 they:9 identically:1 employed:1 now:8 widespread:1 nor:1 possess:3 easily:2 term:2 name:2 2r:3 2k:1 always:2 university:1 hamiltonian:17 b3:5 hermitian:8 findings:1 2a:1 2b:1 each:2 found:8 2n:1 2i:2 characterized:4 referred:1 homogeneous:6 different:9 domain:6 square:1 independent:1 energy:39 ef:24 gaussian:2 related:2 constitute:1 equivalence:2 used:4 c1:6 obtains:1 quantum:28 our:9 avoided:1 nonlinearities:1 special:7 out:7 shown:6 sabatier:2 space:4 restricted:1 nuovo:1 since:9 lagrangian:34 chaos:1 particles:3 hermiticity:1 rl:1 rn:1 induced:2 issue:3 occurs:4 math:9 δq1:1 theory:14 normalized:2 interactions:1 correspondingly:3 mω:2 little:1 free:1 standard:2 manifestly:1 completely:4 necessarily:3 put:5 generate:1 r4:2 andrzej:1 retained:2 r2:57 discussing:1 could:1 unity:1 motion:8 kuna:1 navier:1 consequence:1 retain:1 pitaevskii:2 generalizations:1 think:1 south:1 separable:6 indebted:1 there:10 features:1 probability:1 shapiro:2 relegated:1 xg:1 least:2 xr:3 xp:1 precisely:1 electronic:1 illustrate:1 svetlichny:1 given:3 salient:2 similarly:3 introduction:1 leading:3 condensate:1 system:8 adopted:1 acquired:1 assumption:1 eqm:26 too:1 difference:1 convention:1 postulate:1 scheme:5 cosm:1 boettcher:1 ambiguous:1 detail:1 definitions:1 artifact:1 part:9 jordan:1 authors:3 x2:1 attempt:1 x0:4 separability:10 kind:1 perfectly:1 l47:1 approximations:1 zero:6 ehrenfest:1 matter:1 determined:2 contrary:1 n4:2 amplitude:2 were:1 contrasted:1 solely:2 motivation:1 entail:3 generality:1 correction:2 generalization:2 already:4 manuscript:1 violating:1 manner:2 further:1 seen:1 differ:1 demonstration:1 any:3 solitons:1 relatively:2 sk:1 subsystems:2 pursued:1 latter:4 nonseparable:1 nonlocality:3 note:1 instance:8 potential:2 generalized:2 k4:1 resembling:1 so:6 coincide:1 canonical:3 2mr2:1 even:14 begin:2 added:1 fundamental:9 though:4 who:1 xψ:2 exercised:1 most:5 involving:2 thank:1 phase:10 adds:1 sufficient:2 concerning:1 class:19 cause:2 give:1 observation:2 nonlinearity:2 considered:3 chosen:1 sometimes:3 implications:1 nottale:1 optical:1 principle:4 exp:3 mechanical:10 townes:1 typically:1 satisfies:2 fact:8 quantity:4 drastically:1 particularly:2 phenomenon:1 show:2 modifications:30 anyway:1 purely:1 helv:1 gauge:4 solutions:3 nonfactorizable:2 trivial:1 mycielski:6 make:1 q1:4 q3:1 q2:4 causality:3 just:1 tantamount:1 situations:1 enough:1 supported:1 should:7 only:12 explicitly:2 notes:1 ambiguity:22 postulated:1 integrable:1 hamiltonians:2 local:5 over:3 carolina:1 2mr:3 abelian:1 his:3 quantph:3 meanwhile:1 dependent:1 simplest:1 expectation:6 truly:1 carlos:1 cannot:2 ϕi:7 dx:1 invariant:2 dr:1 neither:2 normalizable:2 evolution:2 resolve:1 densities:7 approach:11 arxiv:1 yield:1 acknowledgments:1 hydrodynamic:3 contain:2 through:1 marek:1 qm:2 require:2 view:1 knowing:1 modulo:1 opposed:3 exists:5 phenomenologically:1 physically:8 uses:1 packet:3 observed:3 see:8 infinite:2 result:5 eliminating:1 terms:6 uncorrelated:1 violates:1 best:1 acquires:1 fails:1 kibble:1 tensor:4 doebner:8 compounds:1 nuclear:1 functionals:5 rejecting:1 importance:1 state:6 convince:1 various:2 between:3 conceptual:1 probably:1 boundary:2 reading:1 conditions:4 law:1 supposed:1 preserve:1 loose:1 recently:3 nature:2 premises:1 restricting:1 weak:2 however:4 vanishing:2 hypothesis:1 extent:1 bose:1 jetp:2 come:1 infinity:1 both:4 essentially:1 goldin:9 many:4 conclusions:2 equal:6 against:1 sov:2 propagation:1 hψ:3 hω:1 present:4 context:1 gisin:3 expression:2 modification:4 otherwise:1 mechanics:14 relevant:1 point:5 simple:4 lagrangians:1 others:1 corresponds:2 insist:1 dimensional:3 maintained:1 inspite:1 consideration:2 polynomial:1 respect:2 mensky:1 throughout:1 accomplishing:1 described:2 transformations:1 tremendous:1 been:12 garmire:1 ai:2 treat:1 interest:4 basic:3 degrees:1 ph:5 linearizable:2 choose:1 contribute:2 corresponding:3 lp:1 received:1 quantities:2 sufficient:1 subscripts:1 requires:2 else:1 relevance:1 coherent:3 observe:2 understand:2 external:1 stems:1 2n3:2 c2:4 2n1:2 general:27 despite:1 former:1 those:3 case:22 k2:1 multi:1 novel:1 abandoned:1 unlike:2 onr:1 value:5 will:11 while:1 momentum:3 behavior:1 applies:1 situation:1 property:18 ucke:4 relativistically:1 unsatisfactory:1 detailed:1 concomitant:1 phenomenological:1 vanishes:1 von:2 thus:5 non:4 reads:2 itself:3 ia:1 limit:1 ic:2 vanish:1 disappear:1 capture:1 containing:1 grant:2 generic:2 kelley:1 intended:1 belong:1 expect:1 same:4 clearly:2 stimulated:1 noninteracting:1 quant:5 arguments:2 set3:1 none:1 finite:1 privileged:1 prerequisite:1 higher:2 status:2 evolve:2 literature:5 columbia:1 exponents:1 cubic:2 hand:3 4m:1 arrived:1 purpose:3 potentials:4 nl:1 weakly:4 schr:34 fully:1 nevertheless:2 changes:1 well:5 obviously:1 thought:1 without:2 components:1 very:2 position:1 model:6 grounds:1 self:1 stem:2 proposed:5 less:4 being:1 rosen:1 rest:1 homogeneity:10 underlying:1 cp:2 alternative:1 scattering:2 yet:3 nlse:5 renewed:1 preprint:7 unable:1 generator:1 density:13 absorption:1 seems:1 b14:1 discuss:2 reasons:1 lett:12 attention:1 reason:1 transformation:3 ought:1 take:1 real:14 acta:2 aspects:1 depends:2 represents:1 read:1 papers:1 possible:2 harmonic:1 czachor:6 completeness:1 entangled:2 variants:2 unique:1 unfounded:1 fractals:1 modifications:4 necessary:5 like:2 particle:4 identifying:1 exquisitely:1 signal:1 δr:10 δs:8 serves:1 pol:1 δl:5 imposes:1 either:1 modified:6 follows:3 degree:1 stationary:3 essential:2 because:1 often:1 deal:2 easy:1 some:24 b0:1 examples:6 choosing:2 moreover:2 extended:2 ourselves:1 energetic:1 happens:3 provided:3 uniqueness:1 describing:1 lead:3 ones:1 integration:1 subclass:1 ubiquity:1 staruszkiewicz:4 does:15 exposition:1 disappears:1 demonstrated:5 compromising:1 fluids:1 varying:1 assumes:1 hse:6 equivalent:1 arbitrary:4 ensures:2 hsm:1 restrictive:2 although:3 2m:25 renders:1 imaginary:3 properties:3 integers:1 about:1 rare:2 extension:3 constraint:1 freedom:1 introduces:1 a3:6 o:1 madelung:2 extensions:1 greatly:2 together:1 mixed:1 mean:1 consequently:3 considerations:4 equally:1 rev:6 presence:2 h2:1 warrants:1 within:2 integral:2 functional:17 nsf:1 negative:1 down:1 appropriate:2 adjointness:1 references:1 einstein:2 operator:11 proportional:2 ann:3 neumann:2 astronomy:1 elastic:1 assumed:3 initial:1 question:16 long:2 why:3 again:1 conservation:1 way:3 forward:2 was:9 δln:12 a2:4 naturally:3 function:8 became:1 medium:1 form:17 hr:1 phenomena:2 smolin:1 removes:1 but:10 hn:5 line:1 level:1 true:3 partially:2 absent:1 made:1 consequences:2 ωt:4 us:11 below:1 owing:1 simplifying:1 demonstrate:2 problem:6 similar:4 called:2 b1:8 originating:1 viable:1 adopt:1 constant:2 reconcile:1 defined:2 certain:5 abstract:1 describe:4 am:3 evidence:1 conserved:4 proves:2 exist:3 governed:2 formulation:4 πx0:1 proceeds:1 physical:7 ni:1 functions:4 beyond:1 discriminate:1 cim:1 no:7 cos:1 when:3 defined:8 reality:1 fairly:1 other:7 spatial:1 department:1 defines:1 operators:4 picture:1 differential:1 denote:3 superposition:1 accidental:1 gross:3 models:2 exceptionality:1 problems:2 includes:1 a1:4 meaning:2 important:3 included:1 birula:5 decoherence:1 structure:3 independently:1 implies:3 assume:2 physics:5 required:2 packets:4 rule:3 dρ:1 dramatic:3 incomplete:1 time:9 recognize:1 observables:2 n2:4 starting:1 original:1 once:1
|
quant-ph9802002.txt |@word sci:1 consider:4 maximum:1 desirable:1 results:5 existing:3 leads:1 peshkin:1 finally:1 tm:1 under:1 include:1 cm2:1 worse:1 very:2 wave:8 electron:21 refractive:3 varshalovich:1 al2:1 condition:2 manyparticle:1 propagating:1 presented:1 did:1 turns:1 solution:1 large:3 kondo:1 vector:2 small:1 noted:3 hora:13 upper:2 smaller:1 zh:2 estimates:1 fradkin:1 second:1 cost:1 traveling:1 pass:1 rigorous:1 further:1 even:2 index:3 brief:1 thickness:3 current:1 experiment:9 above:3 net:1 waveguide:1 outgoing:1 eksp:2 component:2 here:4 perpendicular:1 strontium:1 reported:2 free:2 groups:2 address:1 represented:5 along:2 sine:6 appears:1 change:1 obtained:8 lipkin:1 institute:1 contradiction:1 periodic:2 published:1 usually:1 uniquely:1 spatially:2 explained:1 total:2 use:1 feb:1 remains:1 next:1 nucl:1 therefore:2 m2:1 films:2 theoretical:3 more:9 formally:1 becomes:1 interaction:2 surface:2 hold:1 must:4 account:4 crosses:1 equation:2 theories:1 values:8 thin:2 following:5 trans:1 example:1 indicated:1 give:1 calculation:1 relativistic:3 neglected:1 high:1 assumptions:2 numbers:2 sense:1 quantummechanical:1 axis:3 information:2 discussion:1 instead:1 centimeters:1 parameter:1 sin:2 circular:1 proc:1 modulation:5 plane:4 waves:6 data:2 parallel:1 attempt:1 light:22 akizuki:1 en2:1 ones:1 fundamental:1 order:4 interpretation:3 produced:1 experiments:8 through:2 mentioned:2 p1z:3 fiz:2 better:1 2λp:1 main:1 refracting:1 good:1 ya:1 material:2 effects:1 permissible:1 now:2 yu:1 transparent:1 dielectric:7 represents:2 term:5 becchi:1 sufficiently:2 mode:7 found:1 characterized:1 en:4 energy:3 used:5 frequency:1 exceeded:1 quantum:8 wavelength:8 eq:5 out:2 ru:1 shown:1 factors:1 restricted:1 since:1 rev:2 may:1 formula:4 ref:11 shows:1 okuyama:1 theory:7 sio2:2 possibility:1 usual:1 e0:5 unresolved:1 times:1 vc0:2 turn:1 length:1 instrum:1 gordon:1 1970s:1 teor:2 first:4 origin:1 initial:4 probability:4 2p0:2 number:1 clear:2 another:2 electronic:1 equating:1 longwavelength:1 rewritten:1 πd:1 1z:3 least:2 indicate:1 appl:8 too:1 passed:1 gives:4 pnx:2 pnz:2 statement:1 relationship:2 academy:1 explanation:1 zeroth:1 argon:1 optical:1 somewhat:1 authors:2 absorbs:1 representing:1 than:4 specify:1 distance:3 polarized:1 target:4 accordance:1 approximations:1 intensity:6 determined:5 amplitude:1 were:2 russia:1 peierls:1 generalization:1 seem:1 slab:18 any:2 relatively:1 angle:1 polarization:2 sciences:1 internal:2 take:1 analogy:1 added:1 shall:1 connected:3 phase:2 kc:1 considered:4 average:1 definitely:1 electrons:7 mechanical:4 velocity:3 kx:1 affirmed:1 quantity:4 attempts:2 uniform:1 d0:2 kuo:2 ratio:2 parameters:3 only:5 quasimomentum:3 hutson:1 do:1 srf2:1 dominant:1 zeldovich:1 klein:1 means:1 beat:1 simplest:1 beam:7 cannot:3 report:1 unfortunately:1 conditions:5 arxiv:1 bae:1 london:1 fixed:1 irradiation:1 ser:1 yakonov:1 ωt:1 observed:3 see:3 result:1 optimum:1 surfaces:2 instance:1 pattern:3 review:1 materials:2 written:1 smallest:2 radiated:1 between:9 µa:1 terms:1 reproduced:1 λb0:5 p2n:1 however:6 incident:4 kev:2 jetp:2 improve:2 both:1 cos:2 improved:1 limits:1 many:3 taking:2 uncertainty:1 propagation:1 hω:3 expression:8 experimental:9 cos2:1 among:2 cm:9 conclude:1 color:1 period:3 dimensional:1 simply:1 moreover:1 crystalline:2 mc2:1 appeared:1 strong:1 described:1 basis:2 mizuno:1 three:4 been:7 cosine:2 ph:1 pn:2 pm:1 direction:2 arises:1 corresponding:1 photon:2 angles:2 input:1 c2:1 spin:1 those:1 c4:1 case:6 laser:12 pacs:1 plain:1 appearance:1 value:5 will:1 while:1 optimization:1 suppose:2 ought:1 reliably:1 situation:4 played:1 refs:3 thus:3 discrepancy:5 reports:1 interacts:2 confirmed:1 radiation:7 siberian:1 same:6 quant:1 largest:1 status:2 literature:3 numerical:1 upon:1 effect:7 v0:3 ion:1 infinite:1 changing:1 reflection:2 solidi:2 well:1 roughly:1 without:1 components:1 quantitative:2 model:1 latest:1 ny:1 λp:2 nsc:1 accurate:1 obtain:4 λb:19 previous:1 adv:1 density:4 irradiated:1 had:1 simple:1 add:1 valid:1 treatment:5 propositions:1 role:1 excited:1 momentum:3 possible:1 early:1 vacuum:1 using:5 formal:2 loss:1 necessary:1 particle:3 loses:1 schwarz:19 stationary:2 reduced:2 because:1 methods:1 some:2 repeat:1 sight:1 lead:1 res:1 extensively:1 does:2 morpurgo:1 beating:8 o3:1 ict:1 power:2 agreement:7 step:1 confrontation:1 fluorescent:1 emits:1 meyer:1 tm0:3 tm1:1 about:2 central:1 carried:1 fluoride:1 discussed:3 dependence:6 act:1 considerations:1 soc:1 computational:1 into:4 within:6 acad:1 novosibirsk:1 sov:2 elementary:1 proportional:1 theoretically:1 van:1 assumed:1 there:4 long:4 conservation:2 was:11 function:2 medium:2 illuminated:1 but:1 hk:1 russian:1 technologies:1 directed:1 absent:3 made:2 inside:4 up:4 below:2 limit:2 planes:1 problem:5 2πz:1 calculated:1 detailed:2 resolving:1 denote:1 conserved:1 film:6 physical:1 incorrect:1 handel:1 no:2 when:1 field:8 other:4 electrical:2 branch:1 spatial:9 conclusion:1 quartz:5 superposition:1 accidental:1 models:5 problems:2 chance:1 structure:1 implies:1 2d0:1 established:1 diffraction:3 mass:1 fact:1 time:1 failures:1 n2:3 lett:4
|
quant-ph9802003.txt |@word concept:2 consider:2 rev:5 blanchard:1 focus:1 eds:1 follow:1 research:1 inverse:1 everything:1 diffusions:1 answered:1 uniqueness:2 th:5 under:1 tf:5 stochastic:8 unit:1 kσ:2 case:3 straightforward:1 very:1 rise:3 choice:1 fractal:2 hamiltonian:2 t2:1 solution:1 evy:7 interpolating:2 markov:4 programme:1 intermittency:1 force:1 consistent:2 sign:1 jump:5 imply:1 further:1 dynamics:6 jamison:1 spectral:1 established:1 what:1 appear:1 celebrated:1 above:1 new:2 fields:1 jointly:1 behaviour:1 simon:1 address:1 quite:1 equations:4 box:1 remark:1 property:1 institute:1 involved:2 study:1 action:2 fourier:2 deterministic:2 convolution:1 family:1 replace:1 addressed:1 support:1 ipx:1 ipy:2 planck:1 select:1 feb:1 wealth:1 would:1 positive:9 scenarios:2 phenomenological:1 m2:3 exhaustive:1 theoretical:1 more:2 operators:1 stable:1 odinger:13 surprisingly:1 berlin:2 transient:1 particular:1 known:2 cases:1 iv:1 springer:2 valued:1 henri:1 equation:2 geometry:1 publications:1 shlesinger:1 learn:1 example:2 proof:1 f0:3 impose:1 give:2 process:6 relativistic:1 preserving:1 high:1 νm:1 dxk:1 numbers:1 arise:1 sought:1 reynolds:1 verlag:2 respective:1 verw:1 rather:1 discussion:2 holds:1 how:1 answer:1 instead:1 parameter:1 priori:1 our:4 inessential:1 mapping:1 olkiewicz:3 hence:2 inst:1 designed:1 representations:1 data:7 fm:2 types:1 natural:2 dynamical:4 light:1 grant:1 explicit:1 encompassing:1 so:6 superscript:1 restriction:2 kbn:1 indeed:1 dyk:1 wiener:2 wolf:1 statistical:1 existence:1 y2:1 its:5 suffices:1 group:1 chosen:1 solving:1 a51:1 better:1 microscopic:1 systems:1 mail:1 eventually:1 them:1 fogedby:1 submits:1 evolution:1 number:2 framework:4 they:1 hands:1 now:1 ift:1 represents:1 inversion:1 university:1 dik:1 secures:1 l2:1 found:2 characterized:2 ed:1 gaussian:7 related:2 ball:1 interplay:1 measure:6 quantum:2 assumption:1 special:1 out:2 ultimately:1 space:1 since:2 induces:1 chaos:2 denotes:1 acting:1 formula:4 issue:1 math:1 weron:1 klafter:1 provide:2 free:3 standard:2 admits:1 instructive:1 york:2 ask:1 derivation:1 via:1 transition:6 used:1 times:1 ish:2 place:1 derivations:1 consequence:1 isf:2 origin:1 major:1 initial:1 features:1 probability:13 variables:2 disregarded:1 another:1 given:4 unitarity:1 unknown:1 kt0:1 system:2 intermediate:1 e51:1 gives:1 holomorphic:1 a35:1 tool:1 continuous:5 part:1 lebowitz:1 holland:1 divisible:2 ktm:1 determined:1 intensities:1 fˆ:4 mackey:1 fluctuation:1 topics:1 modern:1 pedestrian:1 any:3 academic:1 studying:1 latter:1 responsible:1 analog:1 analogy:1 kac:3 formulas:1 shall:1 measures:2 simplify:1 diffusion:3 rho:1 probabilistic:3 stands:2 traditional:2 feynman:3 exp:20 kt:3 velocity:1 normally:1 satisfies:1 laws:3 emerging:1 selected:1 random:2 recipe:1 solutions:7 based:1 knowledge:1 parameters:1 insufficient:1 analytic:2 generators:3 rich:1 developed:1 integrable:2 hamiltonians:1 perturbations:1 continuity:1 blumen:1 dk:1 admissible:1 familiar:3 de:4 variate:1 geb:1 dz:1 dx:1 dy:6 dp:1 processes:12 densities:6 arxiv:1 zambrini:1 explanations:1 view:3 kernel:7 set:3 exists:1 klauder:1 namely:1 wroc:1 best:1 exponent:2 positivity:2 between:3 invariant:1 boundary:6 discovery:1 notice:1 attention:1 terms:6 nature:1 premises:1 ikx:1 concentrate:1 here:3 key:1 analyzed:1 come:1 problem:9 σh:2 many:1 taking:1 according:1 propagation:4 poincar:1 receives:1 uni:1 contribution:2 confined:1 relevant:1 point:2 continuation:1 cf:1 infinitely:2 regulated:1 constant:1 mc2:1 semigroups:2 kernels:4 described:1 addition:1 west:1 locally:2 three:1 laplacian:2 cauchy:3 combined:1 marginals:1 ph:2 ann:1 pl:2 lett:1 corresponding:1 external:1 demand:1 c2:1 fokker:1 those:1 c4:1 p2:3 e49:1 choices:1 while:1 karpacz:1 situation:1 endpoints:1 leaves:1 wroclaw:2 unitary:2 freeman:1 chaotic:1 characteristics:1 refs:1 walks:2 thus:1 non:1 σf:3 reads:1 piotr:1 author:1 identities:1 fractals:1 same:3 clearly:1 complex:1 quant:1 emphasize:1 units:1 interpolation:5 extended:1 kis:1 hand:1 moment:1 potentials:3 implements:1 prescribed:1 suitable:2 schr:13 acknowledgement:1 poland:1 variety:1 well:2 analysis:1 concrete:1 without:1 sets:1 mandelbrot:1 detail:1 khintchine:2 questions:1 immediately:1 generator:2 density:10 regarded:1 except:3 exclusively:1 interested:1 extends:1 garbaczewski:6 montroll:2 input:2 semigroup:12 remaining:1 momentum:1 generalized:1 real:1 read:1 possibly:1 know:1 turbulence:1 unique:3 apart:1 necessary:1 like:1 wahrsch:1 admitted:1 arbitrary:2 multiplicative:1 output:2 mathematical:2 satisfactory:1 because:1 methods:1 classical:1 conditional:1 phenomena:3 examples:2 finite:1 transport:1 nonzero:2 provided:2 vol:1 selfadjoint:1 specific:1 eliminate:1 proc:1 considering:1 noise:3 bi:1 additive:1 refers:1 most:2 lasota:1 anomalous:1 plus:1 tailed:2 markovian:4 presence:1 h0:1 within:1 integral:4 functional:1 appropriate:3 references:1 operator:1 amsterdam:1 subm:1 schrodinger:1 statistics:2 strictly:6 there:4 question:1 transform:2 long:2 strict:1 borel:1 way:1 analyze:1 was:1 naturally:1 function:3 north:1 form:6 identification:1 laplacians:1 but:1 reed:1 hm:1 borders:1 versions:1 characteristic:1 mension:1 up:1 us:8 below:1 limit:1 distribution:1 called:3 strongly:1 associated:3 classic:1 certain:2 abstract:1 general:3 proves:1 pˆ:2 rule:1 formulation:1 encompass:1 distributions:1 physical:4 again:1 functions:4 no:2 when:1 defined:3 other:2 spatial:1 pseudodifferential:3 picture:1 mechanical:1 problems:1 deriving:1 generated:2 bounded:1 additionally:1 included:1 factorized:1 physics:3 interval:4 governed:2 time:6 expands:1
|
quant-ph9802004.txt |@word represent:2 concept:3 partial:7 consider:5 funct:1 rev:6 global:1 brownian:4 focus:1 existing:1 leads:1 eds:1 horsthemke:1 broader:1 cameron:1 follow:1 adjustment:1 contributions:2 compact:4 whose:2 preserves:1 inverse:1 const:1 dynamically:1 everything:1 handle:1 fokker:6 deterministic:2 uniqueness:2 those:2 th:3 under:3 stochastic:22 nodes:4 must:3 worth:1 r1:28 subtleties:1 belonging:1 presently:1 preserved:1 g0:1 very:1 homogeneous:2 rise:2 induce:1 choice:6 implicit:1 every:4 allowed:2 fall:1 verh:1 emphasized:1 variance:1 condition:3 bρ:4 identity:1 school:1 beginning:1 subsets:1 solves:3 hamiltonian:4 ref:11 having:1 t2:31 solution:34 identified:1 occurs:1 large:1 admissible:1 interpolating:6 stora:1 small:1 eigenvalues:1 markov:11 specified:1 enforce:1 degeneracy:6 prevent:2 employing:1 force:1 khintchine:1 dealing:1 consistent:5 direct:4 ornstein:1 sign:2 jump:3 likely:1 differentiable:2 displays:3 pass:1 rigorous:1 further:1 dynamics:21 implemented:2 jamison:1 canonical:2 even:6 established:3 what:1 nonlinear:6 developed:2 appear:2 moments:1 euclidean:2 selected:2 lαn:1 current:1 gn:1 above:7 elucidate:1 new:2 appeal:1 method:1 ρt:9 body:1 full:1 nonlinearly:1 excludes:1 respectively:1 pushing:1 fields:1 certainly:3 here:8 behaviour:2 following:1 simon:4 them:1 governing:1 address:1 path:9 quite:4 equations:29 appears:3 ii:1 arena:1 endpoints:2 dividing:1 institute:1 involved:4 study:2 ginibre:1 allows:5 commonly:2 exploitation:2 accomplished:2 resulting:2 krohn:1 action:1 advantages:1 had:1 suitable:8 makes:2 involves:3 york:2 uniquely:2 boundedness:2 lefever:1 via:3 followed:1 secure:1 family:1 ground:7 marginal:2 merely:3 limt:3 replace:1 first:7 diffusions:2 addressed:2 unambigous:1 finiteness:1 establish:2 planck:6 unit:1 derivatives:2 use:2 henri:1 feb:1 proceed:1 would:7 commun:3 distinct:1 positive:22 give:1 differentiability:2 suppl:1 definition:5 next:2 scenarios:1 almost:3 live:1 streit:1 call:1 therefore:1 m2:1 taken:1 generators:1 type:5 theoretical:1 defining:1 separated:2 establishing:1 inaccessible:3 excluded:1 winter:1 started:1 apparent:4 associate:3 odinger:35 validity:4 invoking:1 interplay:1 berlin:6 everywhere:3 normalized:1 particular:12 known:9 dµ0:5 cases:3 hold:3 analogous:1 circumstances:2 involve:1 springer:6 include:1 permits:1 recall:2 equation:24 emerge:1 centrifugal:8 theories:1 reproduce:1 affected:1 labeled:1 obstacle:3 obvious:3 publications:2 believed:1 ingredient:1 specialized:1 example:6 define:4 compare:1 impose:2 renormalization:1 indicated:1 solved:2 process:40 accepts:1 significance:1 preserving:1 share:1 ann:6 sample:17 indicates:1 dxm:1 vol:4 dxk:1 freidlin:1 degenerate:1 arise:2 sought:3 dxf:1 nonnegative:2 conversely:1 occur:1 world:1 absolute:1 nonvanishing:3 respective:8 soc:1 goal:2 rather:2 verify:1 discussion:8 holds:7 feature:1 ilin:1 write:1 how:1 nontrivial:4 criterion:2 get:1 instead:2 field:1 conceptual:1 parameter:1 secures:1 gordon:1 badly:1 product:1 blocks:1 description:2 inherent:1 may:5 demonstrates:1 after:1 averages:1 mapping:2 olkiewicz:4 applications:1 interior:2 inst:2 seemingly:1 representations:2 wave:1 fixed:1 nonetheless:1 namely:1 stress:1 no:6 natural:4 dynamical:4 third:1 geb:2 consequently:2 beurling:1 linear:1 explicit:4 lasota:1 st:1 encompassing:1 spectral:2 maintain:1 so:10 expression:5 fundamental:19 things:1 sc:1 representation:4 zakopane:1 order:6 restriction:1 bull:1 interpretation:1 dx:12 considerations:1 indeed:3 over:2 dyk:1 mainly:1 intuition:2 interpreted:1 course:2 wiener:28 paper:1 through:4 looks:2 statistical:7 grigolini:1 mentioned:1 existence:8 bernstein:1 deducing:3 before:1 effect:1 exclusion:5 singular:6 decay:1 chosen:5 interesting:1 temporal:1 solving:1 actually:1 forms:1 usp:1 strange:1 microscopic:1 choose:3 bypass:1 xc:1 derivative:1 main:1 might:5 subtlety:1 emphasize:1 versus:1 eventually:2 non:2 motivated:2 press:7 propose:1 processes:17 introduce:3 mt:3 obeyed:1 framework:5 touching:1 repulsive:2 they:8 symposium:2 anticipates:1 singularity:8 now:1 discuss:1 nor:1 qt:2 2t:1 represents:1 february:1 equality:1 2q:3 2r:2 always:2 university:4 level:1 2x:1 appropriate:9 displacements:1 2d:1 academic:2 l2:6 breach:1 each:7 crossing:5 2m:2 2n:2 decouple:1 decreasing:1 side:3 characterized:2 mean:1 subset:11 prohibit:1 domain:5 en:3 weight:1 fairly:1 series:1 energy:1 enables:1 gaussian:2 related:7 f0:1 literature:3 perturbations:1 measure:21 quantum:16 our:17 beyond:1 eq:1 event:1 special:2 out:6 stands:3 ezawa:3 carlen:1 space:6 oxford:1 restricted:2 itˆo:2 since:13 induces:1 discouraging:1 denotes:1 particles:1 dτ:21 seriously:1 investigation:1 wolf:1 anal:1 reader:1 formula:11 rn:1 induced:1 issue:7 correct:1 math:14 weron:1 provide:1 theory:11 barrier:3 found:1 derived:1 contain:1 divergence:1 inapplicable:1 free:7 standard:8 admits:1 completely:1 complicated:1 term:1 ask:1 intermediate:2 relat:1 publ:2 monographs:1 surely:1 additional:1 hence:7 pairs:1 dirichlet:4 derivation:3 hg:1 lincei:1 happens:1 could:1 transition:10 moment:1 irrespectively:1 times:8 motion:2 turn:2 place:1 derivations:2 unknown:2 consequence:2 generalizations:1 support:2 origin:1 major:2 there:15 features:2 probability:36 urich:1 consideration:1 variables:7 dynkin:2 number:5 iht:2 linking:1 peculiarity:1 utilized:1 another:1 comprises:2 unattainable:5 open:7 xt:3 equating:1 taniguchi:1 given:10 necessarily:1 exists:3 indicate:1 data:26 adjoint:9 b2:1 system:20 least:4 pinned:2 their:10 eigenfunctions:1 assumption:3 too:2 statement:1 realization:1 postulate:2 borders:1 exponents:1 ωs:3 gives:2 holomorphic:2 originating:2 jaffe:1 tool:2 continuous:31 proving:1 formulate:1 wisdom:1 sizable:1 part:1 somewhat:1 modifications:1 appearence:2 attempt:1 eliminated:1 than:2 intrinsically:1 diffusion:1 albeit:1 analyze:1 gradual:2 qs:1 princeton:6 divisible:1 lnρ:1 older:2 imply:3 limiting:1 reconstructing:1 supposed:1 were:2 mackey:1 contrasted:1 minus:1 motivation:2 financial:1 rend:1 ikeda:1 boston:2 correction:1 modern:1 argument:1 generalization:1 needs:3 substantial:1 manner:1 conjugate:1 need:4 final:1 demonstration:1 clearly:4 viewed:2 accounted:1 paths:19 generic:1 zero:6 depending:1 studying:1 calogero:1 aside:2 definite:1 sciences:1 potential:17 take:2 neither:1 spacetime:1 green:1 subject:1 transparent:1 kac:39 formulas:1 austr:1 unless:1 allow:2 shall:3 whole:4 hit:1 measures:5 reach:2 kalashnikov:1 most:1 madelung:4 connected:5 but:8 pair:7 utilize:2 sufficient:1 probabilistic:5 class:1 involving:1 singled:2 bound:1 parisi:1 constructed:1 observation:1 consequences:1 considered:5 clear:1 justifying:1 stronger:2 drifts:1 traditional:3 feynman:36 points:4 verlag:6 principle:1 exp:59 kt:2 quadratic:1 usual:1 physics:9 notion:2 fact:4 impression:1 emerging:1 phenomenon:3 random:8 anyway:1 katata:1 x2:43 3x2:1 solutions:22 infinitesimal:1 x3:1 kbn:1 diverge:2 availability:1 principal:2 impact:1 chaos:2 zambrini:3 based:4 knowledge:2 parameters:1 semigroups:1 eigenspace:1 situations:1 polon:1 outside:1 should:1 terminal:1 analytic:4 only:7 explicitly:1 candidates:2 specify:2 rich:1 factor:1 parabolic:45 integrable:3 hamiltonians:1 local:2 interested:1 achieve:2 recipes:1 continuity:8 do:3 insight:1 sense:1 subspaces:1 notation:5 means:6 dependent:3 familiar:5 overall:1 assumed:1 variate:2 dym:2 state:7 dz:1 nonequilibrium:3 2md:14 dy:17 dt:2 conjunction:1 procedures:1 ds:2 areas:3 evolution:11 dewitt:1 densities:9 covering:1 x22:1 arxiv:1 unfamiliar:1 comprising:2 factorization:2 aspects:2 imposed:2 bad:2 difficulties:1 conflict:1 though:1 mapped:1 london:1 fixed:1 pertains:1 valid:3 view:5 kernel:37 set:17 reference:1 physically:1 kolmogorov:4 respect:5 lnp:2 lett:4 relative:1 see:6 lebesgue:3 result:4 close:1 lng:1 dµ:7 matters:1 acquires:1 surfaces:1 invoked:1 exponent:1 inappropriate:2 nondegenerate:1 subsequent:2 positivity:2 blanchard:5 its:17 boundaries:5 written:1 unable:1 various:1 pures:1 closed:6 between:6 reproducible:1 invariant:3 boundary:26 conditions:5 discovery:1 preserve:1 suffices:1 notice:7 never:1 terms:7 nature:1 premises:1 attention:2 weak:2 however:8 equals:1 vanishing:2 concentrate:1 jointly:1 key:1 analyzed:1 amer:1 come:3 distribution:2 regular:3 infinity:1 both:5 essentially:2 providing:1 last:1 reverse:2 0t:4 beck:1 taking:1 according:3 attributed:1 display:1 propagation:6 connection:1 densely:1 context:6 hσ:1 contribution:3 inessential:1 comes:3 reside:1 among:2 relevant:3 author:1 point:5 taylor:2 continuation:4 cf:4 inf:1 infinitely:1 exploit:1 strengthening:1 away:2 2t2:2 constant:2 cu:1 reconcile:2 selfadjoint:2 kernels:17 complication:1 duke:1 second:5 capable:1 addition:3 west:1 create:1 locally:4 lα0:1 due:2 laplacian:2 strategy:2 underlying:1 increase:1 cauchy:2 singularities:2 combined:1 interest:2 basic:2 expected:1 marginals:1 ph:7 algebras:1 shepp:3 sufficiently:3 pl:1 location:1 arises:3 corresponding:10 relaxing:1 restrictions:4 nagasawa:1 subspace:1 hits:1 relevance:3 understand:1 proven:1 demand:4 instant:5 albeverio:1 irrelevant:1 høegh:1 present:5 instructive:2 case:30 exception:1 pitman:1 look:1 exponential:1 nski:1 choices:1 will:2 frameworks:1 while:8 karpacz:1 replaced:1 expecting:1 applies:3 stopping:1 situation:3 nonstationary:1 property:6 procedure:3 wroclaw:2 unitary:3 attains:1 coupled:2 phenomenological:3 characteristics:1 refs:3 tω:3 thus:6 surprisingly:2 conditioned:1 respected:1 disjoint:1 reads:1 itself:3 contradiction:1 exterior:2 weakest:1 robinson:1 limit:2 vanish:3 seem:2 piotr:1 nat:1 formalism:1 considerable:1 grant:2 klauder:8 suggest:2 granted:5 cross:2 same:9 any:17 read:2 complex:4 quant:1 arguments:3 units:1 finite:1 verw:2 interpolation:5 status:1 independent:4 ball:2 assigns:1 singapore:1 glimm:1 trajectories:1 interscience:1 hand:7 usually:2 running:1 purpose:1 necessity:1 potentials:13 propagated:1 fukushima:1 expand:1 destruction:1 implements:1 prescribed:1 fourier:1 schr:35 3x:1 mention:3 nevertheless:1 settled:1 poland:1 variety:1 well:11 topics:1 analysis:6 obviously:4 concrete:7 severe:3 without:3 solve:1 components:2 sets:10 accessible:1 redistribution:2 arising:1 dimension:2 left:8 ny:2 ce:2 understood:1 confined:2 being:1 generally:2 guided:1 hands:1 pergamon:1 criterions:1 vanishes:4 assigned:1 confined:1 intervals:1 identify:2 questions:1 immediately:1 touch:2 alternative:2 yet:2 previous:8 vρ:1 accepted:1 generator:9 density:25 diverges:1 grenoble:1 regarded:2 indispensable:1 seems:3 except:1 exclusively:1 realize:1 priori:6 garbaczewski:11 theorem:1 usage:1 input:1 semigroup:17 exit:1 generalized:2 real:9 acta:1 conventional:3 eigenfunction:1 casually:1 eigenvalue:4 rules:2 evaluate:1 results:1 possible:3 harmonic:1 unequivocally:1 possibly:3 game:1 indicative:1 know:2 exploited:1 pertinent:2 emergence:2 unique:9 stable:3 fractals:1 meaning:1 dimensional:2 necessary:2 like:4 identifying:1 follows:2 wahrsch:1 cannot:1 temporally:4 admitted:2 facing:1 anymore:1 true:5 steps:1 either:2 integrals:1 martin:1 evolutions:1 output:1 za:1 stationary:2 preclude:1 mathematical:8 calculus:1 because:3 methods:2 classical:1 polar:1 combe:1 conditional:5 phenomena:3 draw:1 born:2 deduce:1 zheng:1 nothing:2 examples:2 integrability:1 moreover:2 duration:1 enormous:1 finite:4 confining:2 transport:1 generates:1 nonzero:6 provided:1 gradually:1 dense:1 lead:1 broad:1 avoid:1 normal:1 integration:5 conservative:2 generalisation:1 specific:4 does:10 decomposition:1 eliminate:1 provides:1 assuming:2 bratteli:1 prob:1 considering:4 noise:5 run:1 slight:1 drift:8 equivalent:1 arbitrary:4 bi:2 expansion:5 nauk:1 multiplicative:2 step:1 ours:1 nowhere:1 although:2 accompanied:1 receives:1 oleinik:1 properties:3 neighbourhood:3 about:2 kinematical:1 communicating:1 instantaneously:1 theorems:1 discussed:2 dependence:1 o:2 quantal:4 compatible:3 range:1 diffusion:17 plus:1 stand:1 uhlenbeck:1 smoluchowski:4 introduced:2 sept:1 automatically:2 affecting:1 mechanics:3 markovian:5 previously:2 communication:3 into:5 within:1 integral:14 functional:5 lα1:1 variable:2 hermitian:1 right:2 references:1 been:3 determine:1 operator:5 harrell:1 subm:1 technically:1 statistics:1 van:1 deal:5 fields:1 area:3 nodal:2 strictly:18 initial:10 available:2 long:2 ordered:1 strict:2 borel:6 physicists:1 way:1 ed:3 forward:7 conceivable:1 intervenes:1 was:6 eg:1 leading:1 naturally:1 function:22 trivializes:1 journ:1 constants:1 form:10 some:7 acknowledgement:1 identification:2 laplacians:1 extended:3 back:1 heat:1 construction:1 link:1 intern:1 russian:1 line:3 irreversible:1 proposal:1 dist:1 coupling:1 persisting:1 made:1 wise:1 mat:2 versions:1 whether:3 inside:1 smooth:2 up:3 us:23 tell:1 probabilists:1 below:5 convince:1 complications:1 submitting:1 continuously:1 fluctuations:1 problem:30 more:2 called:5 poincare:1 strongly:5 interval:10 associated:14 fokkerplanck:1 difficulty:1 certain:7 abstract:2 received:1 covers:1 general:8 satisfied:1 chap:1 viewpoint:1 exist:1 physica:1 research:1 encompass:2 annoying:1 distributions:1 indirect:1 physical:9 incorrect:1 confine:1 functions:18 transitions:1 eventual:1 ingredients:1 amounts:1 when:4 defined:11 invalid:1 arctan:6 coefficient:2 field:1 other:4 make:1 investigations:1 spatial:5 test:1 mathematics:1 defines:1 conclusion:1 node:6 picture:4 differential:10 repeat:1 conventionally:1 accidental:2 parametrix:1 setting:1 problems:3 carmona:1 much:2 generated:3 important:2 bounded:10 allowing:1 diffusive:2 included:1 double:2 sides:1 structure:1 building:1 x4:8 backward:2 implies:4 factorized:2 assume:5 normally:1 evy:2 required:1 barriers:1 together:1 indirectly:1 4n:1 scientific:1 ln:4 nelson:2 time:43 appl:1 8th:1 original:2 restored:1 basically:1
|
quant-ph9802005.txt |@word since:4 sci:1 consider:5 crucial:1 blanchard:3 results:1 fluids:1 stratonovich:1 eds:4 horsthemke:1 generalize:1 overlap:1 cameron:6 mention:1 exceptional:1 conservative:1 appropriately:1 whose:10 preserves:1 inverse:1 const:2 ginibre:1 arthurs:1 disposal:1 diffusions:2 unboundedness:1 vigier:1 uniqueness:1 ny:7 preserved:1 excluded:1 skip:1 lore:1 stochastic:15 analogous:1 characterised:1 inform:1 started:1 karlin:1 supported:1 consequently:1 verw:3 very:4 brownian:13 construction:1 rise:6 springer:13 seemingly:1 choice:6 katata:1 formula:14 difference:2 fakult:1 encounter:2 generalised:1 obvious:2 narnhofer:1 λat:1 hamiltonian:3 transmission:3 issue:1 notes:5 having:1 omitted:2 solution:9 large:2 discrete:1 interpolating:2 manifestly:1 markov:4 shows:1 der:1 relative:2 prevent:1 unexpected:1 force:8 foliating:1 lecture:1 consistent:2 estimates:1 direct:1 sign:3 jump:1 imply:1 perspective:1 pass:1 further:1 dynamics:9 theories:1 jamison:1 expressions:1 canonical:1 even:1 established:1 what:4 nonlinear:1 filtration:2 stands:3 rate:3 inputoutput:1 nagasawa:2 diffusing:1 expressed:1 current:3 consistently:1 version:2 above:2 glimm:1 shared:1 unrestricted:4 bouleau:1 method:2 publications:1 philippe:1 outgoing:1 ρv:11 nonlinearly:1 degree:1 respectively:2 never:1 here:9 behaviour:1 2m:1 sinh:1 address:1 path:12 along:1 quite:4 equations:7 appears:3 change:2 transfer:1 obtained:1 remark:2 property:4 passing:1 pressure:2 institute:1 involved:2 study:1 larger:1 allows:3 reason:1 reports:2 adopt:1 suggests:1 accomplished:1 symp:1 krohn:3 chaos:1 domains:2 unwanted:1 encountered:1 special:1 changes:1 involves:1 uniquely:2 boundedness:1 lefever:1 deterministic:3 useful:1 family:2 merely:1 substitution:1 h3:1 compare:2 limt:1 coinciding:1 feller:8 univ:3 planck:9 linearly:1 identically:1 henri:3 feb:1 takes:3 would:3 commun:4 probabilities:1 positive:8 h0:1 grounds:1 negative:1 hilbert:1 almost:2 approach:1 call:1 therefore:1 renormalisation:2 hirsch:1 taken:1 scope:1 associated:2 meyer:2 type:4 theoretical:2 reflects:1 more:8 introducing:1 compensated:1 th:1 clearly:3 operators:2 postulated:1 odinger:10 validity:4 integrate:1 berlin:13 basically:4 particular:3 known:8 cases:3 conditioned:1 iii:2 nodes:1 must:6 states:2 account:1 defines:2 reed:2 effectively:2 equation:21 oscillator:2 modified:2 radon:6 reappear:1 remain:2 infinitesimal:1 values:3 ρt:2 concepts:2 following:5 making:1 clarendon:1 trans:2 averages:1 example:7 control:4 f1:2 f2:2 indicated:1 give:7 process:47 inaccessible:14 purposes:1 implementations:1 sample:9 weighting:1 application:1 allowed:1 sought:1 liptser:2 robinson:1 forms:1 absolute:6 needs:1 soc:2 ωdx:1 noises:1 provide:1 discussion:14 means:3 feature:1 bn:1 write:1 located:1 nontrivial:1 larsen:1 criterion:1 adapted:1 significance:1 answer:2 fix:1 field:1 axis:2 parameter:1 ensemble:1 gordon:1 simplicity:1 product:1 description:1 communicating:3 may:3 after:1 singularities:1 expectation:1 consequence:4 breach:1 inst:3 induce:1 physik:1 hn:1 law:4 data:8 parallel:1 namely:2 2x2:1 natural:26 dynamical:3 sobolev:1 light:1 approximation:1 explicit:5 correspond:1 st:1 encompassing:1 so:5 realizes:1 rellich:2 representation:7 element:1 looking:3 make:3 martin:6 restriction:1 holds:3 kbn:1 words:1 kampen:1 indeed:2 over:1 spectral:1 satisfied:1 cross:3 course:2 wiener:25 localised:1 through:5 motions:3 spohn:1 mentioned:1 existence:4 kinetic:2 deducing:3 hloc:1 before:5 girsanov:6 exclusion:1 chandrasekhar:1 la:2 chosen:2 interesting:2 dellacherie:1 tλ:3 vicinity:1 lect:4 attraction:1 permanent:1 microscopic:4 systems:3 τx:1 communication:1 covered:1 τr:5 deformation:1 eventually:1 them:7 h1:1 affected:1 outlined:1 evolution:2 reflected:1 framework:3 touching:1 repulsive:1 effects:2 they:2 half:4 oxford:1 singularity:1 now:2 transparent:1 2t:5 eigenvalue:1 term:1 name:1 profound:1 always:2 university:1 approximant:1 2d:18 ussr:1 l2:4 2a:2 each:5 disregard:1 found:2 universit:1 higher:3 side:2 2j:2 mean:5 homogeneous:4 different:1 domain:4 differential:7 dictated:1 footing:1 formulate:1 dµω:2 ed:4 energy:1 gaussian:1 used:2 applicable:2 poincare:3 frequency:2 ey:1 connect:1 entering:1 measure:28 quantum:7 our:14 operation:1 balance:2 event:2 neighbourhood:1 out:1 respects:3 simplify:1 ezawa:1 carlen:1 demonstration:1 space:6 gradient:2 restricted:5 integrates:1 singular:1 induces:4 investigate:1 rd:2 replacing:2 acting:1 weighted:1 hill:1 izv:1 i0:2 denoted:1 py:1 rn:2 induced:3 ref:13 originally:2 independence:1 hydrodynamic:3 numerical:1 theory:12 barrier:4 associate:2 gardiner:1 divergence:1 little:1 free:1 standard:16 admits:3 completely:1 surely:1 classifying:1 ori:1 transitions:1 relat:2 monographs:1 generate:2 defining:1 definition:2 dirichlet:6 retained:2 r1:36 r2:25 applications:3 via:3 transition:12 notorious:1 times:2 motion:14 turn:2 int:1 place:2 derivations:1 leading:1 hence:5 approaching:1 first:6 origin:3 features:1 probability:23 reveals:1 relate:1 variables:1 number:1 transform:1 least:4 another:4 comprises:1 reached:2 unattainable:2 precisely:2 open:3 appl:2 xt:3 xu:1 taniguchi:1 given:20 necessarily:2 exists:2 unknown:2 adjoint:5 amsterdam:2 system:1 construct:2 priority:1 their:5 dewitt:1 borel:2 bharucha:1 statement:2 convention:2 dt2:1 stora:1 ehrenfest:1 speaking:1 correctly:1 garbaczewski:5 fraction:1 relationship:1 ratio:2 reversed:1 continuous:5 measurable:1 mehler:1 part:1 universally:1 extensions:1 manifestation:1 x2:4 x0:8 representing:1 reverses:1 lebowitz:1 diffusion:48 unexpectedly:1 kind:1 determines:1 holland:2 princeton:4 lnρ:3 approximations:1 evaporates:1 depends:1 modelled:1 classes:1 onedimensional:1 mackey:1 gives:3 distinguished:1 developement:1 derivative:7 respecting:1 fluctuation:1 dynamically:5 modern:2 argument:1 regularity:1 affirmative:1 say:1 decomposition:2 simultaneously:1 close:2 need:1 concentration:1 constrained:5 apparently:5 linked:1 viewed:2 acceleration:2 paths:9 realm:1 newtonian:1 zero:10 academic:5 identification:1 lim:5 self:5 able:1 predominantly:1 oriented:1 high:1 potential:10 absorbed:1 take:1 birkh:1 interior:4 coincide:1 accuracy:1 kac:16 formulas:3 towards:1 fundamental:6 shall:3 measures:4 reach:6 paid:1 falls:1 most:5 boltzmann:1 diffusion:3 smoluchowski:9 ht:2 phase:2 utilize:1 subset:1 probabilistic:4 class:5 conspicuous:1 localizable:1 chemistry:1 especially:1 consequences:1 considered:4 crossing:1 clear:2 sometimes:1 stronger:1 kaiserslautern:1 drifts:9 order:1 traditional:3 feynman:14 points:2 rev:3 principle:3 exp:22 velocity:2 dispersed:1 typical:1 physics:11 notion:1 fact:6 laws:3 shepp:1 drastically:1 particularly:1 nikodym:6 show:1 absorbing:4 random:13 terminate:1 friction:3 converge:1 notations:2 bring:1 solutions:4 label:1 d2:1 ground:1 access:1 based:1 assigning:1 varadhan:1 much:1 enough:1 fortunately:1 should:4 analytic:2 only:2 going:1 corresponds:1 høegh:3 molecules:1 factor:1 irrelevant:1 integrable:4 hamiltonians:1 local:11 interested:2 continuity:8 do:1 narrows:1 hit:1 establishes:1 invoke:1 get:1 dependent:1 familiar:5 zheng:3 de:2 fluid:2 bratteli:1 joint:1 cannot:2 dz:2 streit:3 dx:23 dy:9 geb:3 dt:5 du:6 ds:1 areas:3 processes:17 constituents:1 densities:3 fields:6 arxiv:1 zambrini:3 yield:2 reid:1 bad:1 clocks:1 schemes:1 common:3 characteristic:1 implication:1 pertains:2 valid:3 view:8 happen:1 kernel:11 set:14 modulo:2 statistical:6 reference:4 notational:2 guerra:1 frame:1 kolmogorov:3 lett:3 up:1 observed:2 see:11 individual:1 inequivalent:1 dµ:12 incorporating:1 definitely:3 satisfying:1 likelihood:2 interacting:1 kl:1 αx:1 away:1 definite:2 its:11 boundaries:40 state:1 various:2 gases:1 closed:2 between:9 boundary:28 hold:1 conditions:1 x20:1 available:1 notice:10 infinite:2 terms:6 extend:1 nature:1 importance:1 arises:1 attention:2 weak:1 however:7 physicist:1 vanishing:1 modeling:1 killing:1 come:1 problem:16 observer:1 both:5 essentially:5 instant:2 generator:2 0t:1 many:1 pertain:1 according:4 previously:1 called:4 etc:1 admit:1 purely:1 context:4 distinction:2 contribution:1 expression:3 experimental:2 albeit:4 comment:1 originating:2 xx0:1 co:1 labelled:1 point:10 hλ:1 overview:1 ydy:1 harmonic:5 walk:1 dimensional:3 ii:3 taylor:1 simply:1 math:18 affiliated:1 fukushima:3 respect:14 worthwhile:2 kernels:3 transformations:1 second:6 addition:1 discrimination:1 px:19 locally:2 due:4 expφ:1 hitting:2 devise:1 hille:1 boston:2 technical:1 ph:4 algebras:1 ann:5 pl:1 define:2 ergodic:1 adopted:1 corresponding:2 bypass:1 molchanov:1 restrictions:1 safely:1 sufficient:2 montroll:1 gas:1 modelling:1 kramers:3 observe:1 understand:1 representative:1 angles:1 demand:2 recoil:1 dµx:7 albeverio:5 denote:1 fokker:9 present:1 case:14 limits:1 subsets:1 might:2 originate:1 ǫn:1 value:1 will:1 euclidean:3 while:5 replaced:2 momentum:3 evaluating:1 applies:1 stopping:1 situation:3 endpoints:1 elaborate:1 wroclaw:2 notation:1 coupled:1 chaotic:2 characteristics:1 refs:11 thus:5 non:6 surface:1 equal:3 respected:2 reads:1 exit:1 nenciu:1 adjointness:1 ia:2 mod:1 inf:1 trival:1 piotr:1 different:2 because:2 grant:1 perhaps:2 identities:1 granted:2 belong:2 connection:2 same:12 any:10 khandekar:2 logan:1 dµλ:1 quant:1 emphasize:2 modification:1 finite:14 composition:1 φn:3 interpolation:1 status:1 independent:5 literature:4 infinity:7 skorohod:2 solved:2 singapore:1 i1:1 absorb:1 trajectories:2 mutual:1 flows:2 hand:2 v0:1 usually:1 moment:1 moving:1 auser:1 potentials:1 infinite:5 totally:1 tradition:1 identity:3 prescribed:1 scarcely:1 schr:10 proceed:2 matters:1 nevertheless:1 whole:2 poland:1 no:10 well:11 analysis:3 obviously:3 iv:1 concrete:1 directly:2 without:2 solve:1 components:1 sets:9 analyzable:1 recasting:1 latter:1 left:3 next:1 diffusions:21 less:1 being:4 generally:4 klauder:2 newton:2 vanishes:3 press:8 underlying:1 identify:1 vα:4 world:1 touch:2 λn:2 pertaining:1 previous:4 adv:1 presutti:1 absorptive:1 preprint:1 classification:3 lebesgue:3 density:22 seems:1 except:6 mathematically:1 rˆole:1 extends:2 attractive:2 easy:2 theorem:4 input:5 semigroup:5 formal:1 transformation:2 euler:3 real:1 rescaled:3 aspects:1 mcgraw:1 casually:2 loss:2 rules:1 possible:4 admitting:1 cf:4 possibly:3 vβ:4 know:3 convenient:1 confined:3 pertinent:4 bit:1 unique:7 2q:1 insert:1 theor:1 necessary:3 like:2 semi:7 wahrsch:3 follows:1 reduces:3 incidental:1 exploit:1 admitted:1 yor:1 specific:2 continue:1 either:3 integrals:2 arbitrary:1 multiplicative:1 output:3 accelerations:6 acquire:1 stationary:5 essential:1 terminology:2 lends:1 mathematical:6 calculus:1 satisfactory:1 right:3 gruyter:1 methods:4 deal:4 sends:1 conditional:10 phenomena:2 elements:1 b0:1 examples:1 choosing:1 specified:2 duration:2 finite:1 repelling:1 investigating:1 happens:1 provided:3 vol:11 scale:1 primary:1 dimensions:3 broad:1 avoid:1 though:1 langevin:1 integration:7 comments:1 otherwise:1 flow:2 shiryayev:2 inaccessibility:1 select:2 provides:1 particles:4 bessel:8 prob:5 demonstrated:2 lacroix:1 noise:4 scientific:1 reaching:1 problems:3 equivalent:9 l1:6 restrictive:1 step:1 weil:1 bp:1 although:5 inherent:1 additive:2 relating:1 refers:4 normalisation:2 properties:2 pw:12 stokes:1 about:1 face:2 differentiability:1 pλ:2 am:2 factors:1 o:1 simulation:1 deserves:1 regular:1 ensure:1 obeys:1 yasue:1 schuss:1 germany:1 introduced:4 slightly:2 other:1 automatically:3 considerations:2 mechanics:8 own:1 statements:1 markovian:3 prohibit:1 h2:1 unbounded:2 into:5 within:4 integral:14 functional:6 down:1 tanaka:1 bielefeld:2 references:1 interpreted:1 operator:3 proportional:2 substitutions:2 donsker:1 statistics:5 van:1 weight:1 few:1 normalised:1 nodal:3 strictly:7 there:11 approximate:1 specifically:1 sampling:1 conservation:4 handbook:1 way:5 irrespective:2 forward:7 ψn:1 conceivable:1 analyze:3 was:3 function:4 north:2 form:15 compressible:1 some:3 but:7 volume:5 heat:2 illuminating:2 link:1 related:4 line:5 sense:2 true:3 themselves:1 partially:1 iterates:1 made:1 compute:1 jaffe:1 evident:1 instructive:1 whether:1 wish:1 inside:1 smooth:2 particle:4 us:15 aebi:1 liouville:1 limit:1 ωn:1 distribution:8 display:1 b1:2 detailed:2 sturm:1 trotter:1 constant:6 b2:6 labels:1 classic:2 defined:4 certain:3 abstract:1 b3:1 condition:1 life:1 general:3 transl:1 proper:2 chap:2 associates:1 masi:1 formulation:1 encompass:1 annoying:1 distributions:1 approximated:1 physical:3 again:1 functions:3 compared:1 entirely:2 integrability:3 variety:1 amounts:2 allow:1 when:4 detail:2 field:10 narrowing:1 priori:2 details:2 mathematics:2 shin:1 confine:1 hydrodynamical:3 concerning:1 unbalanced:1 node:1 stat:1 apparent:1 simon:4 conventionally:1 drift:11 carmona:3 2n:1 realisations:1 bounded:6 variable:4 risken:1 structure:2 assert:1 combe:1 implies:10 auxiliary:7 glass:1 assume:3 cauchy:1 4t:1 interval:8 rather:1 barriers:2 together:1 original:3 mass:1 nelson:3 time:28 lives:1 4d:2 backward:10 starting:2 itˆo:4 external:4
|
quant-ph9802006.txt |@word secondly:1 concept:2 partial:1 consider:4 pointing:1 represent:2 hist:1 desirable:1 idealised:4 existing:1 leads:1 eds:2 commute:1 c2:9 consists:1 displaying:1 reasoning:1 whose:3 tr:7 quadruple:1 environment:4 summarised:1 grabowski:1 under:2 passion:1 include:1 indicating:2 ρa:7 attribution:2 stud:1 made:1 orthogonal:11 dynamic:1 springer:3 wave:3 every:2 specific:1 condition:10 interact:2 ceased:1 tra:2 turns:1 applicable:1 leave:1 discrete:2 vector:1 avoiding:1 small:1 trs:2 unsharp:27 noted:2 upper:5 says:1 occurrence:2 dealing:2 measurable:2 second:6 equal:1 further:1 dynamics:1 linear:1 spectral:1 pφ1:1 what:6 developed:1 appear:3 apparatus:5 giving:1 section:3 selected:2 m31:1 current:3 consistently:2 version:1 suspect:1 goes:1 new:1 ever:1 consisting:1 body:1 evolving:1 full:1 notions:1 αij:2 respectively:1 component:2 here:9 desired:1 objects:2 free:1 situation:3 represented:5 along:3 strong:1 equations:1 imperfections:1 mod:1 obtained:1 great:1 technical:1 involved:1 vectors:3 allows:4 p2:4 amount:1 simultaneous:2 θjl:1 domains:1 surely:1 conveniently:2 suitable:2 studies:1 options:1 summarising:1 genuinely:4 uniquely:1 emerge:1 formulated:1 projection:2 family:2 merely:1 explained:1 logical:1 outcomes:6 put:1 flexibility:1 stern:2 resolutions:2 operational:1 establish:1 planck:1 unit:3 diagonality:1 quasi:3 feb:1 takes:2 would:17 physics:1 distinct:1 positive:2 etc:1 eρ:1 finally:2 properties:1 ψj:1 definiteness:3 explicitly:1 totality:1 vi:1 taken:4 themselves:1 type:2 more:5 wavefunctions:1 definition:1 correlate:1 operators:7 pursuing:1 occurred:1 berlin:2 virtue:1 particular:2 known:2 foundations:1 cases:1 iii:1 must:1 me:3 high:2 account:4 valued:3 ρe:1 evolution:2 abner:1 recall:1 representing:1 modified:2 theories:3 reproduce:1 huge:1 ρs:5 values:11 evolved:1 following:7 my:1 example:9 indicated:2 give:2 impossibility:1 sense:1 states:39 ia:4 assumptions:2 want:1 allowed:2 sought:1 sharp:10 dennis:1 conversely:2 occur:5 simple:2 verlag:1 information:2 needs:1 requirements:1 mutually:7 provide:2 describes:1 exceptional:1 feature:1 orthogonality:1 write:1 how:1 pure:5 instead:1 hierarchical:1 map:2 alternative:1 algebra:1 may:10 after:9 variant:1 containing:1 questioning:1 hence:3 independent:1 demonstrating:1 types:1 overtaken:1 correspond:5 assign:1 rather:2 so:6 allow:4 correlation:2 representation:2 sa:10 looking:1 scintillation:3 order:3 talk:1 horne:1 serving:1 interpretation:10 words:2 september:1 essence:1 satisfied:1 lahti:3 course:1 xi:16 including:2 argued:1 still:2 pointer:25 its:4 tendency:1 before:1 controllable:1 group:1 monitor:1 expectations:1 resort:2 permanent:1 microscopic:2 systems:3 persist:1 inconsistencies:1 mail:1 hidden:1 might:1 spreading:1 virtually:1 maximal:1 non:1 influences:1 practice:1 nonorthogonal:6 mention:1 they:9 compound:5 own:1 eigenvalue:1 lies:1 always:1 university:2 θik:1 evade:1 realistic:2 each:1 side:2 referred:1 schemes:2 ei:4 exhaust:1 revised:2 idea:3 deterministically:1 measurement:46 quantum:25 our:1 programmes:1 adequately:1 special:1 out:4 projections:2 stands:1 space:17 since:1 denotes:2 content:1 acting:1 emerged:1 objectivity:1 viable:1 math:1 shows:2 evolve:1 nonorthogonality:1 theory:3 hull:2 mechanisms:2 possibility:1 quite:2 attributions:1 included:1 imagine:1 maths:1 incorporates:1 pairs:1 interaction:2 derivation:1 starts:1 could:6 persists:1 ask:1 wrong:1 times:2 turn:1 place:2 δij:1 δik:1 consequence:1 view:1 think:2 speeds:1 first:5 initial:6 xn:2 features:1 probability:9 radical:1 variables:1 number:1 postmeasurement:2 production:1 microsystems:1 reached:2 precisely:1 open:1 illustrate:1 degeneracies:1 given:13 fair:1 indicate:3 introduction:2 adjoint:2 system:18 approximately:1 realistically:1 their:6 too:1 statement:3 α2i:3 scheme:7 final:7 gives:1 relies:1 imperfect:3 collapse:2 tool:1 serve:3 immediate:1 lnp:2 part:1 somewhat:1 fuzzy:1 objectification:7 than:2 specify:1 distance:1 kind:2 determines:1 third:1 showed:1 accordance:1 ic:1 pointers:9 enabled:1 biorthogonal:3 modelled:4 limiting:1 recording:5 matter:1 supposed:1 reproduction:1 were:1 outcome:4 pvd:4 m2:1 cohen:1 measure:11 say:3 need:1 elsevier:1 seem:2 any:5 forced:1 subsystems:1 genuine:1 describe:1 self:2 able:2 note:1 instance:1 ideal:1 internal:2 take:1 measurability:1 objective:1 solve:1 heisenberg:2 even:5 begin:1 sure:1 trace:1 though:1 α1i:3 measures:12 molecule:1 said:2 preparations:1 device:6 measured:11 class:1 singled:1 deviations:1 considered:1 clear:3 partition:1 implications:1 2nd:1 proceedings:1 points:1 mechanical:2 typically:1 notion:7 fact:6 applied:1 precise:3 momenta:1 selection:1 show:2 characterisation:1 probe:13 spaces:1 relation:2 gerlach:2 decompositions:1 trivial:1 find:1 help:1 completion:1 cell:1 based:2 situations:4 explain:2 should:2 being:1 only:5 experiment:2 intrinsically:1 molecules:3 indeed:1 adequate:1 axiom:1 hope:1 probabilities:2 do:5 mixture:4 above:5 means:3 familiar:1 joint:2 cannot:3 ϕi:1 nearly:3 dx:2 applying:1 becomes:1 regarding:1 arxiv:1 fixes:1 yield:1 investigate:1 hae:4 ascertain:1 fixed:1 pertains:1 require:2 remains:1 predictive:1 θij:5 exists:2 physically:1 notice:3 packet:2 relative:1 edition:1 see:2 individual:1 sec:1 result:2 discussions:1 terms:1 embarking:1 dropping:1 registering:1 consistency:3 subsequent:1 review:1 definite:16 representatives:1 eigenstates:3 symmetric:1 halves:1 state:33 difficulties:3 various:1 mittelstaedt:1 closed:1 between:1 mathematical:1 reading:10 conditions:2 available:1 interpretational:2 ends:1 recently:1 nature:3 screen:10 however:3 ignorance:1 separately:1 uρ:1 holds:1 observer:4 motivations:1 observable:32 interpretations:6 last:2 many:1 region:2 uncertainty:1 according:4 fulfilled:1 april:1 contribution:1 ensure:2 grounds:1 relevant:1 point:1 reasons:1 guaranteed:1 cf:1 imperfection:1 dimensional:1 concluding:1 ψi:1 moreover:1 ae:1 selfadjoint:2 pv:7 raise:1 capable:1 addition:1 three:1 been:6 appears:4 workshop:1 indicators:1 pk:2 ph:1 pi:2 pm:4 arises:4 families:1 both:1 quantities:8 sufficient:2 subspace:1 requires:3 readings:1 observers:1 bohmian:1 prescription:1 c1:9 repetition:1 spin:2 present:4 case:8 noncommuting:2 p1:4 value:11 will:22 while:6 promising:1 ensuing:3 property:1 taking:1 unitary:6 coupled:1 vol:3 reproducibility:5 von:2 thus:3 them:2 encountered:2 φij:1 busch:7 ib:3 disappear:1 different:2 perhaps:1 stein:2 sensitive:3 perform:1 make:5 who:1 princeton:2 unity:1 quant:1 arguments:1 mixtures:1 modification:1 φi:4 ludwig:1 infer:1 development:1 fairly:3 extended:1 infinity:1 assigns:1 assignment:1 upon:1 effect:1 hand:3 moment:1 necessity:1 entanglement:1 changing:1 recent:1 eigenvectors:1 lower:6 stipulated:1 reflection:1 scenario:1 simplicity:1 well:3 inherit:1 severe:1 utrecht:2 involves:1 components:2 sets:1 firstly:1 position:2 model:4 arising:1 proposed:2 moments:2 generally:1 half:6 reviewed:2 product:2 underlying:1 potentiality:1 positions:2 paul:1 reality:1 macroscopic:7 yet:1 captured:1 kluwer:1 regarded:1 seems:3 emphasis:1 pov:12 concerns:1 collections:1 easy:1 theorem:9 constant:1 role:1 unitarity:1 eigenstate:4 momentum:1 real:1 lacking:1 represents:3 rules:3 possible:1 game:1 quest:1 entangled:1 background:1 press:2 world:1 variants:1 unique:2 preparatory:1 tail:1 necessary:2 like:1 particle:4 follows:1 strictly:2 serves:1 facing:1 either:3 arbitrary:2 notorious:1 coexistent:1 essential:1 specifies:1 sketch:1 neumann:2 classical:5 pϕ:1 conditional:9 some:13 urgent:1 nothing:1 examples:1 respect:3 proper:2 happens:1 provided:1 scale:2 describing:3 axiomatic:1 lead:2 sufficiently:1 tools:1 avoid:1 measurements:8 recorded:1 overly:1 overlap:1 ubiquity:1 does:4 decomposition:1 expressing:1 happened:1 minimal:1 measuring:4 pr:3 object:29 run:1 inaccurate:1 dieks:2 pose:1 analysed:1 step:2 shimony:2 described:6 hilbert:8 stage:4 chapter:1 about:2 actual:4 carried:1 extension:2 certainty:1 basis:1 accepts:1 reduced:3 nonvanishing:1 covariant:1 range:1 involving:1 plus:5 modal:13 mixed:2 denote:1 pϕ1:4 automatically:1 considerations:1 localised:6 assignments:1 into:2 within:1 bound:1 due:3 accommodate:2 phase:8 appropriate:2 references:1 registration:1 operator:3 factor:2 statistics:6 normalised:3 assumed:2 suffice:1 there:7 question:6 approximate:1 long:1 why:1 accordingly:1 borel:1 inner:1 way:3 conceivable:2 probes:1 assumes:1 naturally:2 hard:1 form:4 offer:1 δkl:1 regard:1 but:8 construction:1 encoded:1 line:2 ha:2 true:1 happening:1 october:1 compute:1 evident:1 versions:2 whether:5 wish:2 up:3 us:1 dordrecht:1 operationally:1 uk:2 problem:14 stages:1 called:1 mechanics:9 fulfills:1 ac:1 phil:1 associated:2 worthwhile:1 int:1 certain:3 contribute:1 linearity:1 general:6 single:2 exist:3 formulation:1 corresponding:5 formalism:2 distributions:1 physical:1 again:3 mutual:1 compared:1 ideally:1 no:5 amounts:1 when:5 detail:1 χij:2 other:5 remarks:1 spatial:2 department:1 mathematics:1 interpretable:1 forcing:1 deviate:1 briefly:1 elements:2 kinds:1 accidental:1 models:1 stachel:1 june:1 representable:1 variation:1 much:1 ξi:1 chance:1 bounded:1 allowing:1 throughout:1 bases:1 independently:1 correlated:2 implies:1 coupling:4 inevitability:1 practically:1 assume:5 resolution:1 packets:1 theor:1 rule:6 original:1 considering:2 ascertained:2 experimenters:2 time:2 observables:25 starting:1 having:2
|
quant-ph9802007.txt |@word secondly:1 code:29 consider:5 focus:1 unchanged:1 gf:1 commute:7 generalize:1 computation:10 go:1 follow:1 causes:1 relationships:1 whose:1 cardinality:1 alamos:1 finally:1 uniquely:1 swap:1 th:1 under:3 analogous:1 straightforward:2 orthogonal:1 very:2 induce:1 results:5 induced:2 presented:1 transmission:1 turns:4 michael:1 zds:3 large:1 discrete:1 science:1 small:1 eigenvalues:4 ωam:3 zd:6 direct:1 zb:1 likely:3 zx:1 zz:1 further:1 odd:2 linear:3 even:4 established:1 what:1 errors:11 appear:1 section:2 version:2 above:1 values:1 method:1 satisfy:3 full:10 respectively:2 never:1 here:2 inverse:2 along:2 z1:3 change:2 suitably:1 involved:2 qudits:37 changed:1 leaving:1 products:2 m3j:1 permutation:2 tolerantly:2 fourier:3 composed:2 via:1 useful:3 projection:1 extra:1 logical:5 losing:1 decrease:1 apply:3 total:1 tools:1 clifford:23 alamitos:1 use:4 feb:1 takes:1 would:4 prove:1 give:3 toffoli:6 bases:3 overhead:1 therefore:15 m3:9 m2:2 taken:1 themselves:1 more:8 normalizer:1 becomes:2 operators:37 occurred:1 stick:1 particular:1 known:1 foundations:1 hold:1 producing:1 must:3 involve:1 recall:1 originally:2 work:4 cat:7 ij:1 obvious:1 stabilizer:40 following:1 trans:1 root:1 proof:9 control:3 do:6 states:12 performed:7 times:1 information:2 ones:1 syndrome:3 provide:1 verify:1 discussion:1 acts:1 37th:1 maps:4 gate:30 map:1 product:5 blocks:8 may:4 ancilla:23 after:4 derived:1 wrong:1 produce:4 gottesman:3 multiplication:1 representations:1 data:13 grow:1 natural:2 effective:1 computations:1 st:1 perhaps:1 cannot:2 so:16 fundamental:1 xqp:1 m1:2 order:6 operations:7 interpretation:1 ith:4 numbers:1 over:3 move:1 paper:3 through:1 left:1 ieee:2 its:1 before:1 style:1 group:68 thank:1 how:5 chosen:1 conjugation:2 actually:2 forms:1 detected:1 systems:8 potentially:1 main:1 might:1 maximal:1 them:1 stabilizers:1 than:4 introduce:2 primary:1 steane:1 they:8 instead:11 rotation:1 now:11 discuss:1 suppose:5 eigenvalue:7 name:1 always:1 capability:1 t6:1 2a:1 each:3 did:1 2n:1 higher:9 2k:1 em:1 series:1 reduce:1 related:1 society:1 knill:4 measurement:12 quantum:24 laboratory:1 operation:3 beyond:3 out:5 qudit:41 shown:2 accomplish:1 matrix:1 space:7 izi:1 furthermore:1 since:4 rev:6 increase:1 transforming:1 daniel:1 suggesting:1 get:3 gov:1 cause:1 correct:3 theory:3 confidence:1 given:7 like:2 complicated:1 conditioning:1 members:1 put:2 generate:6 pairs:1 could:4 computers:1 tolerant:12 disturbed:1 place:1 unknown:1 corrections:1 first:15 major:1 twodimensional:1 encoding:1 xa:1 coding:5 number:7 xd:6 restrict:2 simplified:1 relations:1 another:1 impossible:1 precisely:1 little:1 their:3 introduction:1 unencoded:3 interact:2 system:4 least:1 needed:1 cats:2 too:1 bits:1 final:1 gives:2 collapse:1 completed:1 exactly:2 part:1 somewhat:1 x2:3 x1:2 completes:3 serv:1 third:3 sloane:2 structures:1 require:1 second:8 individual:1 were:2 extraspecial:1 distinguished:1 correction:8 generalization:9 already:1 say:1 manner:1 initialized:1 need:9 element:2 any:24 vulnerable:1 generalizes:4 issue:1 depending:1 able:3 note:9 instance:1 potential:2 generalized:1 new:2 many:6 added:1 unless:1 though:1 price:1 anticommute:1 simplify:1 significant:1 pair:7 acknowledgements:1 measured:4 class:2 latex:1 discarding:1 clear:1 proceedings:1 subgroup:1 sum:26 fact:4 shor:10 show:3 registers:1 relation:1 find:2 make:1 much:1 state:27 should:4 only:9 anticommutes:1 generators:12 factor:1 interested:1 sure:1 dn:2 abelian:2 his:1 quantph:2 means:4 occuring:2 simplest:2 overall:2 xdt:2 xdr:3 probably:1 during:1 sorts:1 target:1 prime:8 transversal:5 places:1 arxiv:1 processed:1 contain:1 fixed:1 set:12 modulo:1 national:1 up:7 see:3 computer:10 sec:1 result:5 discussions:1 analog:2 creating:1 detect:1 tensor:6 outside:1 various:2 jth:2 between:8 invariant:2 subscript:1 preserve:1 ends:2 ability:2 qubits:10 attention:2 however:6 js:2 jj:3 rapidly:1 ja:1 both:2 protect:1 last:4 fault:14 la:1 against:2 gotten:2 protection:1 present:2 divincenzo:2 qubit:10 otherwise:3 unclear:1 nonbinary:1 point:2 ca:1 corresponds:1 whatever:1 dimensional:20 ab:5 iterations:1 article:1 slots:1 considering:1 complication:1 described:2 transformations:3 addition:1 three:6 been:2 spread:3 z2:2 applying:5 ph:8 universal:7 empty:2 choose:3 generating:1 describe:2 corresponding:5 versa:1 commutes:4 suppress:1 sufficient:2 subspace:2 essentially:1 wish:3 understand:1 worked:1 those:2 case:11 look:1 leave:2 reliable:1 harder:1 eigenstate:3 will:37 replaced:1 error:21 situation:1 leaves:2 procedure:2 unitary:2 laflamme:2 thus:1 non:1 itself:2 greater:1 binary:2 different:9 verified:1 perform:28 things:1 began:1 same:9 tells:1 unity:1 quant:8 arguments:1 pauli:29 units:1 physical:2 difficult:2 independent:2 used:4 raymond:1 largely:1 macro:1 well:3 deal:1 without:1 position:1 kets:1 consisted:1 gates:19 construct:4 protocol:1 calderbank:2 just:5 when:9 rest:1 identify:1 aspect:1 positions:1 followed:1 eigenstates:2 previous:1 adding:1 preprint:1 generator:1 had:1 improvement:2 source:1 valid:2 lett:3 easy:2 extensive:2 transformation:5 nielsen:1 easily:5 possible:4 entangled:5 similarly:1 press:1 using:7 bit:3 correcting:2 mod:5 desire:1 rotate:1 necessary:5 helpful:3 alternatively:1 performing:6 separately:1 communications:2 private:1 imposes:1 steps:3 either:2 arbitrary:3 multiplicative:1 become:2 works:1 parity:1 because:6 often:2 classical:6 sequence:1 conditional:1 some:5 back:1 repeat:1 choosing:2 specified:1 superposition:2 2d:1 dimensions:2 sufficiently:1 avoid:1 measurements:7 exceeding:1 per:1 conditionally:1 everything:3 does:2 provides:1 propagating:1 measuring:3 package:1 power:1 equivalent:1 aj:10 combines:1 step:5 conveyed:1 although:1 hadamard:1 hilbert:2 cnot:6 simpler:1 about:2 actual:1 anything:1 constraint:1 completing:2 codewords:2 factors:1 a2:1 plus:2 done:1 act:1 discard:3 introduced:1 consequently:1 block:20 xz:11 primitive:1 communication:1 into:2 within:2 integral:1 phase:9 appropriate:10 references:1 operator:20 additional:4 prepare:4 suffice:1 there:4 question:1 transform:3 long:1 los:2 pa:3 way:4 call:1 was:7 naturally:1 complete:1 form:6 anywhere:2 but:9 encode:2 repeated:1 construction:10 larger:1 encoded:25 removed:1 true:4 made:4 compute:1 consist:1 versions:2 whether:2 prevents:1 flip:1 us:6 ur:1 below:1 complications:1 demonstrate:1 similar:1 called:2 eigenvector:2 detailed:1 lanl:1 proved:1 ad:1 defined:1 recognize:1 abstract:1 measure:23 general:1 single:12 enable:1 our:3 controlled:1 commuting:1 check:1 constructed:3 again:4 extending:1 codes:23 know:1 no:4 rains:3 storage:1 other:5 d2n:1 symposium:1 elements:10 generates:1 ru:1 problems:1 prepared:1 generated:3 important:2 restore:1 structure:4 correlated:1 longer:1 vice:1 assume:4 required:1 weights:1 situations:1 time:2 far:1 decoherence:1 requires:1 original:2 once:2
|
quant-ph9802008.txt |@word gu:1 midpoint:1 consider:4 generalize:1 houches:1 research:5 contributions:1 rigidity:5 c0:2 monotonically:1 av:4 depending:3 th:4 under:3 indicating:1 sound:1 orthogonal:1 wave:11 electron:1 putting:1 summarized:1 mixing:1 affect:1 difference:1 matrices:1 condition:10 school:1 level:9 solution:3 session:1 progress:1 indices:2 eigenvalues:7 sidelengths:1 degeneracy:1 mishima:4 occurrence:1 findings:1 prediction:7 approximation:1 zero:1 gθ1:1 further:1 dynamics:2 estimated:3 spectral:6 nothing:1 nonlinear:1 appear:1 brackets:1 section:2 associate:2 current:1 poles:1 above:2 new:3 satisfy:1 degree:3 respectively:6 never:1 spacing:4 here:3 okubo:1 ranges:1 ρav:3 gesztesy:1 situation:1 consideration:1 strong:4 appears:1 logarithmic:1 obtained:1 remark:1 sobolev:1 shift:1 changed:1 allows:1 amount:1 krohn:1 poisson:5 akl:1 suitable:2 makes:4 examining:4 yamada:1 family:2 giannoni:1 summation:1 counts:1 feb:1 takes:2 prove:1 remains:2 contains:1 predictions:1 guideline:1 vol:5 ψm:3 taken:2 inthe:1 more:1 separated:1 becomes:2 naive:1 validity:2 dirichlet:1 normalized:1 particular:1 arranging:1 cases:2 iii:1 me:3 springer:1 tokyo:3 ed:1 equation:12 work:1 det:1 theories:1 values:2 hope:1 ms:1 example:1 proof:1 nearest:3 transition:5 renormalization:1 figure:1 expanding:1 organized:1 high:2 indicates:5 handle:2 linearized:2 scat:1 verlag:1 information:5 recovers:1 write:1 located:2 varies:1 assistant:1 enx:3 repulsion:2 allowable:1 parameter:2 sin:2 profile:1 simplicity:2 staircase:2 singular:1 our:2 after:1 different:1 reflect:1 applications:1 summarize:1 engineering:3 natural:1 dynamical:7 parameterized:1 exhibited:1 green:3 sect:5 fundamental:1 decreasing:1 order:3 hiroshi:2 over:2 eqs:2 displayed:1 perturbed:1 paper:4 statistical:5 japan:3 kinetic:1 still:2 its:9 tendency:1 features:1 regions:1 derive:1 xl:4 ln:5 logarithmically:1 coordinates:1 hm:2 microscopic:3 systems:10 main:1 might:2 into:1 lx:3 ly:3 maximal:3 non:1 integral:1 eiθ1:4 noticing:1 mention:1 billiard:12 tails:1 effects:1 they:1 symposium:1 nov:1 now:1 discuss:1 nos:1 represents:1 dirac:2 january:1 university:10 hamiltonian:3 magnitude:2 l2:4 each:3 2m:4 2n:1 mean:1 em:12 domain:1 en:12 another:1 series:1 energy:21 revised:1 gaussian:1 deficiency:2 owing:1 measure:3 quantum:22 laboratory:2 eq:14 iλc:1 shown:2 matrix:9 space:1 goe:8 restricted:1 since:3 rev:2 chaos:19 denotes:1 increase:1 may:1 conjectured:1 denoted:1 formula:2 induced:1 occurs:2 math:1 shows:3 foundation:1 trajectories:1 theory:4 voros:1 interactions:4 divergence:1 diagonal:2 possibility:1 ascending:1 clarify:2 threedimensional:1 complicated:1 york:2 besides:1 put:1 intermediate:1 interaction:2 impose:1 nonnegative:1 counterpart:1 unitarity:1 length:1 place:1 hence:1 ture:1 neglect:1 first:5 xk:12 xn:1 seeming:1 probability:1 relate:1 symbolic:1 number:14 restrict:2 seba:1 enlarged:1 directly:1 changing:1 precisely:1 size:1 given:5 perturbation:1 needed:1 introduction:1 adjoint:8 behaves:1 amsterdam:1 system:8 least:1 πm:3 πs:2 ukl:2 free:1 πx:1 scheme:2 final:1 gives:1 holden:1 tool:1 continuous:1 assumption:1 nolta:1 somewhat:2 authors:1 x1:26 december:1 wide:1 πy:1 gradual:2 holland:1 double:1 namely:2 ranging:1 determined:2 cheon:6 behaviors:1 interests:4 fig:7 saitama:11 generality:1 rewrite:1 argument:3 mehta:1 substantial:3 manner:2 seen:2 their:2 strength:16 min:1 general:4 convenient:1 self:7 billiards:6 note:1 sciences:4 fitting:1 generalized:1 satisfactory:1 indexed:1 so:1 computation:1 unperturbed:1 even:4 multiple:6 axiomatic:1 normal:1 rhs:1 measures:1 impurities:3 most:4 regular:1 connected:1 quantitative:1 phase:1 professor:4 neighboring:1 average:5 physica:1 kl:4 proceedings:1 points:2 tech:2 principle:1 exp:2 mechanical:2 physics:4 width:3 fact:3 drastically:1 honolulu:1 show:3 random:2 converge:1 spaces:1 relation:2 solutions:1 keywords:1 scatterer:14 trivial:1 find:1 principal:1 based:3 ensembles:1 spite:2 inflection:2 distributed:1 should:3 analytic:1 going:1 høegh:1 indeed:1 integrable:4 constant:2 rectangle:1 his:4 hit:1 gains:1 means:2 mainly:2 de:3 satisfied:1 ϕm:2 ϕn:20 kochi:5 dx:1 international:1 ds:2 closure:2 settings:1 approach:2 arxiv:1 motion:2 experiments:2 common:2 fixed:1 krein:2 vision:1 view:1 www:4 kernel:1 hθ:1 set:3 signify:1 exists:1 observed:2 edition:1 depends:2 computer:4 result:3 existence:1 close:3 satisfies:2 best:1 error:1 eigenfunctions:2 pattern:1 currently:4 symmetric:2 written:1 future:1 between:4 limit:1 boundary:4 conditions:3 email:4 notice:1 terms:3 nature:1 jp:8 weak:1 however:4 tum:1 contamination:1 modeling:1 distribution:5 received:4 hits:1 cot:1 irregular:1 freely:1 region:7 according:1 quantization:1 april:1 les:1 berry:1 logic:1 variance:1 whole:3 ck:3 exhibit:1 point:37 robotics:1 coincidence:1 dimensional:5 cancel:1 respect:1 selfadjoint:1 pp:7 described:3 second:1 three:1 been:1 hitting:1 expected:3 degrees:4 ph:5 hardly:1 empty:1 treatment:1 corresponding:4 quantities:1 sufficient:1 spectrum:9 observe:3 albeverio:2 evidence:1 case:12 uncertain:1 solid:3 straight:1 originate:1 appearance:4 examine:1 value:3 rectangular:5 while:2 behavior:1 many:1 aid:1 property:2 unitary:1 chaotic:10 vi:1 vk:22 thus:2 yk:2 iv:1 im:2 vanish:2 technology:3 disappear:1 around:1 confirmed:3 generic:3 same:3 any:6 zinn:1 shifts:1 hθ1:5 parts:1 quant:1 emphasize:2 widely:1 dimensionless:1 several:2 interpolation:1 independent:5 used:1 http:4 numerical:5 effect:4 hand:1 v1:9 levels:2 moving:2 purpose:3 meiji:1 infinite:1 frequently:1 mech:1 center:1 obstacles:2 well:1 analysis:4 academic:1 hx1:1 without:2 position:1 dimension:1 stressed:1 summer:1 among:2 being:1 resp:2 obtain:2 shape:1 intervals:1 aspect:1 world:1 energydependent:1 eigenstates:3 rapid:1 density:3 conclude:1 mathematically:1 valid:1 location:3 easy:2 unmanageable:1 solvable:1 eigenstate:1 real:4 iλ:13 eigenfunction:3 eigenvalue:10 operators:1 possible:1 increases:5 vδ:1 performance:1 press:1 using:4 like:2 semiclassical:1 semi:1 particle:6 follows:7 serves:1 arbitrary:1 reduced:2 scatterers:32 indications:1 because:1 classical:8 some:3 stat:1 calculated:1 deduce:1 table:2 small:2 ourselves:1 recognition:1 happens:1 scale:2 affects:1 though:1 integration:1 does:1 tends:1 ics:6 proc:1 considering:1 obey:1 equivalent:1 broken:3 although:2 worthy:1 losing:1 properties:4 proceed:1 justin:1 extension:3 algebraic:1 discussed:4 dependence:7 o:1 essential:1 practical:1 range:2 extensions:2 neighbor:3 bohigas:1 processor:1 inte:1 mathematical:3 mechanics:8 presence:1 h0:7 within:1 numerically:1 functional:3 latter:1 down:1 equality:1 hermitian:2 square:1 strip:1 operator:6 proportional:1 statistics:10 devices:1 area:1 h01:1 there:3 start:1 mesoscopic:2 mizoguchi:3 resolvent:1 function:10 hx:2 north:1 elsewhere:1 form:3 phenomena:1 δkl:1 regard:1 but:3 hu:4 delta:1 line:6 considerable:1 he:4 inside:7 us:3 distorts:1 below:1 ωm:20 problem:3 define:2 similar:1 called:2 strongly:1 ac:8 ae:1 computing:1 defined:3 recognize:1 uij:1 covers:1 denote:2 single:5 formulation:2 tosa:1 distributions:1 physical:1 functions:2 integrability:1 no:4 when:1 nx:3 ny:8 other:3 electrical:1 spatial:1 department:4 thousand:1 realize:1 conclusion:1 deviation:1 briefly:1 repeat:1 models:1 symbol:1 june:1 deriving:1 important:1 bounded:2 variable:1 implies:2 coupling:9 pointlike:2 interval:6 mass:4 starting:1
|
quant-ph9802009.txt |@word code:29 saturating:1 consider:5 interference:1 reversibility:1 primed:1 four:7 gf:1 computation:4 gi:9 qbc:7 depend:1 leung:1 knill:5 finally:3 does:2 under:2 orthogonal:4 far:1 wave:1 corollary:3 every:15 matrices:1 condition:2 notations:4 roy:1 solution:3 correct:14 discrete:2 zn:1 consistent:1 past:2 rate:19 qeccs:5 concludes:5 further:3 theory:2 putting:1 what:1 errors:39 appear:1 invertible:4 section:3 expressed:1 decoding:1 current:2 version:1 succinct:1 q2i:20 nine:1 ever:1 method:2 q1:1 respectively:4 equals:1 here:4 hku:2 nonbinary:1 address:1 along:1 equations:5 obtained:2 sending:1 remark:1 trans:1 suitably:1 technical:2 shift:14 larger:1 permutation:1 action:1 suitable:1 offs:1 via:1 followed:1 family:1 namely:1 logical:1 replace:2 sloane:3 linearly:1 readily:1 additive:9 handled:1 would:4 remains:1 continuous:1 qcc:18 few:1 handles:5 therefore:2 memory:1 encode:18 los:6 more:3 convolutional:21 introducing:1 knows:2 clearly:3 occurred:1 reversibly:1 reversible:3 particular:2 known:1 hold:3 must:1 me:5 high:3 keeping:1 valued:10 ma:1 ibm:1 equation:1 work:1 dev:1 theories:1 unknowns:2 obvious:1 ρw:1 following:8 making:2 arrive:1 my:1 example:11 proof:13 give:2 process:1 bennett:3 states:2 contradicts:1 performed:1 sense:1 conversely:2 occur:1 information:1 serves:1 rather:1 divided:1 holds:3 write:1 hi:4 map:2 blocks:2 transforming:2 earlier:1 mapping:3 collection:1 applications:1 abuse:1 gottesman:1 fi:15 constants:4 efficiently:1 imply:2 whenever:1 lemmas:2 register:9 summing:3 so:3 block:11 definitions:1 affecting:1 discussion:1 six:2 help:1 feb:1 numbers:1 developed:1 over:5 satisfied:1 kong:3 pulses:1 looks:1 satisfies:1 still:1 ieee:1 nonadditive:1 before:1 perfect:3 style:1 thank:2 chosen:1 interesting:1 forms:1 k2i:20 systems:3 defining:1 theo:1 non:2 good:3 affected:2 greater:1 coding:2 introduce:1 steane:3 effects:1 they:1 trade:1 now:3 university:1 each:6 found:1 soc:1 macchiavello:1 2i:10 constraints:1 schemes:1 ei:19 doing:1 idea:1 arrives:1 obtains:2 measurement:1 quantum:97 operation:1 eq:32 special:1 out:1 divincenzo:1 matrix:1 space:2 res:1 since:3 rev:14 denotes:2 may:3 acting:3 investigation:1 ref:3 ri:5 occurs:2 after:2 linear:2 written:1 complicated:1 corrects:12 besides:1 e1:2 e3:2 e2:2 definition:3 qj:1 r2:2 geometry:1 ordering:1 length:1 pasting:3 δij:1 hence:5 first:5 encoding:11 variables:1 powerful:1 number:3 lond:1 entanglement:1 alternatively:1 simplified:1 least:3 directly:1 impossible:1 electronic:7 given:3 similarly:1 introduction:2 eqs:3 system:2 construct:11 their:4 returns:1 assumption:1 majority:1 scheme:3 bits:2 exactly:1 proving:1 authors:1 than:4 coefficients:1 kind:3 wootters:1 see:7 computations:1 zz:12 generality:1 correction:13 mind:2 outperforms:1 say:1 archive:6 unaffected:2 any:9 resultant:1 able:2 k2:8 k1:7 internal:1 performance:1 mit:1 channel:1 regard:2 multiple:1 most:1 detect:1 eight:6 encodes:4 phase:17 class:1 latex:1 dordrecht:1 kj:10 clear:1 later:1 ko:1 kn:2 km:16 braunstein:2 kp:9 hamming:1 mechanical:1 physics:1 ak1:1 fact:2 shor:7 show:5 supported:1 discovered:2 ki:28 registers:32 lloyd:1 keywords:1 find:2 µnp:1 based:1 situations:1 behind:1 should:1 lemma:14 only:7 bases:1 essence:1 handle:3 above:9 notation:1 zurek:1 flips:2 famous:1 ones:1 words:2 report:5 years:1 procedures:1 hardin:1 arxiv:1 acknowledgments:1 sum:1 investigate:1 µ2p:1 processed:1 qi:15 fixed:3 set:11 modulo:1 constructing:2 slotine:1 δji:7 ends:1 up:9 depends:2 computer:1 result:5 discussions:1 particle:1 analog:1 subject:1 instance:1 said:2 ways:1 siam:1 state:14 various:3 simplest:2 αi:3 consecutive:13 approach:1 available:1 notice:1 ability:2 qubits:1 comp:1 complement:2 p2i:12 however:1 ji:57 article:1 picking:1 ket:1 both:6 protect:1 last:1 many:2 taking:1 density:1 according:1 lo:2 qubit:2 kets:1 ci:2 unclear:1 cm:1 point:2 simple:2 asymptotically:1 cf:1 moreover:4 considering:2 better:1 described:1 basis:4 addition:1 create:3 ai1:1 been:2 ai:6 basic:2 pj:1 ph:8 pi:29 abstract:1 corresponding:1 linearity:1 sufficient:2 subspace:1 c2:6 c1:5 general:14 spin:26 those:1 case:4 p1:1 laser:1 unlike:1 miquel:1 straight:2 single:1 will:3 while:1 suppose:6 error:45 unitary:2 laflamme:5 refs:6 thus:5 equal:1 respected:2 im:3 dual:2 binary:4 hong:3 qecc:20 grant:1 perform:1 paz:1 government:1 same:9 tells:1 complex:11 quant:7 arguments:1 modification:1 proved:3 finite:2 higher:3 independent:10 extended:2 i1:2 i2:3 hand:1 compared:1 uses:1 infinite:3 fourier:3 macro:1 well:4 without:1 sets:1 abilities:3 calderbank:3 being:1 obtain:1 actions:1 λa:2 λg:2 λf:3 λe:4 using:11 useful:1 λh:1 eigenstates:1 sixteen:1 preprint:6 kluwer:1 infinitely:1 nilpotent:1 regarded:1 ideal:1 δpi:3 rgc:1 lett:5 easy:1 theorem:9 mod:3 transformation:1 demands:1 possible:6 possibly:3 five:4 know:1 press:1 integer:1 bit:2 unique:3 correcting:12 occurring:6 necessary:2 like:3 lost:1 follows:4 δp:1 separately:1 δj:1 δk:8 arbitrary:3 δe:1 reduced:1 because:2 methods:3 classical:13 sequence:1 some:15 b1:1 b2:1 specified:1 happens:1 provided:2 per:3 efficiencies:1 exit:1 provides:1 dholakia:1 proc:1 either:2 measuring:1 package:1 slight:1 bm:1 bi:2 zzn:6 bp:7 although:1 pokfulam:1 hilbert:1 actual:1 a0:1 capable:3 important:1 done:1 mixed:1 consequently:4 road:1 outlook:1 cambridge:1 communication:1 into:2 bound:1 down:1 pair:2 hermitian:1 references:1 operator:1 additions:1 reducing:1 often:1 span:1 comparing:1 there:2 transform:1 start:1 way:4 worst:1 forward:2 analyze:1 was:2 debbie:1 function:12 form:5 smolin:2 converse:1 but:4 hk:1 construction:1 λei:2 encoded:3 line:1 true:1 applying:1 instructive:2 flip:21 us:1 different:1 below:1 converted:1 ωn:6 alamos:6 similar:1 called:1 multiplications:1 constant:4 choosing:1 computing:1 defined:3 certain:2 ak:3 combining:1 am:1 proven:1 denote:1 chap:2 promised:2 aw:3 chau:5 inf:1 eric:1 again:2 functions:3 codes:33 rains:5 ekert:1 encodings:1 when:3 other:5 details:3 department:1 a1:1 µip:10 a2:1 algebraic:1 implies:5 assume:1 required:1 together:2 having:1 time:1 decoherence:2 starting:3 original:1
|
quant-ph9802010.txt |@word proposition:2 secondly:1 concept:1 consider:4 global:3 idealised:1 leads:1 eds:3 commute:2 grateful:1 shimony:1 follow:1 tenable:1 certainly:1 careful:1 violate:1 contained:1 finally:1 does:3 under:3 worth:1 norm:1 case:2 conjecture:1 made:1 p3:23 far:1 void:1 translations:2 results:2 corollary:4 every:4 condition:5 common:1 generalised:2 four:1 school:1 presented:2 altering:1 michael:1 forbes:1 deals:1 assignments:1 convenience:1 vector:9 o1:34 eigenvalues:1 il:1 shows:3 upper:1 smaller:1 says:1 past:3 second:4 street:1 irreducibility:1 concludes:1 further:2 haag:2 even:4 nothing:1 what:1 appear:1 apparatus:1 section:3 expressed:3 rescale:1 version:4 causes:1 above:2 sup:1 new:2 net:1 led:1 degree:1 respectively:2 equals:1 here:2 selective:4 them:1 separation:4 represented:2 calculate:1 remark:4 suitably:1 changed:1 contradiction:1 p2:8 published:1 proof:10 spacetime:8 annihilates:1 formulated:2 projection:3 family:1 merely:2 vii:1 rivi:1 private:1 api:5 pp:17 viz:1 apply:1 lansing:1 causal:4 unit:5 contractions:7 use:1 feb:1 proceed:1 would:2 prove:3 distinct:2 positive:2 generate:1 predict:1 noting:1 call:2 therefore:3 type:3 theoretical:2 more:6 separated:16 diamond:1 hermitean:1 clearly:3 operators:5 ap1:4 lightcone:1 odinger:1 berlin:1 appendix:2 everywhere:1 particular:4 known:1 foundations:1 cases:1 hold:2 iii:1 must:2 kraus:2 springer:1 oi:2 abner:1 science:2 setup:1 work:1 ere:1 minimum:1 values:1 concepts:1 following:7 root:11 example:2 def:7 history:1 wedge:1 process:1 relativistic:4 purposes:1 states:6 effectively:2 assumptions:1 o:26 want:1 sense:4 sharp:2 p2φ:1 association:1 occur:1 verlag:1 summers:3 thing:1 verify:1 discussion:5 holds:5 regions:11 how:2 pair:2 opposite:1 description:3 algebra:7 may:3 max:1 philosophy:2 derived:2 hence:4 studies:1 choice:3 natural:1 third:4 approximation:2 register:1 element:5 extremal:1 generic:1 so:4 correlation:3 representation:1 order:3 operations:1 horne:1 interpretation:3 closely:8 developed:1 over:1 move:1 produced:1 experiments:3 through:1 its:1 before:3 perfect:3 write:2 group:4 decay:1 chosen:1 fruitful:1 according:2 choose:3 redhead:4 hidden:2 might:1 maximal:7 non:12 incompleteness:2 affected:1 pure:2 landau:7 framework:5 effects:2 they:5 identically:1 oxford:2 now:10 silver:1 nor:1 eigenvalue:1 term:3 realist:4 always:3 university:2 covering:1 identified:1 fabian:1 each:4 found:2 feldman:1 realism:1 majorized:1 domain:2 directly:1 formulate:1 energy:3 revised:1 idea:1 used:2 investigated:1 expect:3 measurement:11 quantum:30 organised:1 approximated:6 special:2 out:1 shown:6 space:4 restricted:1 3rh:1 since:2 rev:2 particles:3 replacing:1 acting:3 reader:1 denoted:2 supports:2 math:8 streamlined:1 after:1 theory:25 hull:1 free:1 quite:1 difficulty:1 conditioning:1 put:1 subalgebras:3 axioms:5 9ew:1 r4:1 definition:1 r1:1 applications:2 impose:2 david:1 counterpart:2 turn:1 consequence:2 first:6 major:1 already:1 probability:3 variables:1 powerful:1 hitherto:1 intuitively:1 philosophical:1 meshes:1 another:2 precisely:1 open:7 min:1 interchange:1 given:6 reference:2 their:1 introduction:2 adjoint:5 system:3 least:2 needed:2 assumption:1 calculations:1 perfectly:1 recovered:1 gives:2 commutativity:2 collapse:1 academy:1 tool:1 continuous:2 part:2 authors:1 schr:1 translation:1 than:1 specify:1 distance:2 kind:1 determines:1 roles:1 cyclic:3 double:1 cimento:1 see:3 annihilation:1 future:2 pmax:2 wheeler:1 outcome:6 san:1 generality:1 nuovo:1 localized:1 modern:1 argument:10 say:1 close:2 seen:1 any:21 involutive:1 cε2:27 refute:1 convenient:2 latter:2 violates:1 note:2 sciences:1 take:1 spectral:1 unless:1 axiomatic:3 shall:2 object:1 singlet:1 algebraic:6 preparations:1 automorphism:1 unmeasured:1 remarks:1 why:1 bound:1 considered:2 clear:3 sometimes:1 stronger:1 proceedings:1 points:3 mechanical:3 reed:1 posses:1 physics:3 sum:1 incomplete:1 incorporate:1 show:4 violation:7 isotony:1 relation:1 conditional:6 trivial:2 find:7 fredenhagen:1 q1:33 aφ:1 aω:3 aψ:2 bemerkungen:1 apriori:1 inextendible:1 should:1 lemma:24 only:4 annals:1 candidates:1 coefficients:3 instrumentalist:1 employed:1 local:14 axiom:2 abelian:2 his:1 triangle:2 closed:1 means:1 zurek:1 malament:3 expectation:8 joint:2 cannot:2 words:1 import:1 runs:1 podolsky:2 arxiv:1 proposing:1 paper:2 predicted:1 contain:2 qi:2 fixed:2 view:1 apparatuses:1 strengthened:1 requirement:1 set:15 exists:7 achieved:2 violated:10 correlations:6 maximum:1 edition:1 depends:1 result:7 terms:1 nonlocality:1 subject:2 inequalities:7 review:1 vol:18 state:36 difficulties:1 αg:3 between:1 invariant:2 approach:1 publishers:1 notice:2 recently:1 complement:2 weak:1 however:5 wi:5 vanishing:1 key:1 2pi:1 configuration:1 distribution:1 both:2 interpretations:1 qft:2 many:2 region:8 infinitely:1 equal:3 context:2 faces:1 argue:1 arbitrarily:10 mechanics:2 relevant:1 conclude:3 corresponds:2 2nd:1 directions:1 werner:2 proved:6 ensures:4 described:1 commutative:1 addition:3 three:1 been:2 pmin:2 ai:2 cauchy:1 ph:2 algebras:12 meeting:1 cohen:1 empty:2 define:2 direction:1 corresponding:2 observable:4 concerning:1 propositions:1 subspace:1 covariance:1 spectrum:2 wilce:1 maximally:5 spin:2 present:2 independence:1 applied:3 specialised:1 p0:1 p1:15 subsets:1 rigorously:1 value:10 will:5 while:1 ar:1 replaced:2 viii:2 situation:2 property:10 procedure:1 detailed:1 unitary:1 spacelike:22 played:1 almost:3 vi:1 von:6 thus:9 surprisingly:1 iv:1 ii:6 cluster:1 cone:1 dual:1 claimed:1 return:1 supremum:1 greater:1 perhaps:1 lett:3 same:4 poincar:5 princeton:2 unity:1 quant:2 arguments:4 finite:2 difficult:1 extended:1 trivially:1 ni:2 comprehensive:1 effect:1 hand:3 intersects:1 entanglement:3 schlieder:13 acknowledgement:1 reprinted:1 locality:4 epr:11 analysis:3 bohr:1 bohm:2 academic:2 without:3 very:1 claims:1 self:5 subgroup:1 unified:2 just:2 among:1 true:1 wagner:1 starting:1 actions:2 vanishes:1 underlying:1 distant:2 potentiality:1 λi:1 scattering:1 previous:1 york:2 kluwer:2 application:1 la:1 bell:28 setting:2 treatment:1 theorem:43 ado:1 east:1 transformation:1 momentum:1 explained:1 aspects:1 psa:1 possible:5 additivity:1 know:1 similarly:1 vacuum:29 press:3 using:3 shadow:1 unique:1 loss:1 necessary:3 like:1 particle:3 follows:6 automorphisms:1 schwarz:1 arbitrary:2 spins:1 mathematical:1 because:1 functional:2 neumann:5 classical:3 butterfield:1 creation:1 some:7 b1:16 b2:13 respect:1 complementarity:1 proofs:1 2qi:1 specific:2 cω:1 dense:1 measurements:5 comments:1 inequality:22 passion:1 provides:2 assuming:2 o3:6 o2:32 demonstrated:1 measuring:3 run:1 performed:3 bi:2 although:2 approximating:1 hilbert:3 cε:9 projector:8 zur:1 a1:16 about:1 anything:1 commun:4 dependence:3 oa:1 recalling:1 a2:13 ensure:1 biennial:1 act:1 introduced:1 projectors:6 cambridge:2 aq1:4 communication:1 into:4 clifton:1 attains:1 device:1 appropriate:3 references:1 einstein:2 operator:21 methods:1 existed:1 strictly:5 there:22 approximate:1 specifically:1 class:1 strict:1 accordingly:1 structure:2 forward:2 was:5 assumes:1 toeplitz:1 himself:1 belonging:1 complete:3 collapsed:1 but:3 aµ:10 reeh:9 active:1 proposal:1 he:1 again:1 pi:13 instructive:1 whether:1 minkowski:2 attached:1 up:1 devices:1 localised:3 dordrecht:2 problem:1 piece:1 similar:1 called:4 strongly:1 associated:2 defined:2 abstract:1 general:10 aq:14 separating:3 single:3 proves:1 au:1 our:4 formalism:2 commuting:2 operation:1 physical:3 hellinger:1 compared:1 lightlike:1 us:4 no:15 commutes:1 rosen:2 detail:1 reality:6 field:15 other:3 diego:1 spatial:1 department:2 mathematics:1 enlarged:1 hyperentangled:1 sufficient:1 conclusion:1 briefly:2 elements:4 kinds:1 corrected:1 printing:1 prepared:1 cb2:2 generated:1 important:1 bounded:13 variable:1 lemmata:1 simon:1 lane:1 correlated:1 implies:2 assume:1 typically:1 required:3 curve:1 together:1 licht:1 fact:3 stachel:1 observables:5 requires:1 furthermore:1
|
quant-ph9802011.txt |@word represent:1 concept:2 consider:2 skip:1 option:1 idealised:1 existing:1 leads:1 ceased:1 grateful:1 go:2 technique:1 tr:7 quadruple:1 summarised:1 those:5 include:1 brown:2 conjecture:1 supported:1 stud:1 orthogonal:1 very:1 rise:1 springer:2 me:1 condition:8 induced:1 eds:1 did:1 positions:1 applicable:2 vector:1 small:1 unsharp:21 says:1 occurrence:2 measurable:1 second:3 further:1 dynamics:1 choices:1 linear:2 even:2 established:2 what:2 apparatus:4 trivial:2 near:1 above:2 increasing:1 supporting:1 respectively:2 never:1 component:2 residual:1 here:4 represented:2 november:2 my:5 elaborate:1 vectors:1 allows:1 conveniently:1 studies:1 genuinely:4 formulated:1 projection:3 merely:1 explained:1 outcomes:3 apply:1 resolutions:1 operational:1 establish:1 use:1 feb:1 would:8 probabilities:4 positive:2 grabowski:2 ρsa:1 definiteness:4 therefore:1 taken:4 exhaustive:1 more:2 operators:4 berlin:3 virtue:1 hold:2 had:1 ρa:15 account:2 valued:2 pursue:1 challenge:1 modified:2 theories:1 ρs:1 assumptions:1 values:10 concepts:1 following:5 spontaneous:1 dissolve:1 proof:6 claim:2 indicated:1 give:3 allowed:1 neglected:1 states:18 abner:1 his:1 dropped:1 sense:2 sought:1 sharp:6 conversely:1 occur:2 verlag:2 information:2 requirements:1 rather:2 pure:1 alternative:1 contribute:1 algebra:1 may:3 after:1 different:1 hence:1 natural:1 overtaken:1 correspond:1 so:4 allow:4 correlation:1 representation:1 sa:14 order:1 talk:3 horne:1 serving:1 wigner:2 furnished:1 indeed:1 lahti:7 experiments:1 same:1 differs:1 still:3 pointer:32 its:2 before:1 manuscript:1 late:1 persist:1 mail:1 hidden:1 loophole:1 h0:4 happened:1 maximal:1 them:1 finish:1 they:4 compound:3 now:2 eigenvalue:4 always:1 university:1 identified:1 applied:2 each:4 found:1 side:2 mean:1 subset:1 schemes:2 formulate:1 independent:1 series:1 eg:1 revised:1 idea:3 deterministically:1 extended:1 measurement:33 quantum:16 our:1 programmes:1 out:2 shown:2 space:5 nuovo:1 rev:2 denotes:2 am:2 objectivity:1 ri:1 theory:3 hull:2 possibility:3 admits:1 approaches:1 besides:1 maths:1 interaction:1 derivation:1 starts:1 could:2 persists:1 place:1 consequence:1 onto:1 strictly:1 first:2 xi:31 probability:9 radical:1 variables:1 done:1 comprises:2 open:1 given:6 necessarily:1 fair:1 introduction:2 system:7 least:1 assumption:3 statement:2 scheme:7 structures:1 final:2 gives:1 collapse:2 happily:1 continuous:1 serve:1 immediate:1 part:1 objectification:11 than:1 distance:1 kind:1 determines:1 showed:1 edition:1 require:2 see:2 submitted:1 reproduction:1 were:2 outcome:2 pvd:4 generality:1 rewrite:1 cohen:1 measure:5 mine:1 elsevier:1 any:3 ray:1 forced:1 nonlocality:1 note:1 potential:2 chairman:1 objective:1 negligible:1 spectral:1 sure:1 trace:1 shall:2 measures:3 most:2 preparations:2 device:1 measured:4 class:2 dordrecht:1 adopt:1 cover:1 proceedings:1 inaccuracies:1 mechanical:1 left:1 physics:1 notion:6 fact:2 precise:4 saying:1 probe:3 responsibility:1 interpretation:3 fine:2 based:3 explain:1 should:3 lemma:4 only:4 do:2 mixture:7 means:3 there:2 cannot:4 words:1 resolve:1 arxiv:1 fixes:1 qi:1 fixed:1 pertains:1 pointers:6 exists:3 achieved:1 mentioned:1 namely:1 result:6 close:1 embarking:1 said:1 shimony:9 definite:13 yet:1 hist:1 state:7 difficulties:1 various:1 captured:1 between:1 reproducible:1 probably:1 reading:6 conditions:2 available:2 interpretational:2 ends:2 recently:1 however:4 ignorance:1 extent:1 uρ:1 remaining:1 observable:16 interpretations:2 taking:1 according:2 fulfilled:1 contribution:1 argue:1 adapted:1 experimental:1 detailed:1 conclude:1 pov:5 overview:1 speaker:1 corresponds:1 satisfaction:1 simply:1 respect:2 pr:2 addition:1 due:2 been:5 strategy:1 much:1 expected:1 ph:1 meeting:1 pm:5 arises:3 corresponding:4 commutes:1 quantities:2 subspace:4 readings:1 bohmian:1 understand:1 systematic:1 repetition:1 present:2 case:4 look:1 might:1 value:9 eigenstate:4 will:8 while:2 error:1 situation:1 property:1 unitary:3 coupled:1 reproducibility:4 thus:3 equal:1 turns:1 busch:14 disappear:1 containing:1 make:4 who:2 parts:1 quant:1 arguments:2 development:1 exhaust:1 used:2 upon:1 effect:4 entanglement:1 changing:1 recent:3 acknowledgement:1 nevertheless:1 safely:1 well:1 severe:1 solve:1 sets:1 undertaken:1 usual:1 being:3 reviewed:1 paul:1 macroscopic:2 eigenstates:4 mittelstaedt:5 previous:1 aiming:1 density:1 seems:2 reasons:1 valid:1 theorem:12 mod:1 espagnat:2 real:1 stein:6 rules:1 possible:3 admitting:1 early:1 game:1 five:1 press:1 using:2 unique:2 apart:1 modifications:2 tail:1 necessary:2 follows:3 serves:1 facing:2 yields:2 either:3 arbitrary:4 essential:1 terminology:1 specifies:1 classical:1 conditional:1 some:7 happens:1 provided:2 scale:1 lead:1 realistic:2 measurements:6 overly:1 does:3 passion:1 provides:1 minimal:2 measuring:2 object:22 run:1 inaccurate:1 equivalent:1 step:2 hilbert:4 about:1 extension:2 certainty:2 theorems:2 o:2 compatible:1 remains:2 plus:3 mixed:1 introduced:1 denote:2 raised:1 presence:1 into:1 obtaining:1 suppl:1 lies:1 references:1 operator:4 technically:1 statistics:2 extremely:1 premisses:1 initial:4 question:3 postmeasurement:2 long:1 appeal:1 way:3 opens:1 himself:1 form:3 but:3 link:1 gain:1 ha:5 true:1 applying:1 whether:3 up:2 us:1 uk:2 problem:15 minutes:1 called:2 mechanics:6 fulfills:1 ac:1 partition:2 associated:2 worthwhile:1 int:1 certain:4 abstract:1 describe:1 linearity:1 general:3 formulation:2 watched:1 formalism:3 distributions:1 again:1 compared:1 cim:1 no:7 when:4 impossibility:3 other:1 papers:1 department:1 mathematics:1 theor:1 conclusion:2 nonzero:3 elements:1 kinds:1 completes:1 models:1 felt:1 problems:1 bounded:2 allowing:2 structure:1 implies:2 coupling:2 practically:1 assume:2 required:2 resolving:1 ascertained:3 stachel:1 inaccuracy:1 observables:13 requires:3 once:1
|
quant-ph9802012.txt |@word represent:2 concept:1 consider:3 magnetic:2 separates:2 concern:1 results:15 jˆ3:6 ge:1 overlap:1 jˆ2:3 expressions:1 jˆ1:5 inverse:1 calculate:1 γr:3 intensive:1 quasi:2 does:2 indicate:1 those:4 include:3 applied:2 belonging:1 supported:1 advantage:1 very:3 springer:4 subject:1 wave:15 figs:1 lecture:1 redefinition:1 tridiagonal:2 nieto:1 exact:2 hamiltonian:4 transmission:1 irreducible:3 notes:1 tanh:1 solution:2 large:2 solved:1 red:1 dealt:1 small:5 eigenvalues:8 degeneracy:1 andrews:2 unexpected:1 sturm:2 findings:1 sukhatme:1 dealing:1 coefficient:2 direct:3 modified:2 approximation:2 second:7 compensates:1 evaluated:1 further:2 defining:1 salam:1 odd:7 approached:1 even:13 will:2 appear:1 advantageous:1 morse:2 trivial:1 section:3 axes:1 xφ:1 near:3 expressed:3 version:2 establishes:3 frank:1 3c:4 new:6 falling:1 increasing:1 ever:1 method:5 contrast:1 body:2 inspect:1 fiz:2 respectively:4 discrete:3 here:10 understanding:1 following:1 objects:2 expansion:1 groups:1 situation:2 alone:1 strong:4 implicit:2 baye:2 box:1 tunneling:1 exemplified:1 algebra:11 institute:2 involved:1 inspired:2 studied:1 allows:1 expression:1 controversy:1 suggests:1 simultaneous:1 characterizing:1 pick:1 usually:2 khare:3 suitable:1 studies:3 plotted:1 oschl:3 varshni:1 formulated:1 besides:5 extra:2 ground:1 hermite:1 merely:1 explained:1 highly:1 apply:1 select:1 readily:2 seligman:1 presents:1 use:7 charge:7 feb:1 handled:1 would:2 commun:1 sake:1 positive:3 contains:2 finally:2 next:1 almost:1 nucl:1 ψn:6 therefore:6 taken:1 care:1 type:9 theoretical:5 reflects:1 more:13 fractions:2 flat:1 zh:1 becomes:4 operators:7 diagonal:1 odinger:5 berlin:4 normalized:1 particular:3 known:4 central:1 cases:9 iii:5 keeping:1 impenetrable:2 wunner:1 ρh:5 equation:10 work:5 oscillator:30 centrifugal:5 ρn:8 reviews:1 remain:1 values:12 publications:1 ginocchio:6 making:5 sturmian:10 example:12 performed:2 compare:1 transition:2 challenging:1 figure:3 give:2 calculation:2 introduces:1 allowed:5 2lc:3 states:2 junker:2 numbers:2 employs:1 arise:1 interpreted:3 hydrogen:1 axis:2 recapitulating:1 notation:7 kustaanheimo:2 rather:4 discussion:4 six:1 feature:4 orthogonality:1 arrangement:1 write:1 maps:1 gcs:4 adapted:2 fourth:2 significance:1 instead:3 roy:1 parameter:8 secures:1 ρ2n:1 map:2 de:2 description:3 singular:12 replacing:1 ladder:4 after:1 derived:1 confirmed:1 applications:3 plane:1 fd:1 seemingly:1 waves:1 representations:2 summarize:1 choice:8 heidelberg:1 types:3 goal:1 realized:1 short:4 natural:2 asymptotics:2 third:3 resetting:1 spectra:1 correspond:1 su:13 element:1 complexity:1 cannot:1 so:5 sect:1 taking:4 representation:4 order:3 transformation:3 separable:1 s0:1 interpretation:1 help:1 cutoff:1 developed:4 displayed:1 unacceptable:1 years:1 course:1 paper:2 through:1 wolf:1 statistical:1 signs:1 mentioned:1 existence:1 kinetic:2 recovers:2 its:15 fischer:1 supplemented:1 group:2 located:1 chosen:6 interesting:4 solving:1 varies:1 gen:1 forms:2 attraction:2 offers:2 fig:6 inspecting:1 pergamon:1 derivative:2 hidden:1 main:1 debrecen:1 setting:4 eur:1 maximal:1 them:2 good:1 susyqm:2 integer:1 reflected:1 repulsive:7 effects:1 they:8 half:2 oxford:1 souza:1 singularity:10 now:5 discuss:1 teller:3 represents:3 term:21 gets:1 indeed:1 always:1 level:1 casimir:2 sin:1 possibilities:2 realistic:2 theory:2 c2ρ:3 editor:1 reasonable:2 radial:4 2l:1 2m:2 2n:10 truax:1 domain:3 differential:6 significantly:1 formulate:2 series:5 energy:7 hypergeometric:6 reduce:3 related:3 recapitulate:1 each:1 elementary:1 extended:9 obtains:1 quantum:13 our:6 approximated:2 avoided:1 eq:12 special:4 out:4 try:1 shown:2 matrix:12 space:3 furthermore:2 since:3 rev:8 cancels:2 research:1 particles:1 transforming:1 hill:1 formula:2 get:4 ref:16 oscillators:1 eksp:1 shows:4 wiley:1 linear:2 barrier:5 interactions:2 singularities:3 abramowitz:1 differ:1 possibility:1 difficulty:1 completely:1 complicated:3 york:4 members:2 erent:1 rutherford:1 beginning:2 e2:2 definition:1 pairs:1 interaction:3 r2:2 agree:1 could:1 shells:1 plot:1 dutt:1 teor:2 onto:1 adjoint:1 first:6 origin:10 intuition:1 features:4 symmetry:1 laguerre:5 variables:2 powerful:1 number:1 rounded:1 ddimensional:1 done:1 directly:3 reached:3 angular:6 size:1 given:4 necessarily:1 rewritten:1 utilization:1 introduction:4 mcgraw:1 eqs:1 behaves:1 relations:1 their:4 confirming:1 inversion:1 too:7 calculations:14 realization:3 9c:1 loudon:1 recovered:5 gives:1 haines:1 academy:1 tool:1 continuous:6 eliminates:1 rejected:1 obsolete:1 part:6 authors:1 corresponded:1 off:2 sign:1 than:1 coefficients:1 oscillate:1 past:1 analyze:2 herold:1 showed:1 accordance:1 holds:4 approximations:3 see:4 limiting:5 roberts:1 determined:3 coulombic:2 williams:4 onedimensional:2 naturally:2 treated:1 lowest:2 comput:1 unchanged:1 spectrum:5 generalization:1 interrelation:1 inherit:1 close:6 disjoint:1 seen:4 seem:2 recover:2 clearly:1 viewed:1 relatively:2 strength:1 zero:3 depending:1 convenient:1 latter:3 note:10 sciences:1 potential:93 square:2 generalized:34 forces:1 green:11 singh:1 δnn:4 switching:1 exactly:13 beyond:1 investigations:1 object:1 reach:2 systems:1 accessible:1 accurately:1 most:5 regular:6 formulae:2 phase:2 analytically:6 class:10 interacting:1 spector:1 constructed:1 considered:1 neighboring:1 calculated:2 later:2 implications:1 typeset:1 2nd:1 proceedings:2 verlag:1 principle:2 exp:5 mechanical:4 hn:1 usual:3 physics:5 wigner:1 fact:2 dover:1 science:1 incorporate:1 mexico:1 show:4 atom:1 connect:1 relation:3 solutions:33 hungary:1 dimension:5 d2:1 find:3 fifth:1 principal:2 partners:1 x1:1 based:3 parameters:7 situations:2 original:1 written:2 analytic:1 only:7 bases:1 generators:2 subsection:3 transcendental:1 factor:2 equivalents:1 elucidates:1 constant:2 local:1 do:4 dj:3 above:2 hungarian:2 means:5 dependent:1 between:7 joint:1 ones:2 negative:2 supplies:1 carries:1 imitating:1 dr:4 having:1 nearly:1 areas:1 runs:1 ushveridze:1 fields:1 arxiv:1 summary:1 aspects:4 common:1 contain:4 analytical:5 including:1 discussing:1 require:1 approaching:1 satisfy:2 redefine:1 set:2 reference:1 subatomic:1 2c:1 vol:2 proc:1 observed:1 depends:4 electrostatic:1 result:1 muonic:1 terms:9 best:1 techniques:4 closer:1 still:1 commutation:1 doebner:1 nuclear:3 review:1 below:2 tend:1 symmetric:3 state:11 interrelated:1 various:7 closed:2 simplest:2 invariant:7 recently:1 reflection:6 extend:2 nature:3 pogosyan:1 were:1 weak:2 however:4 reproduces:1 horizontal:1 cˆ2:1 analyzed:5 separately:3 jf:1 atoms:2 distribution:2 originates:1 adapting:1 both:9 essentially:3 last:2 candidate:1 limits:8 desired:1 many:2 region:1 infinitely:3 parts:1 previously:2 laplace:1 etc:3 connection:1 colloquium:1 angew:1 bristol:1 lo:3 sense:1 safely:1 otherwise:2 ck:1 strongly:2 relevant:3 supply:1 simple:5 asymptotically:2 harmonic:27 expectations:1 dimensional:38 simply:2 applicability:1 cancel:2 respect:2 16r:2 math:5 considering:2 unusual:1 jetp:1 described:5 transformations:1 symposium:1 basis:23 three:6 been:9 appears:4 much:1 combined:2 basic:1 expected:1 flexible:2 ph:1 algebras:4 ann:2 treatment:4 gesztesy:1 obtained:2 generating:3 supersymmetric:3 erd:1 offered:1 ik:1 geyer:1 fund:1 determination:1 2ik:1 panel:1 presented:3 former:3 present:9 case:20 transl:1 leschke:1 irregular:3 pacs:1 might:3 ǫn:3 value:4 choices:3 aim:1 technical:2 while:17 5c:1 behavior:6 aid:1 di:1 property:2 study:1 procedure:1 identical:1 unitary:3 engl:1 llano:1 played:1 phenomenological:1 refs:3 communicating:1 thus:2 non:5 iv:3 ii:3 canceled:1 reads:1 itself:3 properties:1 attributed:1 conf:1 accounting:1 limit:16 vanish:6 technology:1 different:7 pis:1 verified:1 degenerate:1 grant:1 suggest:1 kosteleck:1 belong:1 lett:3 same:3 any:2 member:2 another:1 complex:3 quant:1 virtually:1 largest:2 avoids:1 figures:1 finite:12 φn:8 higher:5 independent:2 used:14 eds:2 singapore:2 numerical:5 effect:2 potentials:60 infinite:4 changing:2 invariance:1 landau:1 normalization:1 recent:4 weakly:2 schr:5 center:2 nevertheless:2 whole:1 modeled:1 well:5 analysis:1 peculiarities:1 without:2 studying:1 coordinate:1 ces:2 model:3 arising:3 possesses:1 l107:1 charged:2 unified:1 just:1 being:7 stegun:1 newton:2 obtain:1 physically:1 vanishes:2 assigned:2 shape:11 identify:1 atomic:1 aspect:1 using:11 uller:1 alternative:1 scattering:2 adding:1 generator:1 density:2 point:2 seems:1 except:1 exclusively:1 reasons:1 valid:3 attractive:4 theorem:1 relevance:1 iπ:1 mod:1 solvable:12 remaining:2 momentum:4 ck0:1 real:3 iθ:1 iν:10 analogy:1 eigenvalue:1 couple:1 possible:1 implied:1 corresponds:9 increases:1 unification:1 makes:2 similarly:1 confined:1 world:3 unique:1 helpful:1 necessary:2 like:21 particle:2 follows:2 reduces:3 specific:4 anymore:1 2d:1 arbitrary:1 become:2 jˆ:2 essential:2 mathematical:3 deviation:1 because:5 often:2 classical:1 stiefel:2 narrow:1 physicists:1 some:12 self:1 supplementary:2 polynomial:1 qes:1 2qc:1 choosing:1 cr:1 gave:1 neglecting:1 march:1 scales:1 shapes:3 gradually:1 scale:1 describing:3 dimensions:10 avoid:2 ter:1 integration:1 subclass:1 conditionally:1 behave:1 straightforward:2 lifshitz:1 demonstrated:2 either:4 core:2 scientific:2 rep:1 equivalent:4 confluent:7 conventional:1 illustration:1 natanzon:12 revtex:1 wells:1 although:3 found:2 contracts:1 hilbert:2 von:1 asymptotic:2 actual:3 extension:3 getting:1 discussed:4 dependence:2 o:5 reduced:2 practical:8 remains:1 range:8 important:3 extensions:2 sissakian:1 slightly:1 elyi:1 considerations:1 outlook:1 publishing:1 parity:1 h2:1 unbounded:1 into:5 splitting:1 bound:13 due:8 pair:1 appropriate:2 extending:1 references:1 scherer:1 operator:13 proportional:2 reducing:1 or1:1 methods:5 rely:2 acknowledgements:1 weight:1 area:1 support:1 there:8 approximate:2 long:4 workshop:1 handbook:1 inner:1 way:3 ed:1 resolvent:1 was:9 opposed:1 function:14 considerably:1 hard:1 atakishiyev:1 complete:1 form:4 enough:2 believe:1 reine:1 but:7 construction:1 link:3 justify:1 line:1 manifests:1 true:7 utilizing:1 decades:1 made:1 antonyan:1 wish:1 mat:1 up:2 us:1 until:1 liouville:1 complications:3 demonstrate:1 problem:33 define:3 similar:6 called:3 examples:3 mechanics:7 interval:1 associated:16 introducing:1 defined:12 certain:4 abstract:1 wybourne:1 am:4 nattermann:1 textbook:1 general:9 continued:2 separating:2 single:1 associates:1 dutra:1 dθ:1 integrable:2 controlled:1 formalism:5 distributions:2 physical:8 vertical:1 functions:25 nk:1 completeness:2 otka:1 no:2 qθ:3 when:3 detail:1 envisaged:1 field:6 other:7 role:1 justification:1 spatial:4 ruder:1 really:1 sufficient:3 node:1 picture:1 elements:6 denote:1 calculating:1 separate:1 models:3 problems:16 polynomials:4 includes:1 generated:1 evai:13 nucleus:2 peak:2 variable:3 cooper:3 plessas:1 papp:5 structure:2 nasa:1 ago:1 algebraic:2 land:1 implies:1 coulomb:104 corresponding:5 starting:1 required:2 curve:2 together:1 4q:1 cordero:1 4j:1 4h:3 time:2 international:1 n2:1 2mω:2 n4:1 cρ:3
|
quant-ph9802013.txt |@word concept:1 consider:2 remarkable:1 rev:7 magnetic:1 four:1 code:1 computation:1 chain:1 alamos:3 under:4 analogous:1 include:2 division:1 amplitudes:19 frequencies:2 wave:2 polytechnic:1 resonant:4 condition:1 level:3 science:3 c00:12 c01:12 programme:1 grateful:1 insignificant:2 pulse:22 second:3 dynamics:4 substitute:1 pic1:1 new:1 margolus:1 error:1 atoms:2 consideration:1 equations:7 change:3 shift:1 larger:1 commonly:1 action:10 changes:2 exited:3 king:1 via:1 decrease:1 angle:1 use:1 feb:1 beginning:2 jal:1 theoretical:1 today:1 odinger:1 recall:1 equation:1 work:1 grover:1 values:9 ms:1 following:3 ferry:1 example:2 control:8 ions:1 figure:5 bennett:1 states:2 indicates:2 end:10 provide:1 six:1 gcn:6 pure:7 gate:23 brassard:1 may:1 after:1 confirmed:1 explored:1 effective:1 computations:3 grant:1 negligible:1 representation:1 indeed:1 paper:2 guadalajara:2 captions:1 ieee:1 imc:7 derive:1 chosen:2 interesting:1 fruitful:1 parts:2 itano:1 choose:1 into:2 combination:1 numerically:1 introduce:1 effects:1 symposium:1 rotation:1 now:1 discuss:1 university:2 hamiltonian:4 arrows:2 found:1 2j:3 gennady:1 σ2z:1 energy:1 idea:3 society:1 frequency:3 quantum:25 laboratory:1 special:1 divincenzo:1 shown:6 matrix:2 interference:1 research:2 increase:1 investigation:1 rec:7 achievements:1 foundation:1 free:3 drives:1 indices:1 reason:1 york:1 put:1 org:4 jozsa:2 interaction:3 transition:4 motion:1 corrections:1 eqs:1 first:4 opez:2 number:2 long:1 checked:1 gif:8 top:1 deutsch:1 system:9 1a:1 1b:1 calculations:1 frame:2 transverse:1 part:3 than:1 coefficients:3 population:1 iωt:2 polarized:1 target:3 see:5 computer:2 amplitude:2 collins:1 toward:1 weinfurter:1 any:2 gustavo:1 zero:1 responsible:1 note:1 take:2 accuracy:2 experienced:1 shall:1 simplify:1 brooklyn:1 connected:1 significant:1 phase:5 exico:1 physica:1 proceedings:1 exp:14 nuclear:1 effect:1 physics:2 shor:3 show:3 supported:2 dependences:1 rotating:2 lloyd:1 ground:2 based:1 parameters:6 implementation:8 only:4 factor:3 do:2 get:2 simplest:1 probably:1 during:1 stoc:1 prime:1 evolution:8 arxiv:5 factorization:1 investigate:1 common:3 moduli:3 national:1 ωt:2 depends:1 defense:1 discussions:1 terms:1 phases:5 interacting:1 pattern:1 review:1 state:12 between:2 progress:1 conditions:10 available:4 barenco:2 recently:1 nonresonant:6 vertical:2 qubits:1 attention:1 weak:2 jm:5 sleator:1 linkage:1 both:1 last:2 σn:2 taking:1 hint:1 logic:2 qubit:6 experimental:1 otherwise:1 cn:18 conclude:1 simple:1 corresponds:10 dimensional:1 ic10:1 ps:4 pp:1 described:1 addition:1 been:1 describes:2 nato:1 ph:5 fig:10 lived:1 corresponding:1 concerning:1 spin:9 2ic:5 value:1 will:1 near:3 behavior:2 applies:1 35th:1 annual:1 mexico:1 thus:1 ik:8 ic:4 monroe:1 different:1 cjm:1 circularly:1 lett:4 same:2 complex:6 quant:5 independent:2 used:1 http:4 numerical:1 monotonic:1 doolen:2 changing:1 opportunity:1 implements:1 lower:1 weakly:1 schr:1 center:1 well:1 gates:3 agency:1 σnz:1 obtain:2 campbell:1 previous:1 zoller:1 application:1 iϕ:2 add:1 transformed:1 projects:1 versa:1 c11:10 c10:10 transformation:2 generalized:4 real:1 bik:2 format:4 spanned:1 know:1 press:1 nanotechnology:1 postal:1 advanced:1 mod:1 necessary:1 follows:1 mhz:2 arbitrary:2 spins:2 because:2 successfully:1 duration:1 indirect:1 recognition:1 nonzero:1 bottom:1 electromagnetic:1 eliminate:1 provides:2 proc:1 demonstrated:1 equivalent:1 b213:1 substitution:1 imaginary:3 panel:1 ϕik:3 dependence:3 practical:2 important:4 introduced:1 slightly:2 wineland:1 h0:1 within:2 rotations:1 references:1 gary:1 operator:1 r2493:1 initial:12 fast:2 los:3 was:4 function:2 form:1 smolin:1 but:1 properly:1 atom:1 true:1 directed:1 october:1 cik:10 characteristic:1 up:2 below:1 ωn:2 similar:1 cirac:1 constant:1 computing:1 defined:1 abstract:1 describe:3 oscillations:2 our:2 apartado:1 physical:1 nm:1 ekert:2 field:2 digital:3 department:1 ny:1 elements:1 superposition:1 excitation:1 berman:2 a1:9 a2:9 ising:2 algorithm:2 vice:1 assume:1 curve:8 investigated:2 time:7 cleve:1
|
quant-ph9802014.txt |@word gr:1 similarity:1 woods:4 entropy:14 expressions:4 localized:1 equiprobable:1 particles:4 depend:2 clarification:1 ohya:1 alamos:1 charge:1 th:1 under:1 indicating:1 conjecture:1 wave:2 print:1 electron:3 affect:1 nishioka:1 turns:1 solved:1 upper:1 employing:2 force:1 consistent:2 second:1 chem:1 analogue:1 sum:3 mycielski:2 3n:1 above:3 net:1 acknowledgments:1 respectively:1 equals:1 here:2 atoms:12 sinf:1 consideration:1 strong:1 equations:1 obtained:3 property:3 study:3 fourier:1 dimitrova:1 highly:1 linearly:1 plot:1 use:1 feb:1 would:1 commun:1 remains:1 finally:1 next:1 nucl:2 bialynicki:2 theoretical:3 more:1 odinger:1 normalized:1 cases:3 hold:1 high:1 springer:1 middle:1 equation:1 oscillator:2 fock:4 values:5 norm:4 concepts:1 following:6 hansen:1 figure:1 stated:1 states:1 verlag:1 normalize:1 information:15 respective:1 discussion:1 holds:2 may:1 thermodynamic:2 derived:4 effective:2 sr:26 lines:1 correspond:1 sk:26 so:1 fundamental:1 years:1 through:1 jaynes:1 its:2 derive:1 thank:1 fit:1 sodium:1 ln:36 interesting:2 coordinates:1 actually:1 systems:3 saxon:4 massen:4 clusters:17 hidden:1 eur:3 good:1 13n:1 scaling:1 skyrme:6 they:1 easily:1 university:1 inequality:1 radial:1 found:3 2n:2 mean:6 ea:1 related:1 sears:1 measure:1 quantum:6 our:10 meth:1 ev:1 shannon:2 out:1 space:8 open:2 since:1 rev:5 content:1 conjectured:1 denoted:2 ref:4 math:2 theory:2 estimate:1 incorporates:1 interaction:4 r0:2 quantummechanical:1 counterpart:1 length:1 hence:2 first:2 probability:1 striking:1 number:9 approximate:1 approximately:1 electronic:1 leading:1 system:7 relations:3 calculations:5 final:1 mostly:1 parametrized:1 parr:1 authors:1 than:1 approximations:1 were:4 conjugate:1 seen:2 seem:1 relationship:1 convenient:1 self:2 metallic:1 note:1 potential:7 take:1 analogy:2 circles:4 though:1 boltzmann:5 letter:2 inserted:1 kb:1 considered:1 professor:1 stronger:1 physica:1 electrons:5 exp:1 mechanical:3 physics:1 fitted:5 quantity:2 thomas:2 nagy:1 spaces:3 relation:10 rough:1 uniform:1 find:1 ock:1 treasure:1 giai:1 local:1 panos:4 do:1 his:1 dk:1 joint:1 ones:2 dr:1 gen:1 regarding:1 densities:2 arxiv:1 petz:1 thessaloniki:2 see:2 individual:2 greece:1 nuclear:7 lalazissis:1 written:1 various:2 between:2 invariant:1 discovery:1 extend:1 however:2 jr:1 configuration:1 many:4 uncertainty:3 according:3 microstates:1 expression:7 comment:1 mechanics:1 simple:2 corresponds:1 dimensional:2 concluding:1 associated:1 three:1 ph:1 fig:1 corresponding:4 diffuse:1 present:2 case:4 pacs:1 solid:2 while:1 match:1 balance:1 played:1 thus:2 cluster:1 vw:1 fermion:4 same:2 quant:1 several:1 used:1 numerical:2 v0:2 arrived:1 delicate:1 potentials:2 normalization:3 recent:1 lower:1 schr:1 well:2 coordinate:1 position:5 model:3 spherical:1 obtain:1 atomic:10 yet:1 represented:1 density:4 seems:2 parametrization:4 versa:1 mottelson:1 momentum:7 gave:1 harmonic:2 background:1 press:1 using:6 mod:2 like:1 particle:4 follows:1 separately:1 informative:1 nucleons:2 reasonably:1 unexplored:1 heisenberg:1 ermi:1 methods:1 calculated:3 entropic:1 does:1 unit:1 measuring:1 bf:1 bn:1 agreement:1 step:1 comparison:1 valence:2 dependence:1 o:2 slightly:1 into:1 numerically:1 functional:3 appropriate:1 because:1 parametrizations:1 van:1 there:6 transform:2 los:1 low:1 hirschman:1 was:2 synthesis:1 function:3 form:9 but:3 neutral:2 ho:2 atom:1 characteristic:1 us:1 fermi:2 distribution:3 similar:1 jellium:1 entropies:11 detailed:1 constant:1 int:3 universal:4 am:1 single:3 aristotle:1 distributions:6 archive:1 physical:1 functions:2 na:1 field:6 other:2 role:1 department:1 important:3 nucleus:2 birula:2 vice:1 curve:3 n0:6 nuclei:15 dover:1 starting:1
|
quant-ph9802015.txt |@word drastically:1 consider:2 campbell:2 show:5 indeed:1 magnetic:3 both:1 splitting:1 effects:1 rotating:3 projects:1 experiments:4 same:2 computation:2 differs:1 captions:1 cnls:2 its:5 berman:3 perfect:1 note:1 derive:1 based:1 submitted:1 parameters:2 field:4 implementation:1 alamos:3 less:1 state:8 decreases:2 preprint:1 detected:1 permanent:2 isica:1 systems:3 molecules:2 under:5 rabi:1 c11:3 c10:3 macroscopic:7 division:2 supported:1 amplitudes:2 rev:1 far:1 frequencies:2 de:2 wave:1 electron:2 entangled:9 polytechnic:1 resonant:3 using:1 thus:1 now:2 advanced:1 mod:1 easily:1 evolution:8 precession:2 transversal:1 monotonically:1 hamiltonian:3 conditions:2 university:1 arxiv:1 arrows:2 cik:2 paper:2 each:1 c00:3 c01:3 side:1 spins:13 development:1 dilute:1 significantly:3 classical:7 gennady:1 dealing:1 national:2 creation:1 phenomena:1 pulse:18 maximum:1 observed:2 understood:1 see:5 individual:1 result:1 indicate:2 ez:3 quantum:8 laboratory:2 dynamics:3 iˆi:2 analog:2 divincenzo:2 shown:1 vertical:2 factors:1 nuclear:2 definite:1 near:1 research:1 case:3 written:3 does:5 simplest:1 between:1 new:1 paramagnetic:1 after:1 terms:1 theory:1 do:1 nature:1 initially:1 component:5 proper:1 weak:1 oscillations:1 departamento:1 standard:1 small:5 approaches:1 objects:1 ratios:1 doolen:3 represented:1 described:2 understanding:1 equations:4 properties:1 improve:1 obtained:1 comparison:1 interaction:3 defense:1 transition:1 equal:1 zeeman:1 motion:5 hψ:2 plane:2 2j:1 universidad:1 usually:1 hospitality:1 observes:1 first:1 via:1 figure:1 simple:1 into:1 corresponds:1 reaches:1 negative:1 directions:1 right:6 decrease:1 frame:2 gary:1 leads:1 apply:1 total:1 eiωt:1 jozsa:1 feb:1 temperature:2 second:3 their:2 remains:1 positive:1 interact:1 contains:1 system:7 approximately:1 los:3 sample:1 positing:1 low:1 time:4 transformed:1 ph:1 exico:1 was:1 theoretical:2 today:1 fig:7 function:1 direction:3 only:1 partly:1 form:2 gyromagnetic:1 vanishing:1 initial:4 stable:1 odinger:1 but:2 mainieri:1 sharply:1 schr:1 lop:3 spin:21 than:2 those:1 applied:1 iωt:1 kind:1 october:1 vladimir:1 solid:1 science:1 equation:1 work:1 zero:3 value:3 ur:2 ωi:1 considered:3 labeled:1 frequency:10 values:4 indicating:2 amplitude:2 following:1 situation:1 example:2 ions:1 references:1 ab:1 constant:1 behavior:1 indicated:1 mexico:1 beginning:2 abstract:1 bennett:2 influence:2 states:7 middle:1 ik:2 application:1 our:1 xy:2 sharp:3 concentration:1 action:7 agency:1 different:3 gustavo:1 i1x:3 i1z:3 rather:1 ekert:1 six:1 when:1 lett:1 guadalajara:2 stability:1 end:4 ny:1 complex:1 quant:1 analogy:2 department:1 mathematics:1 require:1 ensemble:1 conclusion:1 deviation:4 independent:1 used:1 la:2 shall:1 i1:3 i2:2 molecule:7 drives:1 ion:1 brooklyn:1 produce:2 connected:1 ising:1 i1y:1 grateful:1 acknowledgements:1 extremely:1 sides:1 reference:1 recent:1 i2x:3 i2y:2 i2z:4 quasiclassical:12 center:1 effective:1 assume:3 average:6 remain:1 physica:1 points:2 so:2 components:2 electromagnetic:1 very:3 position:1 decoherence:1 monotonic:1 physics:2 figs:2 left:7
|
quant-ph9802016.txt |@word sci:1 consider:3 magnetic:2 results:1 four:14 computation:6 consists:1 certainly:1 calculate:1 alamos:3 γh:1 under:4 indicating:1 division:2 r15:1 r11:5 very:2 frequencies:5 manipulated:1 figs:1 polytechnic:1 resonant:16 difference:1 condition:2 hamiltonian:2 small:4 c01:1 grateful:1 insignificant:1 pulse:18 feasibility:1 second:2 manipulating:1 dynamics:9 estimated:1 even:1 errors:1 plays:2 interactions:3 3j:3 new:1 coefficient:1 margolus:1 desired:2 possibility:2 2kb:3 active:7 consideration:1 equations:1 change:5 obtained:1 noticeable:2 shift:1 study:1 changed:1 ignoring:1 knill:1 usually:1 hospitality:1 studies:1 involves:1 marked:1 rkn:1 total:1 unit:1 rkk:1 use:1 feb:1 usa:1 remains:1 positive:1 laflamme:1 next:3 monotonically:1 theoretical:3 minor:1 more:1 separated:1 gyromagnetic:1 holm:1 correspondingly:1 particular:1 cases:1 given:2 room:6 vladimir:1 science:2 work:1 modified:1 ibz:1 values:3 following:2 example:1 control:5 figure:1 give:1 process:2 bennett:1 suggestions:1 implementations:1 states:19 effectively:1 performed:1 r22:4 end:3 precessing:1 six:2 feature:1 pure:3 gate:18 sin:1 containing:1 independent:1 plane:2 realized:2 dynamical:1 effective:1 computations:1 correspond:3 circularly:1 so:1 order:1 operations:1 gershenfeld:1 satisfied:1 experiments:2 pulses:4 same:2 differs:1 captions:1 excitations:3 its:2 la:1 decreases:1 permanent:1 isica:1 systems:8 rabi:1 main:1 non:11 rotations:1 effects:3 they:2 accumulate:1 now:2 inversion:1 university:1 arrows:1 ensemble:13 2d:3 applied:1 2a:4 2b:1 each:4 significantly:1 r33:4 gennady:1 energy:3 idea:1 frequency:6 ez:2 quantum:27 laboratory:2 operation:1 divincenzo:1 shown:6 dominates:1 matrix:13 since:1 rev:3 research:1 re:2 rn:1 associate:1 diagonal:6 departamento:1 c00:1 completely:1 complicated:1 jozsa:1 e0:1 interaction:5 transition:2 motion:1 universidad:1 first:3 initial:19 number:2 xy:2 differ:1 temperature:9 indicate:2 deutsch:1 system:9 their:1 iax:1 calculations:4 iaz:2 frame:1 convention:1 part:1 simulate:1 coefficients:1 population:2 polarized:1 target:2 approximations:1 zero:1 havel:1 supposed:3 amplitude:1 curves:1 further:2 weinfurter:1 any:2 implemented:2 gustavo:1 convenient:1 agency:1 isolated:1 schematically:1 accuracy:1 shall:3 molecule:6 brooklyn:1 significant:2 phase:2 acknowledgements:1 exico:1 considered:1 neighboring:1 calculated:1 drive:1 physica:1 points:1 physics:1 fact:1 shor:1 set:1 show:4 supported:1 rotating:1 chuang:1 cnls:2 ground:3 ratio:1 parameters:5 implementation:6 enough:2 only:4 candidates:1 molecules:8 factor:1 hamiltonians:1 jab:3 do:1 notation:3 fahmy:1 zurek:1 de:2 overall:1 cannot:1 during:1 evolution:5 arxiv:1 investigate:1 paper:1 through:1 require:1 ignored:1 multiplying:1 reference:1 national:2 maximum:1 see:3 defense:1 r00:6 close:2 nuclear:1 initially:1 state:10 simplest:2 progress:1 conditions:15 barenco:2 vertical:2 importance:1 implementing:1 sleator:1 suggested:1 both:3 cos:1 last:1 many:1 logic:5 qubit:10 whole:1 ck:1 cn:18 conclude:1 simple:1 corresponds:10 dimensional:1 r44:1 γba:1 sequences:1 quan:1 cory:1 described:3 invert:1 three:2 been:1 describes:2 expected:3 ph:2 fig:19 field:2 direction:1 corresponding:1 6j:1 understand:1 c3:2 c2:2 c1:2 c0:2 spin:29 present:1 case:4 inhibit:1 value:8 behavior:2 promising:1 situation:1 rnk:8 mexico:1 00i:1 ink:1 thus:1 ij:1 im:3 ia:2 interacts:1 binary:1 different:4 perform:1 lett:2 guadalajara:2 parts:2 quant:1 finite:3 evolve:1 investigated:1 numerical:7 action:3 phy:1 levels:2 doolen:3 contribution:1 recent:2 off:1 center:1 nevertheless:1 changes:2 well:1 analysis:1 without:2 solve:1 gates:5 decimal:1 campbell:3 eigenstates:1 preprint:1 density:9 passive:1 projects:1 natl:1 c11:1 c10:1 excited:2 real:2 rnn:3 decomposed:1 entangled:1 using:6 unique:1 advanced:1 like:1 arbitrary:1 become:1 reasonably:2 spins:7 twelve:1 because:1 namely:1 sequence:3 creation:1 acad:1 confirm:2 electromagnetic:3 investigations:1 does:2 provides:2 proc:1 ba:1 2c:2 mainieri:1 imaginary:1 refers:12 between:2 central:1 mixed:1 create:2 ising:6 into:2 numerically:3 right:1 references:1 gary:1 operator:1 arrow:1 additional:1 there:1 los:3 lop:2 analyze:3 was:4 function:1 constantly:1 smolin:1 but:1 true:2 characteristic:1 ωt:2 ur:1 ωk:6 ωa:3 problem:2 average:3 constant:3 abstract:1 describe:1 influence:1 single:5 our:3 partly:1 formalism:1 physical:2 no:1 ekert:1 when:4 application:1 other:5 role:2 digital:2 department:1 mathematics:1 ny:1 deviation:3 elements:6 berman:4 problems:2 prepared:1 important:1 bullets:1 allowing:1 bullet:1 assume:3 required:2 curve:11 time:4 cleve:1
|
quant-ph9802017.txt |@word ideality:1 bypassed:1 consider:4 switched:1 rev:12 magnetic:1 iib:3 dynamic:10 results:5 unchanged:1 extends:1 four:1 known:1 scalar:5 gd:55 current:4 variations:1 follow:1 expressions:2 zinn:1 contributions:1 cb:2 reynaud:3 whose:3 dimensionality:1 depend:1 calculate:12 similar:2 simplify:1 tr:1 corrections:7 shall:1 profound:1 finally:2 behave:1 manifolds:5 th:1 analogous:1 c0s:2 sound:1 g4:4 amplitudes:2 g2:4 advantage:1 orthogonal:1 very:4 frequencies:20 tends:1 radius:1 none:1 maia:3 wave:2 electron:2 wishes:1 colloquia:1 softened:1 fall:1 resonant:8 experimentally:2 difference:4 capillary:5 deformations:17 minute:1 transversality:1 treating:1 europhys:2 exponential:2 purely:2 did:1 dψi:2 anisotropy:3 list:1 applicable:2 ri:2 large:1 discrete:2 vector:3 math:2 small:11 generalize:1 equation:3 upper:2 smaller:2 force:24 oscillation:1 efforts:1 d3:1 direct:1 literature:4 cosh:1 rate:2 enhancement:2 further:1 hca:2 implemented:1 odd:2 leakage:1 quite:2 linear:4 even:2 will:4 what:1 appear:4 64h:1 section:2 abk:1 dtd2:3 uniform:3 reminiscent:2 3h:1 issues:1 above:7 waals:3 new:4 avenues:1 pendry:1 method:12 contrast:3 pioneering:1 barton:1 mutual:1 full:1 iran:2 hd2:1 degree:2 respectively:1 proper:2 spacing:1 residual:1 here:1 atoms:1 reported:3 objects:2 focused:1 separation:9 directions:2 path:11 photonic:4 xα:11 z0:6 appears:1 change:2 obtained:7 transmittivity:1 great:1 crystal:3 institute:3 involved:2 study:3 studied:2 allows:2 vibrating:3 experience:1 suggests:1 amount:1 resulting:7 action:7 resonance:4 implement:1 fourier:6 studies:2 lamoreaux:1 frictional:1 emerge:1 offs:1 via:1 followed:2 scales:1 inducing:1 namely:1 sign:2 sample:2 private:1 replace:2 expect:1 inequality:2 rg:1 sgn:2 summation:2 controlled:1 total:1 mistakes:1 aµ:3 f5:2 retarded:1 use:6 additive:4 sβ:3 would:4 distinct:1 involving:1 contains:1 direction:1 negative:1 jaekel:2 next:4 ψj:3 few:1 depicted:1 tm:1 m0:7 usp:1 conservation:3 associated:1 type:2 refs:2 more:11 separated:2 introducing:1 h1:46 neglected:1 naive:1 mismatch:2 emission:1 curvature:1 introduces:1 ip0:1 appendix:11 iia:4 discrepancy:1 rod:2 particular:3 worthwhile:1 r0:4 cases:1 iii:2 must:2 logarithm:1 high:5 keeping:1 te:1 ma:1 integrating:1 mm:1 der:3 work:2 det:3 modified:2 mk:1 remain:2 ij:1 could:1 pλ:1 following:4 cond:1 modifies:1 dec:1 example:10 decoupled:1 f1:3 f2:2 f3:2 f4:3 renormalization:6 f6:2 mirrors:7 predict:1 expanding:1 arise:1 organized:1 purposes:1 generically:1 topic:1 sphere:1 lorentz:2 performed:5 want:1 sense:2 yα:30 deforming:1 rods:1 yβ:5 occur:4 junctions:2 axis:1 sis:1 regularization:1 end:1 g1:4 rather:3 describes:1 s1:2 holds:1 s6:1 roughness:3 regions:3 necessary:1 nontrivial:1 get:1 justin:1 optimal:1 those:1 parameter:4 sin:5 tension:5 rise:1 mat:1 may:6 earlier:1 residues:2 dc:1 davis:2 plane:6 tackle:1 waves:5 fi:2 summarize:1 choice:2 divergences:2 parallel:6 man:1 included:1 criticized:1 amenable:1 dα:1 third:1 akad:1 light:1 spectra:2 explicit:1 cosmology:1 provide:1 green:6 s2:3 goulian:1 integrand:1 order:10 gµν:6 prefactor:3 neto:3 restriction:2 s0:2 rounded:1 words:1 meade:1 correlation:1 developed:2 over:9 move:1 satisfied:1 presence:2 thermal:1 paper:4 including:2 same:3 statistical:1 fac:1 argued:1 suffer:1 its:10 roots:1 perfect:2 treat:1 decay:3 ln:15 interesting:7 lateral:8 inclusion:1 imperfection:1 coordinates:3 actually:1 better:2 previously:1 absence:1 production:1 microscopic:1 fig:4 pergamon:1 derivative:3 freely:1 might:1 deformation:10 shear:3 them:2 good:1 nonideal:1 greater:1 combination:2 matches:1 rotations:1 practice:1 impossible:1 introduce:3 landau:1 framework:1 walls:4 effects:8 they:3 cosh3:1 oxford:1 diag:2 rotation:2 now:9 discuss:1 dielectric:3 g0i:1 easily:5 february:1 finite:10 2p:2 2q:1 2s:1 always:1 university:2 b3:1 quantizing:1 realistic:3 vibrations:3 mode:2 each:1 deformed:1 found:5 soc:1 difficult:3 2h:1 2i:1 characterized:1 em:2 ann:2 domain:2 square:1 england:2 determine:1 golestanian:3 simplicity:1 quadratic:2 series:1 energy:11 joannopoulos:1 displacement:3 related:4 inverted:1 line:1 frequency:24 static:7 obtains:3 b1:3 measure:2 quantum:13 our:8 transitions:1 extract:2 χij:5 special:2 out:2 δri:1 shown:3 matrix:9 resonators:1 space:21 gradient:1 furthermore:1 since:3 squared:1 denotes:1 particles:1 eiq:1 unrelated:1 formula:1 wick:2 induced:4 ref:18 correct:1 rj:3 sinh3:1 sinh2:1 after:3 theory:9 interactions:3 δseff:2 divergence:7 diagonal:2 free:1 standard:6 difficulty:2 approaches:3 complicated:3 corrects:1 yαi:1 care:1 definition:1 enormous:1 qj:1 cured:1 geometry:5 starts:2 collapsing:1 round:1 motion:10 length:1 along:1 δij:1 forms:3 hence:5 moving:7 linearized:1 undergo:3 first:4 corrugated:12 dmr:1 corrugation:1 symmetry:1 kernel:1 attractions:1 variables:1 number:4 iqi:1 xx:1 done:1 reflectivity:6 another:4 representations:1 zh:5 angular:3 dψα:2 mercury:4 πc:2 given:3 perturbation:4 embeddings:1 likely:1 similarly:1 introduction:2 leading:3 eqs:5 system:3 vibrate:1 response:22 zanjan:2 their:6 eddy:1 assumption:4 too:1 calculations:8 perfectly:5 behaved:1 ranging:1 relations:1 gives:5 exploring:1 excellent:1 wavelength:1 explanation:1 exactly:1 stress:1 artifact:2 prediction:1 part:8 somewhat:1 authors:1 x2:7 natural:3 eliminated:1 x1:2 uninteresting:1 than:9 observed:2 effective:9 novel:1 was:1 require:2 see:8 submitted:1 final:2 states:1 future:2 braz:1 unphysical:2 were:2 p0:2 tackled:1 separate:1 led:1 treated:1 klimov:1 perturbative:2 lowest:2 resistivity:1 lambrecht:1 dielectrics:1 generality:1 contradict:1 bare:1 fluctuation:3 correction:6 argument:2 generalization:3 crossover:1 say:2 ford:1 variable:2 vilenkin:1 close:1 need:3 seen:1 fµν:2 give:1 any:9 mij:1 angle:1 newtonian:1 academic:1 randjbar:1 lim:4 latter:2 mid:1 mechanism:2 metallic:1 note:11 laterally:1 ideal:2 potential:2 machado:1 take:3 forces:7 hs:2 so:1 outlook:1 techniques:3 accuracy:1 formulas:2 play:1 continuous:4 multiple:1 gβ:1 gα:5 normal:2 probed:1 whole:1 who:1 viscosity:5 systems:1 most:4 rigidly:1 connected:1 comparing:1 pair:1 transverse:3 measured:1 cs:2 causality:3 deviations:1 acknowledges:1 don:1 observation:1 surprising:1 lines:1 kj:1 calculated:7 kh:5 ko:1 playing:2 reflecting:3 dynes:1 gignoux:1 exp:8 mechanical:11 velocity:6 typical:2 physics:2 notion:1 wavenumber:1 applied:2 perspective:1 drastically:1 phenomenon:3 gold:2 show:1 supported:1 friction:5 notations:1 implying:1 attempts:1 spaces:1 gauge:7 xd2:2 substituting:1 rough:1 thickness:1 d2:14 find:9 fifth:3 d1:2 symmetric:2 iq:11 q2:13 ratio:3 chang:1 transformation:1 choose:1 less:2 should:5 analytic:4 only:9 experiment:1 candidates:2 factor:3 identification:1 g00:1 density:4 hope:1 pj:3 plate:26 explorations:1 xdd:7 iωt:3 dependent:9 dd:24 membrane:1 overall:1 fluid:2 da:2 superconductor:1 dynamically:2 cannot:1 listed:1 closely:1 wise:1 dt:1 major:1 aν:3 ds:2 areas:1 signatures:1 continuum:1 m0j:1 approach:6 arxiv:1 expansions:1 summary:1 trunov:1 experiments:1 predicted:1 dodonov:3 characteristic:1 qi:1 through:1 fixed:2 voltage:1 intervening:2 coefficient:1 set:6 ned:1 opposed:1 achieved:1 undergoes:1 exerted:1 hα:3 respect:5 hopefully:1 detection:2 edition:2 depends:5 individual:2 sec:4 result:10 klimchitskaya:1 discussions:1 terms:7 transmissivity:1 contour:1 analog:1 subject:5 surfaces:9 satisfying:1 singularity:1 tensor:4 placed:1 phonons:1 scattering:1 review:1 consequence:2 fulling:2 diverge:2 boundaries:12 written:2 difficulties:1 various:4 closed:1 between:12 without:2 invariant:3 boundary:8 previous:3 conditions:6 ydd:2 speed:1 p20:5 emitted:3 recently:1 reproduced:1 relative:1 nature:7 weak:1 ωn:1 focus:3 however:14 vanishing:1 concentrate:1 limitation:1 beyond:1 configuration:1 distribution:1 pointed:1 both:8 cos:3 limits:2 tractable:1 powers:3 region:8 conclusions:2 c5:2 quantization:2 mostepanenko:2 deform:1 context:1 casimir:23 distinction:2 contribution:2 expression:6 finds:1 experimental:2 ck:6 suggest:1 presumably:4 relevant:1 fields:10 pendulum:1 point:4 wall:1 continuation:3 ca:1 multiplier:1 corresponds:2 daemi:1 dimensional:12 xβ:4 ψi:5 diverges:1 simply:3 applicability:1 lagrange:1 occuring:1 symmetries:1 cq:4 li:1 considers:1 appeared:1 torsion:1 considering:3 kernels:15 sine:1 corrugations:2 transformations:2 second:10 basis:1 addition:1 help:1 48h:1 due:16 been:8 balian:1 ai:2 much:2 slowly:2 z2:10 interest:2 basic:2 anisotropic:6 applying:1 ph:2 pi:3 hardly:1 ak:1 define:1 pβ:2 determinant:2 describe:2 corresponding:5 tµν:1 kronig:1 reaction:1 sufficient:1 wet:1 photon:1 wires:2 spectrum:6 kramers:1 1mm:2 external:5 wavevectors:1 receive:1 c2:7 former:1 present:5 mashhoon:1 case:10 eip:8 intriguing:2 handling:1 josephson:5 solid:1 reliable:1 appearance:1 examine:6 value:1 easier:1 intimately:2 euclidean:1 while:12 p2:4 overcome:1 behavior:5 promising:3 ramin:1 situation:3 conformal:2 taking:2 procedure:2 resolved:1 larger:1 levitov:1 phenomenological:1 ip:9 metric:4 conjugate:1 thus:7 non:3 surface:11 iv:2 ii:2 quantize:2 reads:2 examined:1 properties:2 commonly:1 crystals:2 limit:5 mod:1 vanish:1 technology:1 currents:1 around:2 acknowledgments:1 different:4 develop:1 grant:1 perform:1 media:1 make:4 radiation:9 lett:13 plated:1 orders:1 princeton:2 kardar:4 parts:6 quant:1 arguments:1 diagonalize:1 plates:35 dimensionless:2 several:1 start:1 ac:1 higher:6 breakdown:1 independent:4 calculation:2 used:4 infinity:2 singapore:2 numerical:3 effect:14 possible:3 parametrized:2 usually:2 conductors:3 necessity:1 potentials:1 infinite:5 changing:1 invariance:1 pν:2 adopting:1 expand:2 keep:1 implements:1 lower:1 integrations:2 off:10 modes:8 satisfy:1 changes:4 variety:1 well:7 generation:1 double:1 concrete:1 accompanied:1 solve:1 components:2 fixing:1 model:1 knight:1 dimension:2 bodies:1 translational:1 manifold:2 proposed:1 examining:1 being:1 when:6 paragraph:1 obtain:8 rest:1 shape:3 underlying:1 atomic:1 using:19 momenta:1 macroscopic:5 yet:1 multiples:1 elaborating:1 york:1 dispersive:1 cut:5 preprint:1 cm:2 integer:2 sciences:2 mµν:1 photons:10 seems:2 emphasis:1 undulating:1 wavevector:5 lattice:1 add:3 valid:1 transformed:2 attractive:3 theorem:1 usage:1 reach:1 extensive:1 gava:1 excited:5 momentum:4 build:1 real:11 fluctuating:5 reparametrization:1 read:2 term:3 additivity:1 test:1 seff:1 vacuum:11 press:4 world:4 unique:1 moreover:1 advanced:2 helpful:1 loss:1 modifications:1 rotate:1 imposed:1 like:3 particle:3 shaped:2 follows:1 signal:1 velocities:1 δr:1 accelerating:1 specific:3 δm:12 yields:1 either:1 integrals:1 arbitrary:1 completely:1 become:1 stationary:3 essential:1 accessible:1 because:1 methods:3 classical:3 do:1 resonances:2 creation:5 phenomena:9 back:1 artificial:1 b4:1 understood:3 b6:1 a16:1 eberlein:2 examples:3 b2:2 mirror:6 oscillations:1 gen:1 electric:2 provided:1 davies:1 represent:1 dimensions:11 lead:4 fourth:1 cavity:13 electromagnetic:7 measurements:1 integration:6 stops:1 manipulations:3 electrodynamics:2 everything:1 duplantier:1 does:3 provides:4 assuming:1 steps:1 proc:2 lifshitz:1 inserting:1 varying:1 object:1 scientific:2 power:2 derivatives:1 m0i:1 problems:2 2c:1 oscillating:3 perpendicular:1 expansion:5 interval:1 pressure:1 many:2 unlike:1 although:2 2m:1 described:5 imaginary:14 exciting:3 kd1:3 simpler:2 gνλ:3 conducting:4 pα:2 actual:1 geometries:1 constraint:1 krech:1 freedom:2 based:2 discussed:3 dependence:6 o:2 reduced:2 range:4 a2:1 extensions:1 2ck:1 analogy:1 diverging:1 ci:4 introduced:2 consequently:1 contours:1 a4:1 wire:1 equally:1 cambridge:1 a7:1 plethora:2 h2:38 communication:1 into:2 within:2 integral:13 nsf:1 three:1 phase:5 appropriate:3 extending:2 references:1 degrees:2 sov:1 operator:1 proportional:7 t00:1 theoretically:1 envision:1 a3:1 performing:1 regarded:2 van:3 additional:5 area:3 law:2 support:1 there:14 subdivide:1 transform:1 specifically:1 strict:2 restricts:1 detectable:1 quanta:1 low:5 way:1 dtdt:2 viscous:1 bubble:1 gij:1 damping:1 function:24 semicircle:3 complete:1 form:2 winn:1 a9:2 some:9 differences:3 agrees:1 but:3 gaussian:1 hk:1 neutral:1 magnitude:1 link:1 m00:1 hz:3 delta:1 hc:2 optical:6 removed:1 dissipative:2 versatile:1 2πc:1 made:1 compute:1 consequences:1 embedded:2 b5:1 2πi:1 minkowski:1 best:1 generating:2 up:8 us:1 assume:1 below:3 superlattices:2 complications:1 critical:2 sum:5 fαβ:1 fluctuations:11 problem:4 yα1:1 average:5 distance:3 mechanics:1 requiring:1 partition:4 constant:5 moore:2 flat:5 defined:5 ki:1 specified:1 condition:2 dyα:4 dyβ:2 modify:1 single:9 enable:1 fi0:2 a12:2 formulation:4 accounting:1 uniaxially:1 formalism:5 regime:6 bordag:1 functions:15 compared:1 d4:5 no:5 eq:24 zang:1 generally:1 vanishes:3 field:21 other:7 role:3 details:3 a6:1 department:1 conclusion:1 a15:1 a14:2 a17:1 repeat:1 a11:1 a10:2 a13:1 fdc:1 excite:1 setting:1 uniformly:3 a18:1 inherently:1 δcs:2 a1:1 a0:3 generated:1 important:4 a5:2 massachusetts:1 suited:2 iω:1 dissipation:20 a8:2 structure:1 source:1 sinh:1 oscillates:1 implies:2 coupling:1 dω:2 dφ:2 dτ:2 required:2 having:1 2c4:1 mass:19 fact:3 time:31 qualitatively:2 signals:1 requires:1 original:2
|
quant-ph9802018.txt |@word limited:2 externally:1 code:8 consider:1 represent:1 magnetic:6 lack:1 focus:1 leads:1 roy:4 computation:6 consists:1 whose:2 preserves:1 depend:1 alamos:2 refocus:1 technique:2 factoring:1 compensate:2 preserved:1 th:3 under:1 include:1 logarithm:4 supported:1 returned:1 advantage:1 evolves:1 very:1 springer:1 induce:1 results:4 wishes:1 experimentally:2 difference:1 logarithmically:1 method:1 four:5 school:1 incoherent:1 hamiltonian:2 t2:4 t1:1 large:2 small:6 darpa:1 application:1 grover:1 fragility:2 pulse:2 rate:2 compensates:1 spect:2 implemented:4 spectral:1 3z:1 errors:10 appear:1 3s:1 sum:6 dephasing:7 decoding:14 experiment:6 subspaces:1 nine:1 net:3 public:1 simultaneously:1 ms:2 degree:1 exchange:1 component:1 here:2 desired:1 magnetism:1 relaxation:3 ratio:1 along:3 extreme:1 obtained:2 trans:1 accomplishes:1 clarendon:2 institute:1 involved:1 amount:1 products:1 knill:2 usually:1 resonance:2 implement:1 suitable:1 makes:1 subjected:1 involves:1 king:1 iy:1 stabilization:1 ratios:2 9e:1 highly:1 iz:8 total:4 establish:1 9t:2 linearly:2 alamitos:2 use:2 feb:1 would:2 army:1 laflamme:2 toffoli:2 program:1 characteristics:1 abragam:1 theoretical:1 today:1 more:3 separated:1 gyromagnetic:3 iu:1 operators:2 corrected:4 occurred:2 validity:1 realized:1 carrying:1 normalized:1 varying:3 known:2 foundations:2 encountered:1 must:1 ρa:2 states:14 ρc:1 ρb:1 ma:2 room:1 science:6 work:2 modified:1 theories:1 labeled:2 itself:1 values:2 evolved:3 modifies:1 coherences:3 example:2 control:6 figure:3 give:1 process:1 preserving:1 implementations:1 sample:2 mixture:1 numbers:3 1s:1 axis:3 information:8 syndrome:1 destroying:1 imprecision:1 breaking:1 delay:3 far:1 pure:4 iθ2:2 iθ3:2 iθ1:2 ensemble:5 profile:1 map:1 product:4 our:6 ancilla:2 fz:1 after:7 variant:1 fa:1 designed:1 fits:2 data:2 constants:1 efficiently:1 scrambling:1 no:2 natural:3 liquid:5 computations:2 interpolations:1 element:1 rather:1 chief:1 so:3 fundamental:1 eich:1 order:9 operations:1 gershenfeld:1 pulsed:1 help:1 office:1 over:1 flips:2 thermal:1 experiments:12 london:4 affect:1 fidelity:3 ieee:2 its:1 before:1 sciences:1 rapidly:1 thank:2 fit:4 decay:3 decreases:2 symptoms:1 absence:1 degrees:1 systems:5 h3:1 stoc:1 overcome:1 versus:1 non:3 thereby:1 processes:4 steane:1 slichter:1 they:2 half:1 oxford:2 rotation:1 now:1 yu:1 bigger:1 february:1 always:1 classified:1 2z:1 sufficiently:1 reasonable:1 each:9 found:2 bona:1 square:4 directly:1 inputs:1 generation:1 series:1 energy:2 displacement:2 constitute:1 frequency:1 gates:1 measurement:1 quantum:32 laboratory:1 eq:4 principles:3 shown:5 matrix:7 3rd:1 space:1 gradient:7 since:1 rev:5 ry:7 research:1 particles:2 combinatorial:1 acting:1 fy:1 term:1 formula:1 induced:4 occurs:1 red:1 shows:1 gate:6 turning:1 linear:3 diagonal:1 difficulty:1 completely:3 california:2 corrects:1 generate:2 advance:1 angle:1 created:1 computers:1 motion:2 place:2 exponentially:1 circuit:1 target:2 broken:1 first:15 initial:11 fx:1 encoding:9 number:3 preservation:1 echo:1 entanglement:3 set:1 approximately:1 another:1 impossible:1 precisely:2 zalka:1 angular:1 aharonov:2 given:3 temperature:4 width:1 leading:2 1z:1 system:5 least:2 unruh:1 their:4 returns:1 quadratic:1 rates:1 scheme:1 bits:6 final:1 imperfect:1 reversed:1 continuous:1 contribute:1 accurately:1 part:1 simulate:1 nh2:1 than:4 havel:2 diffusion:4 relative:1 polarized:2 ben:2 effective:1 require:1 imply:2 determined:3 intensities:5 were:8 result:2 boston:1 correction:29 measure:1 curves:6 randomly:1 substantial:1 close:1 seen:1 demonstration:3 any:5 i1z:14 estimated:2 computationally:1 zero:2 depending:1 latter:1 agency:1 isolate:1 ideas:2 polarization:8 majority:1 high:4 internal:1 take:2 finding:1 green:1 techniques:2 accuracy:1 cl:3 even:1 added:2 unless:1 recovery:2 shall:1 price:1 molecule:1 most:1 involving:1 phase:14 measured:7 pages:2 gain:1 mass1:1 consequences:1 considered:1 medical:1 phil:1 inferred:1 physica:1 feynman:1 proceedings:2 points:2 verlag:1 principle:1 clean:1 physics:1 applied:1 slope:5 shor:3 intensity:1 show:2 text:2 random:8 chuang:1 lloyd:1 threshold:1 correct:2 trivial:1 ground:1 slow:1 based:2 simulating:1 implementation:3 carbons:3 delays:2 should:1 only:1 explicitly:1 molecules:1 factor:4 partially:1 local:2 equilibrium:2 do:2 his:1 cryptography:1 get:1 dependent:1 fahmy:1 zurek:3 between:3 overall:1 ones:1 nearly:1 bodenhausen:2 report:1 during:2 procedures:1 unfortunately:1 evolution:2 densities:1 fields:8 arxiv:1 yield:1 across:1 predicted:1 contain:1 traceless:1 view:1 reveals:1 alanine:6 kitaev:1 achieved:1 physically:2 national:2 observed:2 ancillas:7 depends:1 computer:4 usefulness:1 separately:1 terms:2 uncorrelated:1 best:1 subject:5 phases:2 interacting:1 nuclear:3 state:38 simplest:1 warren:1 corruption:1 recently:1 ability:1 useful:1 nature:1 initially:1 ikz:1 iky:1 ikx:1 however:1 outputs:1 harvard:1 answers:1 key:1 fluctuations:4 carbon:1 suppressed:1 improve:1 both:5 protect:1 reverse:1 goal:1 annual:1 according:1 against:1 σz:3 figures:1 exceeds:1 ernst:2 contribution:1 argue:1 experimental:5 arbitrarily:1 point:1 simple:3 corresponds:1 proton:3 exploit:1 applicability:1 sequences:1 cancel:2 constant:3 described:6 second:2 capable:1 locally:1 due:8 been:5 reduction:1 much:2 slowly:2 expected:1 itano:1 ph:6 fig:3 direction:1 θi:2 controlled:1 coherence:11 subspace:1 6s:1 coherently:1 c3:1 c2:3 c1:4 spin:19 former:1 those:1 case:4 exponential:2 pacs:1 single:9 value:1 remaining:1 dept:1 while:3 behavior:5 error:44 labeling:1 procedure:1 schumacher:1 pessimistic:1 ix:1 unitary:3 coupled:2 vol:1 molecular:2 thus:5 equal:1 ii:1 obstacle:1 contract:1 triple:5 ave:1 orthogonal:1 technology:1 monroe:1 around:1 different:2 verified:1 combination:1 grant:1 acknowledgments:1 realizing:1 accomplished:1 same:3 quant:6 pauli:1 units:1 regime:2 fide:1 used:9 see:2 i1:1 i3:1 i2:2 effect:6 counterparts:1 ion:1 compared:3 infinite:1 ideally:1 validate:1 judgment:1 identity:1 i1x:7 i2x:7 i2y:4 i2z:9 weakly:3 off:1 traps:1 landauer:1 nevertheless:1 obstacles:1 well:2 thought:1 insurmountable:1 without:1 solve:1 does:1 components:2 inability:1 model:4 plotted:1 left:1 comment:1 magnetization:3 just:1 able:1 accurate:1 obtain:1 followed:1 momenta:1 tce:6 adding:1 note:1 preprint:1 zoller:1 density:6 jeff:1 ideal:1 improvement:2 lattice:2 other:2 lett:1 input:8 transformation:2 identical:3 fluctuating:2 reuse:1 showing:1 possible:3 press:7 using:5 bit:9 correcting:6 loss:8 particle:1 exploiting:2 signal:3 specific:1 steps:1 arbitrary:1 output:5 security:1 reduced:2 spins:6 accessible:1 acad:1 methods:2 classical:2 sequence:1 successfully:1 phenomena:1 searching:1 n2:1 strongest:1 elements:1 b1:5 b2:5 b3:5 provided:1 dimensions:1 lead:1 confirm:2 overly:1 behave:1 manipulate:1 prog:2 proc:4 demonstrated:2 noise:1 nmr:12 power:2 bi:1 expansion:1 bk:1 how:1 although:2 standpoint:1 cory:2 bz:4 gained:1 about:1 oh:1 freedom:1 o:3 mixes:1 ensure:1 preskill:1 mixed:3 allowing:1 soc:4 cambridge:1 presence:1 wineland:1 communication:1 into:2 within:1 three:8 fidelities:1 lies:1 determine:1 operator:4 proportional:5 support:1 there:1 long:2 los:4 describes:2 ed:1 slopes:3 was:14 knowledge:1 naturally:1 function:1 decoded:1 hr:1 some:1 precise:1 differences:1 removes:2 but:2 gaussian:1 gore:1 cycle:1 encoded:6 irreversible:1 coupling:1 pseudopure:4 october:1 applying:1 understood:1 up:1 devices:1 below:3 decays:1 limit:1 demonstrate:5 problem:2 similar:1 average:1 detailed:1 cirac:1 associated:1 computing:10 describe:1 moved:1 levitt:1 engineering:1 enable:1 exist:1 simulations:2 corresponding:2 formalism:3 quantph:1 physical:2 2dt:1 codes:2 i1y:5 nm:1 variety:2 whereas:1 when:3 detail:1 meekhof:1 field:6 setting:1 nat:1 becomes:1 test:2 i1a:2 artificially:1 deviation:5 symposium:2 permitting:1 may:1 superposition:1 separate:1 models:1 problems:3 attributed:1 prepared:1 important:2 bounded:1 massachusetts:1 variable:2 decoherence:12 network:2 correlated:3 longer:2 algorithm:1 established:1 required:4 curve:1 together:2 mimic:1 time:12 nuclei:2 original:2 restored:1 external:4
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.