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quant-ph9810018.txt |@word limited:1 soliton:22 partial:3 consider:2 gupta:1 varying:2 results:4 leads:2 quadrature:5 mnm:1 grateful:1 c2:1 experiment:1 gl:4 localized:2 compact:1 whose:1 replacements:3 depend:4 re:2 c7:3 show:3 presents:1 finally:3 according:3 squeezing:23 c5:1 under:2 cumulants:40 td:29 include:1 applied:4 val:1 evolves:1 very:2 frequencies:1 2re:1 rise:1 conditions:4 wave:4 electron:1 figs:16 sidebands:2 application:2 difference:4 exact:1 electronics:3 condition:6 yu:1 illustrated:2 specify:1 subsets:1 presented:3 positions:3 solution:9 t0:5 damped:8 large:4 solved:8 convenience:1 defocusing:1 small:12 hairer:1 inspection:1 round:1 fleischhauer:1 lˆ:2 upper:1 smaller:1 coordinate:2 deutsch:1 consistent:2 pulse:39 cosh:1 approximation:25 second:20 video:1 enhancement:1 rigorous:2 further:11 estimated:1 schenzle:1 ues:1 linear:8 spectral:7 index:1 what:4 nonlinear:17 plays:1 appear:4 brackets:2 adjustable:1 section:2 axes:1 bergman:1 expressed:5 d3:1 ˆa:3 ˆb:10 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quant-ph9810019.txt |@word concept:1 localizes:1 results:5 leads:2 commute:1 go:1 whose:1 ıs:1 depend:1 subjected:2 deterministic:1 γk:1 stochastic:14 norm:5 case:4 choice:1 dispersions:2 solution:3 deals:2 discrete:4 small:3 eigenvalues:1 second:2 even:2 what:1 apparatus:2 brief:1 version:1 above:3 new:2 increasing:1 bn:5 movement:2 satisfy:1 simultaneously:1 answers:1 following:5 tracks:1 free:6 concluding:1 quite:1 equations:4 obtained:4 instituto:2 benatti:1 allows:1 simultaneous:1 action:1 pearle:3 scales:1 inducing:1 wataghin:1 causal:6 use:4 feb:1 superpositions:1 probabilities:1 ψs:2 chooses:1 few:1 therefore:3 usp:1 taken:1 associated:1 becomes:1 odinger:5 jmn:15 normalized:1 particular:3 known:1 cases:3 hold:1 account:1 ma:3 equation:29 work:1 modified:2 values:6 evolved:1 tnm:3 making:1 spontaneous:3 grassi:1 γdt:1 council:1 give:1 process:6 preserving:3 involve:1 indicates:1 attain:1 want:1 sense:1 csl:5 noises:1 spreading:1 ghirardi:5 write:2 how:1 instead:1 parameter:3 description:1 may:1 after:2 different:2 wave:15 dynamical:1 correspond:1 used:1 representation:2 order:4 superscript:1 helv:1 interpretation:12 developed:1 paper:3 statistical:1 satisfies:1 jnm:2 decay:1 ln:2 solving:1 gleb:1 exhibits:1 microscopic:2 systems:1 main:1 easier:1 weber:2 non:7 views:1 processes:1 tails:1 they:4 cep:2 arriving:1 now:3 term:7 sufficiently:1 2a:1 2b:1 each:1 2m:2 ifi:1 reproducing:1 homogeneous:1 differential:3 formulate:1 displacement:3 related:1 frequency:1 quantum:4 our:1 eq:2 fundamentally:1 space:4 rep:2 rev:5 research:1 particles:2 equate:1 adapt:1 dxdz:2 reader:1 induced:1 shows:1 linear:4 localization:7 ısica:3 departamento:2 standard:2 approaches:2 besides:1 could:1 transition:3 turn:1 length:1 consequence:1 first:3 probability:5 variables:1 number:1 restrict:1 done:1 given:9 publication:1 width:1 introduction:1 eqs:1 system:3 master:1 white:3 gpr:3 gives:4 collapse:1 continuous:3 part:1 authors:1 than:1 diffusion:3 distance:2 showed:2 zero:1 future:1 treated:1 function:14 fluctuation:1 increment:2 need:1 recover:1 any:1 note:1 generalized:1 play:1 phase:2 observation:1 average:2 coincides:1 face:1 exp:8 velocity:1 beables:6 fact:1 quantity:1 show:1 escobar:2 solutions:1 keywords:1 find:2 parameters:1 written:1 only:1 continuity:1 do:3 beable:15 notation:1 de:6 db:5 expectation:1 da:1 dz:1 dx:6 despite:1 dw:8 dt:18 dp:5 evolution:9 continuum:3 arxiv:1 worried:1 investigate:1 stuff:1 dpm:1 precaution:1 view:2 vink:9 set:1 guerra:1 packet:1 observed:1 result:1 eliminating:1 brazil:2 nuclear:1 definite:1 sites:2 state:3 between:2 approach:6 preserve:1 notice:3 terms:5 extend:2 restricting:1 however:4 distinguish:1 configuration:1 problem:1 both:3 interpretations:3 last:2 acknowledge:1 according:2 chosen:1 connection:1 expression:1 comes:1 unitarily:1 point:2 corresponds:1 moreover:1 considering:1 described:2 lattice:4 addition:1 trajectory:1 due:2 quickly:1 describes:1 treat:1 degrees:1 ph:2 pn:14 po:1 choose:1 describe:1 observable:1 great:1 2im:1 fokker:1 those:1 p2:1 unlike:1 expanded:1 procedure:1 unitary:2 thus:1 ih:3 ib:2 fermion:1 acknowledgments:1 santos:1 perform:1 things:1 same:3 paulo:4 quant:2 mixtures:1 status:2 independent:1 extended:1 estadual:1 trajectories:2 drives:2 campinas:2 hand:1 phy:1 schr:5 well:2 bohm:3 solve:1 position:13 model:11 dimension:2 usual:2 proposed:3 λt:1 being:2 obtain:4 assigned:1 questions:1 using:2 macroscopic:3 guides:1 stratonovich:2 cut:1 density:2 bell:11 mathematically:1 source:1 add:1 transformed:1 treatment:1 momentum:11 acta:1 fluctuating:1 world:2 vague:1 particle:13 follows:1 δn:4 remind:1 δm:2 indication:1 right:1 classical:1 lead:1 avoid:1 measurements:2 langevin:1 planck:1 does:4 exposition:1 expressing:1 assuming:2 tmn:13 noise:2 jumps:2 revtex:1 br:2 found:1 hilbert:1 bz:1 takes:1 om:8 dzg:1 freedom:2 dzk:2 introduces:1 dependence:1 o:7 side:1 obeys:1 ox:1 mean:1 consequently:1 op:2 into:2 nonsense:1 remarks:1 references:1 presupposes:1 deal:1 support:1 there:2 approximate:2 fast:1 start:1 way:3 brazilian:1 forward:2 was:1 naturally:1 rimini:4 form:4 removes:1 but:2 gaussian:1 cnpq:1 he:1 made:1 compute:1 up:1 discretized:1 limit:3 distribution:1 pm:12 gisin:1 mechanics:2 constant:1 reconcile:1 defined:2 abstract:1 contribute:1 ao:4 single:1 exist:1 typeset:1 commuting:2 universidade:2 grw:4 locality:1 when:3 vanishes:1 field:1 other:3 role:1 nelson:4 polar:2 repeat:1 intend:1 unicamp:1 matrix:1 independently:1 dψ:1 dφ:2 mass:1 presenting:1 observables:2 tales:1
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quant-ph9810020.txt |@word limited:8 partial:2 remarkable:1 illustrates:1 squared:2 excellent:1 dynamic:25 results:16 intracavity:13 leads:1 quadrature:6 generalize:1 comments:1 assessment:1 consists:2 follow:1 a45:1 contributions:5 causes:1 reynaud:1 devoted:2 whose:1 certainly:5 amplification:2 depend:4 calculate:1 comunidad:1 γs:9 concerned:2 reckoned:1 γt:10 ıa:3 estructura:1 program:1 squeezing:69 spain:3 excluded:1 stable:4 γc:13 stabilizing:1 include:1 worth:1 necessary:1 ki2:5 applied:2 2γn:10 supported:1 advantage:2 very:15 frequencies:3 account:4 2γc:14 every:1 should:5 summarized:1 resonant:28 experimentally:3 exact:1 condition:10 2γs:2 timely:1 splitter:2 din:2 obvious:1 impressive:1 presented:1 schiller:6 evaluation:2 proposals:1 solution:2 cascading:8 large:9 2ki:4 vector:1 minimal:1 clearly:1 small:1 eigenvalues:3 refer:3 optics:2 linearizing:1 configurations:4 prevent:1 strongly:2 slower:1 specially:1 oscillation:1 dealing:3 consistent:1 l2m:1 direct:1 literature:1 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quant-ph9810021.txt |@word limited:1 four:3 supplement:1 entropy:1 consists:1 row:1 amplification:11 subjected:1 technique:6 protocols:6 must:5 worth:1 sent:1 string:1 orthogonal:1 springer:1 level:1 transmission:7 eve:5 large:1 small:1 measuring:1 sign:1 elegant:1 rate:1 further:1 odd:1 theory:1 even:1 established:1 what:1 errors:3 section:1 above:1 conduct:1 shared:4 public:2 edited:1 hash:1 degree:2 exchange:1 desired:1 china:1 compressed:1 obtained:2 provably:1 receive:1 amount:1 action:1 bob:23 suitable:1 secure:3 plenum:1 chaum:1 tools:2 select:1 confidence:2 proceed:1 would:1 distinct:1 chooses:1 sherman:1 call:1 taken:1 themselves:2 more:4 share:1 corrected:1 known:1 presumed:1 states:3 keeping:1 permits:1 values:1 following:1 trans:1 example:1 wang:1 figure:7 give:1 process:3 bennett:6 distillation:1 high:4 allowed:1 times:1 guarantee:2 information:7 provide:2 verify:2 discussion:1 acts:1 b92:1 feature:1 maps:1 renyi:3 verlag:1 divides:1 brassard:3 circular:1 blocks:2 influenced:1 may:9 after:5 derived:1 diagram:3 improving:1 horizontal:1 law:1 data:12 dynamical:1 third:2 inform:1 complexity:1 so:2 fundamental:1 keeps:1 order:1 developed:1 over:4 course:1 paper:1 eavesdropping:3 existence:1 ieee:1 before:1 supplemented:1 probability:4 chosen:1 cryptology:2 absence:1 disclosed:1 them:1 practice:3 nonorthogonal:1 front:2 possess:1 represents:1 university:1 crypto:1 establishing:1 did:2 each:5 schemes:1 undetectable:1 series:1 idea:1 sifted:1 quantum:33 laboratory:1 impersonation:4 shown:2 rev:2 denotes:1 re:1 receiving:1 correct:1 maurer:1 linear:1 given:1 polarize:2 base:4 york:2 constructs:1 quantummechanical:1 exponentially:1 hence:1 first:2 xi:1 randomizes:1 number:1 open:1 city:1 little:1 necessarily:1 privacy:12 unknown:1 system:2 their:4 attack:1 scheme:3 bits:7 final:4 completed:1 leaking:1 rivest:1 specify:1 wiesner:1 second:2 distill:1 matter:1 crepeau:1 providing:1 ingenious:1 correction:5 measure:1 raw:5 manner:1 conjugate:1 demonstration:1 any:2 built:1 efficient:1 latter:1 take:2 transmit:1 techniques:2 channel:2 heisenberg:1 refereed:1 added:1 object:1 most:1 pair:2 inserted:1 class:1 ka:8 salvail:1 adopt:1 km:3 proceedings:1 principle:4 physics:2 sum:2 fact:1 violation:1 random:6 keywords:1 fifth:1 based:3 distributed:1 only:2 bases:1 oct:1 cryptography:9 truly:1 legitimate:4 words:1 new:2 him:1 processes:2 arxiv:1 method:2 apparatuses:2 set:1 art:1 reference:1 national:1 sifting:4 depends:1 captions:1 subject:1 learns:1 inequalities:1 use:3 symmetric:1 state:2 correctly:1 between:6 recently:1 vertical:1 nature:1 initially:1 however:2 key:33 distinguish:1 distribution:8 improve:1 protect:1 last:2 uncertainty:2 according:3 against:3 agree:1 figures:1 logic:1 adapted:2 experimental:1 otherwise:1 conclude:1 reasons:1 acted:1 cryptosystem:1 iterations:1 pv:1 basis:2 three:1 been:4 secret:9 basic:2 expected:1 ph:1 choose:1 compromised:1 those:1 publicly:5 bb84:2 will:2 while:5 error:7 procedure:3 non:1 equal:2 itself:1 different:1 make:1 same:2 shorter:1 authentication:2 parts:1 quant:1 schematic:3 advances:1 several:1 used:3 identity:10 relies:2 obviously:2 bohm:1 sets:1 position:1 possesses:1 left:1 proposed:3 obtain:4 identify:1 yes:1 yet:1 previous:3 photons:2 bell:3 guaranteed:2 improvement:2 signals:1 lett:2 theorem:1 useless:1 devised:1 sums:2 possible:1 possibly:1 using:1 bit:3 appearing:1 like:2 follows:2 signal:3 alice:24 steps:1 either:3 arbitrary:1 security:10 because:5 classical:1 sequence:4 sends:2 conditional:1 some:2 choosing:1 proper:1 establish:1 measurements:1 recorded:1 locate:1 who:2 communicate:1 bi:1 step:9 although:1 described:3 comparison:1 about:3 constraint:1 eavesdropper:6 island:1 plus:1 practicable:1 act:1 block:2 communication:1 into:2 obtaining:1 variable:2 right:1 parties:1 existed:1 compression:1 initial:2 long:1 way:2 function:2 smolin:1 but:1 encoded:1 removed:1 he:3 compute:1 up:2 us:1 verification:8 problem:2 called:2 mechanics:2 leaked:1 classic:1 abstract:1 measurement:2 zeng:1 general:2 single:1 check:4 inc:1 again:1 no:1 ekert:2 other:2 compares:1 users:5 leak:1 generated:1 included:1 generalized:1 cryptographic:1 independently:1 required:1 rule:2 time:1 observables:3
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quant-ph9810022.txt |@word limited:1 unavoidable:1 partial:1 consider:7 pointing:1 caused:1 hara:1 results:4 sympathetic:1 four:1 quadrature:5 computation:1 expressions:2 research:1 whose:1 preserves:1 pax:1 depend:1 re:1 technique:2 finally:4 γh:9 squeezing:2 γn:1 th:1 under:1 stochastic:5 analogous:4 applied:2 kρ:1 g2:2 straightforward:1 orthogonal:2 very:7 rise:1 ρc:14 wave:20 resonant:11 experimentally:2 associated:3 condition:6 cool:4 vibrational:32 hamiltonian:17 altering:1 mirror:1 make:1 damped:2 large:6 vector:1 cohadon:1 small:3 eigenvalues:1 becker:1 optics:1 simultaneously:1 heidmann:1 application:2 smaller:2 force:2 versatility:1 hamann:1 sin2:3 approximation:1 superimposed:1 zero:2 ρa2:1 further:2 dynamics:5 implemented:2 leakage:1 theory:1 even:4 trapping:5 rate:8 section:5 xρ:2 shares:1 find:1 current:1 below:1 homodyning:2 above:3 new:1 increasing:1 method:7 satisfy:1 outgoing:1 hansch:1 ρaa:1 degree:4 respectively:2 2kx:1 here:3 atoms:1 localisation:6 desired:1 free:1 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quant-ph9810023.txt |@word casimirs:1 consider:6 similarity:3 crucial:1 equalities:1 results:1 extends:2 illustrated:1 supplement:1 expressions:1 whose:3 inverse:4 depend:1 nonpositive:1 tr:9 finally:1 dressing:2 p2:1 conjecture:1 very:1 conditions:2 choice:2 stays:1 zµ:6 associated:1 difference:1 matrices:3 condition:3 look:2 leads:1 riemann:1 hamiltonian:2 turns:1 solution:9 solved:2 vector:1 recall:1 gauge:1 optics:2 unexpected:1 dealing:1 direct:1 imply:3 perspective:2 further:1 dynamics:2 zp:1 zs:5 trick:1 what:3 nonlinear:14 developed:1 section:4 current:1 version:2 poles:1 above:6 new:2 method:4 clausthal:3 simultaneously:1 implying:1 naudts:2 respectively:1 here:3 ρy:1 objects:1 address:1 consideration:1 standard:1 equations:17 change:1 obtained:8 institute:1 shift:3 study:1 vectors:1 resulting:2 poisson:1 action:1 technique:8 followed:1 perspectives:1 inverses:1 apply:1 use:3 discus:1 prove:1 covariant:5 positive:8 negative:1 properties:6 anticommutes:1 therefore:5 means:1 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quant-ph9810024.txt |@word limited:1 partial:4 consider:1 eaires:1 perelman:1 leads:1 maxima:1 expressions:1 localized:1 increase:1 depend:1 spin:20 equivalence:1 ts:3 intensive:1 finally:2 squeezing:2 present:1 under:1 presentation:1 case:7 orthogonal:1 very:7 geometrical:13 difference:1 categories:2 four:1 tani:1 presented:4 solution:1 large:3 vector:4 small:1 eigenvalues:2 work:2 periodicity:1 l2i:2 direct:1 zero:1 l2y:4 l2x:4 odd:1 scientific:1 even:2 section:5 expressed:2 above:1 fractional:11 expresses:1 increasing:2 exercise:1 movement:1 satisfy:3 subdivided:1 degree:1 respectively:2 modify:1 cos2:1 sinh:3 directions:2 consideration:1 along:1 strong:1 equations:1 change:3 obtained:2 remark:2 algebra:2 institute:1 root:1 study:6 vectors:1 allows:2 published:1 action:1 studies:1 jackiw:1 formulated:1 spatially:1 family:3 highly:1 visible:1 unit:2 recurrence:1 use:1 feb:1 takes:1 would:1 prove:1 quasi:3 france:1 few:1 nucl:4 therefore:3 associated:1 more:3 separated:1 multiplying:1 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quant-ph9810025.txt |@word represent:2 partial:1 consider:14 pointing:1 illustrates:1 rev:18 edh:3 wi0:1 results:6 four:9 supplement:1 entropy:27 follow:3 expressions:2 research:2 causes:1 whose:2 careful:1 depend:2 calculate:2 transferred:1 disposal:1 tr:2 send:3 finally:2 monotonically:1 present:1 th:1 under:3 analogous:1 must:1 sent:1 p2:6 conjecture:12 wjm:3 amplitudes:1 straightforward:1 orthogonal:1 very:2 preceeded:1 conjectured:2 connects:1 choice:1 corollary:1 putting:2 hewlett:1 formula:2 experimentally:1 little:1 matrices:2 convexity:2 look:2 entire:2 school:1 quantitatively:1 level:1 transmission:2 turns:1 having:3 large:3 teleportation:1 proposition:1 science:1 eigenvalues:4 optics:1 noted:1 upper:18 smaller:1 decompositions:2 degrading:1 direct:2 zero:4 further:1 implemented:1 peredachi:1 even:7 aim:2 what:6 stands:3 rate:2 t2n:1 giving:1 section:18 expressed:1 uniform:1 henceforth:1 version:1 above:18 deal:1 shared:41 net:1 method:2 heuristically:3 edited:2 hasn:1 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quant-ph9810038.txt |@word consider:1 illustrates:1 desirable:1 results:1 amplified:7 ebeling:1 amplification:2 depend:1 quasi:1 squeezing:2 γn:1 amplitudes:1 straightforward:1 far:12 frequencies:2 springer:1 electron:1 difference:2 presented:4 gatti:1 large:1 solved:1 smaller:1 2k0:2 oscillation:1 modified:1 rate:3 value:1 dynamics:4 expressions:1 even:1 index:1 appear:1 ambipolar:1 optoelectronics:1 current:1 above:2 expresses:1 increasing:1 mef:4 arb:3 here:2 relaxation:1 strong:1 equations:7 obtained:1 holger:1 institute:1 pinning:2 usually:1 resonance:2 narrow:1 formulated:1 spatially:4 marked:1 total:1 finally:1 therefore:1 feq:5 associated:1 today:1 more:1 emission:24 hofmann:3 particular:3 hole:1 account:2 quantized:1 ρl:1 crossed:1 spontaneous:22 example:1 deg:3 figure:4 carriers:1 feature:1 how:1 product:1 may:7 derived:1 parallel:1 effective:1 light:11 correlation:10 wigner:3 indeed:1 move:1 interpreted:2 lasers:4 mentioned:1 linewidth:1 its:1 temporal:1 coordinates:1 fig:3 non:1 diodes:1 band:6 effects:3 february:1 always:1 mode:4 principles:1 inhomogeneous:3 frequency:10 measure:2 quantum:16 our:1 operation:1 eq:1 peaks:2 matrix:1 space:1 rev:6 semiconductor:9 mediated:1 dominated:1 cause:1 integrated:1 shows:3 lugiato:2 theory:1 ork:1 estimate:1 interaction:3 geometry:1 transition:3 major:1 already:1 another:1 angular:1 passes:1 given:5 temperature:2 introduction:1 system:3 stimulation:1 assumption:2 nilsson:1 continuous:1 interband:1 part:2 undoubtedly:1 than:1 diffusion:1 zero:1 submitted:1 matter:1 determined:1 amplitude:2 renormalizations:1 spectrum:2 manner:1 recover:1 angle:3 responsible:1 k2:1 ideal:1 take:1 added:1 unless:1 most:2 germany:1 jul:1 significant:1 phase:2 analytically:1 considered:1 optical:5 electrons:2 mechanical:1 usual:1 typically:1 fact:1 spatiotemporal:3 show:1 threshold:6 d2:2 based:2 analytic:1 explicitly:1 factor:8 parabolic:1 emitting:1 local:1 oct:1 equilibrium:1 dependent:1 expectation:1 processes:1 densities:4 fields:1 arxiv:1 common:1 analytical:5 correlations:2 intensity:7 result:2 close:2 hess:4 pattern:5 dipole:9 dlr:1 pump:1 between:4 wf:1 terms:4 nature:1 emitted:3 however:1 butions:1 article:1 suppressed:1 originates:1 both:1 many:1 taking:1 conclusions:1 equal:1 stuttgart:1 context:1 expression:3 point:1 corresponds:1 dimensional:2 respect:1 described:1 basis:1 radiative:1 three:3 been:3 describes:1 ph:1 systems:2 corresponding:2 coherence:7 photon:1 gap:3 coherent:2 angles:2 present:2 case:1 multi:2 laser:11 profiles:1 spontaneously:2 technical:1 ultra:1 region:1 characteristics:1 thus:2 reads:1 different:1 same:1 stimulated:1 complex:3 quant:1 coworkers:1 units:3 finite:1 independent:2 literature:1 vcsel:1 stripe:1 modes:5 modeled:1 well:5 physics:3 patterns:3 edge:3 very:1 model:1 maxima:1 being:3 guided:1 obtain:1 yamamoto:3 scattering:1 halfway:1 density:13 absorption:1 iω:1 source:1 lett:2 momentum:1 opt:1 increased:1 bands:1 increases:1 particle:1 either:1 integrals:1 output:1 towards:1 b0:1 moreover:2 oscillations:2 cavity:3 broad:6 footing:1 dipoles:1 assuming:1 noise:3 bj:1 notably:1 recombinations:1 imaginary:2 discussed:2 dependence:4 o:4 carrier:16 consequently:1 bloch:7 machida:1 maxwell:7 into:5 karlsson:1 device:1 references:1 area:6 low:1 fraction:1 function:3 medium:1 but:1 pfaffenwaldring:1 gain:2 injection:1 castelli:1 arrays:1 prevents:1 maximum:1 devices:6 farfield:1 below:1 fermi:4 kuhn:1 fluctuations:2 distribution:5 similar:1 ωf:8 constant:1 defined:2 abstract:1 describe:3 influence:1 single:1 distributions:4 approximated:1 defines:1 generally:1 slusher:1 arctan:2 field:32 spatial:9 np:2 deviation:1 june:1 important:1 dissipation:1 structure:2 ig0:4 values:2 holes:2 berlin:1 investigated:1 mass:1
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quant-ph9810039.txt |@word limited:1 monte:3 partial:1 consider:2 remarkable:2 represent:5 interference:1 results:1 gg:18 ge:5 computation:9 perturbations:1 scr:1 depend:2 leung:1 environment:3 th:2 stable:1 applied:1 string:1 far:2 frequencies:3 choice:1 p1:3 sidebands:2 resonant:5 difference:1 matrices:1 pertubative:1 condition:1 leads:1 retaining:1 vibrational:38 hamiltonian:4 proposals:1 applicable:2 large:2 small:2 equation:2 upper:2 revolution:2 oscillation:2 direct:1 pulse:1 sign:2 surrounding:1 second:6 gn:3 qualitatively:1 dynamics:2 carlo:3 even:3 trick:2 unpopulated:2 detuned:1 sum:1 selected:1 access:3 above:3 new:3 method:1 contrast:1 paradoxical:1 margolus:1 full:3 simultaneously:1 degree:1 exchange:2 unobserved:1 equals:1 diagonal:1 desired:1 operating:1 address:1 represented:1 path:2 ggn:8 change:4 institute:1 changed:1 eberly:1 p2:2 accomplished:2 resonance:3 changes:1 involves:1 via:2 νt:4 castin:1 counteracted:1 turchette:2 poyatos:1 apply:4 total:1 use:3 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quant-ph9810040.txt |@word represent:1 monte:3 pointing:1 limited:1 interference:2 lack:1 results:5 integration:1 gg:6 ge:2 commute:1 computation:2 contributions:1 particles:6 depend:1 th:1 under:2 case:1 amplitudes:1 string:4 straightforward:1 evolves:1 very:1 frequencies:6 choice:1 resonant:4 experimentally:1 difference:2 matrices:2 four:3 vibrational:20 hamiltonian:12 suffices:1 correct:1 large:2 vector:2 small:3 optics:1 degeneracy:1 smaller:1 surrounding:2 second:2 greenberger:1 dynamics:2 functioning:1 odd:4 theory:1 even:6 adds:1 appear:1 near:1 access:2 experiment:2 above:3 deal:1 net:1 method:6 exercise:1 full:2 simultaneously:2 satchler:1 degree:1 exchange:1 realizations:1 component:2 here:1 atoms:1 desired:3 separation:1 investigating:1 represented:3 along:2 ggn:4 obtained:5 clarendon:1 institute:1 involved:1 study:1 studied:1 recently:1 products:1 suggestion:1 permutation:1 action:2 resonance:2 implement:1 mutual:1 composed:1 regardless:1 projection:1 ions:45 castin:1 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quant-ph9810041.txt |@word represent:1 unavoidable:1 sci:2 consider:7 pointing:1 switched:1 rev:7 forbidden:1 alternatives:2 focus:2 extends:1 leads:5 eds:2 scalar:1 commute:2 philosopher:2 foundations:2 consists:1 centimeter:1 localized:2 gr:2 devoted:1 whose:1 certainly:4 amplification:1 terms:8 referring:2 spin:3 deterministic:1 ts:2 γu:2 finally:1 program:1 present:3 th:2 under:1 stochastic:1 analogous:1 fatal:2 belonging:1 presently:1 orthogonal:10 far:2 detlef:1 unavoidably:1 story:1 results:1 putting:1 govern:1 mixing:1 difference:2 condition:1 immediately:5 presented:3 turns:3 solution:1 replaced:1 occurs:2 large:10 discrete:2 vector:1 math:2 succession:1 indices:1 eigenvalues:1 der:1 limitations:2 smaller:4 occurrence:3 equated:1 dealing:1 unbounded:1 located:1 imply:2 perspective:1 rigorous:4 ill:1 dynamics:7 salam:1 0m:2 linear:5 even:9 index:1 what:2 nonlinear:1 contained:1 appear:4 apparatus:20 deeply:1 section:5 associate:2 expressed:1 experiment:1 issues:1 above:8 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quant-ph9810042.txt |@word limited:1 monte:1 code:1 consider:6 illustrates:1 lack:1 results:1 four:1 computation:2 consists:3 causes:1 terms:1 superpositions:1 wavepacket:2 disturbances:2 braginsky:1 nonlocal:1 finally:2 compensate:1 under:2 nodes:3 amplitudes:5 advantage:1 orthogonal:5 far:1 emphasizes:1 pictures:1 summarized:1 resonant:3 experimentally:1 exact:2 newly:1 arrange:1 splitter:9 receiving:5 level:16 transmission:24 ri:4 convenience:2 vector:3 science:2 c00:1 c01:1 degeneracy:3 pulse:6 sign:4 jump:2 fold:1 second:8 displays:1 further:2 carlo:1 linear:1 even:4 established:1 what:1 errors:21 plays:1 discus:1 section:9 experiment:1 subspaces:1 new:2 d1:42 method:1 contrast:1 paradoxical:1 revealing:1 margolus:1 respectively:1 realizations:1 component:3 teleportation:9 here:3 atoms:21 desired:8 protection:1 possibility:1 represented:2 equations:1 imperfections:3 change:6 sending:6 incoming:1 institute:3 shift:5 vectors:2 prior:1 action:2 unwanted:1 implement:1 suitable:2 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quant-ph9810043.txt |@word consider:1 brownian:4 focus:1 leads:5 edu:1 expressions:2 those:1 whatsoever:1 under:3 stochastic:1 anharmonic:1 applied:1 g1:1 very:1 rise:1 choice:3 every:1 matrices:1 illustrated:1 hamiltonian:1 irreducible:1 solution:3 vector:2 small:1 upper:1 second:2 dynamics:1 canonical:6 even:1 what:1 brief:1 expressed:3 above:2 satisfy:1 led:1 respectively:1 here:2 alone:1 path:17 along:2 box:1 glm:3 suitably:1 allows:1 suggests:1 adopting:2 involves:1 followed:1 projection:2 integrations:1 assertion:1 ipq:5 apply:1 derivatives:1 conventional:2 usa:1 covariant:1 positive:3 negative:2 classically:1 therefore:2 more:1 introducing:2 operators:4 odinger:2 curvature:2 carrying:1 normalized:1 states:8 quartic:1 equation:2 oscillator:1 theories:1 following:1 fulfill:1 example:3 chosen:1 involve:1 sphere:1 conversely:1 evidently:1 regularization:8 viewpoint:1 how:1 dg:1 instead:1 ordinary:1 may:8 after:1 applications:1 plane:1 fl:1 natural:2 dynamical:2 su:2 diffeomorphism:1 so:1 suggest:1 representation:2 subsequently:1 interpretation:1 noteworthy:2 indeed:2 over:3 insight:1 soon:1 years:1 wiener:3 including:1 argued:1 before:1 ln:1 temporal:1 lm:1 exhibits:1 choose:2 mail:1 defining:1 propose:1 d3x:3 fully:1 university:2 appropriate:2 each:1 found:1 entirely:2 constraints:6 ei:9 challenged:1 measure:6 quantum:6 beyond:1 out:1 fundamentally:1 space:18 rev:3 denotes:2 formula:1 suffices:1 integrated:1 math:2 theory:1 midpoint:2 free:1 πa:1 generate:1 definition:2 βq:2 florida:1 keep:1 motion:3 turn:1 hence:1 onto:3 first:3 variables:5 iht:7 done:1 another:1 xp:1 given:5 cartesian:2 introduction:2 adjoint:1 john:1 final:2 gives:2 continuous:3 x2:3 determines:1 generality:1 ann:3 any:5 paths:2 lim:6 self:1 gravity:4 polarization:2 k2:1 reproducing:4 calculus:1 formulas:1 track:1 price:1 measures:1 most:1 involving:1 significant:1 preliminary:2 pair:1 class:1 constructed:1 kl:3 feynman:2 kq:1 exp:15 usual:1 physics:2 fact:2 eνt:1 paul:1 relation:1 based:2 dp2:2 behind:1 should:1 only:2 generators:1 ambiguity:1 oct:1 dm:2 dk:2 notation:1 df:1 familiar:1 nearly:1 dx:4 dy:2 dt:18 procedures:1 dp:13 dq:22 evolution:1 arxiv:1 daubechies:2 kernel:5 set:1 physically:1 namely:1 curvilinear:1 best:1 evaluation:1 ways:1 review:1 definite:3 symmetric:2 state:9 invariant:1 terms:1 however:1 jm:3 multiplier:3 concentrated:1 both:1 ill:1 gainesville:1 quantization:8 etc:1 admit:1 contribution:1 expression:10 otherwise:1 conclude:2 appeared:1 jk:4 corresponds:2 dimensional:1 ab:1 coordinates:4 quantizations:1 wider:1 moreover:1 transformations:3 geometries:1 basis:1 been:1 interest:1 ph:1 define:2 general:4 offered:1 subspace:3 coherent:16 observe:2 convergent:2 present:1 case:3 novel:1 employ:1 while:1 p2:1 fiducial:1 evaluating:1 applies:1 ǫy:1 ir2:1 procedure:2 iy:2 ultralocal:2 iq:1 ip:5 metric:4 surface:1 different:4 pay:1 make:1 same:1 unity:1 quant:1 units:1 defines:1 used:3 parametrized:1 pseudosphere:1 recent:2 lower:1 schr:2 well:3 analysis:1 exceedingly:1 without:1 coordinate:5 latter:1 left:1 being:1 when:1 hphys:1 klauder:9 useful:1 alternative:2 stratonovich:1 heuristic:1 field:1 mathematically:1 lattice:1 add:1 adoption:1 mod:1 transformation:1 identical:1 rules:1 advances:1 iβ:1 possible:3 possibly:1 press:1 imposed:2 projects:1 formal:7 necessary:1 like:1 follows:1 indication:1 gjk:4 integrals:5 weiner:1 mathematical:1 right:1 classical:2 lagrange:3 some:2 regularized:2 choosing:2 integration:2 overlap:1 conditionally:2 economical:1 yields:1 preceding:2 ufl:1 equivalent:1 use:2 step:2 hilbert:4 metrical:3 discussed:1 meaning:1 o:1 regular:1 ensure:1 stand:1 act:3 introduced:2 automatically:1 lieb:1 cambridge:1 into:1 within:1 integral:15 functional:1 phase:9 hermitian:1 references:1 determine:1 operator:2 deal:2 removing:1 support:1 there:1 start:1 was:2 propagator:1 assumes:1 function:3 form:5 but:1 construction:2 he:1 iqp:3 us:2 below:1 limit:2 continuously:1 definitions:2 constant:2 flat:2 defined:8 abstract:1 resultant:2 diverse:1 dπ:3 formulation:2 corresponding:1 quantph:1 physical:3 reexpress:1 functions:1 no:1 generally:2 application:1 other:1 spatial:1 department:2 mathematics:1 briefly:1 denote:2 symbol:3 problems:1 generated:1 bounded:1 a8:1 matrix:1 ago:1 implies:2 using:1 assume:1 dσ:3 rule:3 time:1 resolution:1 original:1
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quant-ph9810044.txt |@word least:1 just:2 noteworthy:1 moments:1 gainesville:1 particular:1 choose:2 stability:2 convergence:1 attempts:1 paper:1 thanks:1 edu:1 expressions:1 postulates:5 chosen:2 temporal:2 discussions:1 systems:3 indeed:1 mail:1 hamiltonians:1 defining:1 oct:1 continuity:2 dj:1 therefore:1 means:1 very:1 iγ:2 bound:5 units:1 indicative:1 world:1 dt:3 accepted:1 gen:1 four:2 evolution:1 hamiltonian:2 suffices:1 university:1 arxiv:1 requires:2 labeling:2 specific:2 discrete:3 convenience:1 math:2 reasonable:1 follows:1 references:1 2n:1 gazeau:2 set:2 functional:2 classical:3 ej:1 dealing:2 klauder:6 some:1 past:1 namely:2 radius:1 quantum:1 our:2 dynamics:1 ρn:8 analog:1 canonical:2 nondegenerate:1 restricted:1 singapore:1 brief:1 expressed:1 denotes:1 reminiscent:1 state:6 expresses:1 approach:1 acknowledgments:1 minimal:1 refer:1 satisfy:4 ufl:1 scientific:1 nature:1 attention:1 ensures:1 here:2 standard:2 along:1 e1:2 properties:1 e2:1 box:1 both:2 skagerstam:1 property:1 σn:1 σm:1 discussed:2 dependence:1 o:1 remains:1 present:2 action:10 adopting:1 suitable:1 expression:1 first:2 uniquely:1 referenced:1 conclude:1 h2:1 variables:3 number:2 iht:1 dimensional:1 appropriate:1 en:10 limn:1 long:2 operator:1 angle:3 analyses:1 existed:1 given:1 publication:1 usa:1 introduction:1 there:1 question:1 system:1 been:4 e0:2 their:1 however:1 normalization:1 interest:3 series:1 taken:1 ph:1 john:1 cited:1 define:1 introducing:1 becomes:1 ien:3 distribution:2 coherent:17 observe:1 atom:6 known:1 cases:2 denote:1 postulate:2 specify:1 case:3 include:1 coefficients:1 extension:1 recall:1 work:1 oscillator:2 ωt:3 submitted:2 remaining:1 while:1 ωj:2 harmonic:2 ρm:1 problem:1 more:1 example:1 manner:1 mechanics:1 fulfills:1 constant:1 penson:1 ln:1 defined:1 florida:1 abstract:1 thus:2 spectrum:4 general:1 states:19 characterize:1 presented:1 numbers:1 hydrogen:6 well:1 physical:2 generally:1 requirements:2 author:1 rather:1 discussion:1 when:2 note:2 unity:2 other:2 quant:1 fourth:2 department:2 mathematics:1 dimensionless:1 confine:1 continuous:2 shall:1 models:1 earlier:1 hand:2 mixed:1 letter:2 infinite:1 frequently:1 fl:1 identity:4 narrow:1 third:2 assume:1 physics:1 spectra:1 lines:1 portion:3 without:1 so:1 time:3 addition:1 resolution:2
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quant-ph9810045.txt |@word scl:1 since:12 consider:4 pointing:1 represent:1 particular:1 results:9 leads:5 eds:1 scalar:1 gc:25 edu:1 go:2 gn:2 expressions:3 zinn:2 contributions:2 c1:2 whose:2 certainly:1 inverse:1 calculate:2 graph:2 concerned:1 vs:1 corrections:1 groundstate:2 recurrence:1 finally:11 does:1 present:2 elliptic:5 under:4 anharmonic:10 include:2 presentation:1 indicating:1 hill:2 applied:2 particularized:1 g1:6 g0:9 very:2 implicitly:1 exception:1 choice:2 indication:2 monopoles:1 putting:1 fall:1 mottola:1 ln:8 exact:2 condition:4 resummations:1 four:1 pre:3 diagrammatics:1 hamiltonian:1 did:1 suffices:1 notes:1 tanh:5 weinberg:1 solution:7 correct:1 large:2 solved:4 convenience:1 bypassed:1 catastrophes:1 dealt:1 small:2 eigenvalues:1 hospitality:1 barbara:1 too:1 wronskian:1 force:1 publ:1 dealing:1 estimates:6 sign:4 approximation:16 zero:5 evaluated:1 qualitatively:1 odd:1 d4:1 theory:8 even:5 stegun:1 developed:1 appear:1 often:1 brackets:3 fact:12 sum:3 effort:1 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quant-ph9810048.txt |@word consider:1 leads:2 comments:1 follow:2 expressions:2 concerned:1 tr:1 presents:1 those:1 under:1 analogous:1 must:2 worth:1 case:5 returning:1 very:3 frequencies:1 resonant:2 deformations:1 illustrated:1 hamiltonian:1 turns:1 t2:3 solution:3 t1:3 insights:1 vector:1 optics:1 upper:2 unexpected:1 compensated:1 specially:1 periodicity:3 cessa:1 sin2:1 past:1 second:2 enhancement:2 dynamics:4 odd:13 cˆn:4 ˆr:4 appear:1 section:3 goes:2 new:1 increasing:1 acknowledgments:1 ˆn:1 full:1 respectively:2 never:1 atoms:2 behaviour:4 possibility:1 address:1 coupling:3 change:7 gerry:1 buck:2 instituto:1 thirty:1 matsuo:1 allows:1 periodic:6 resulting:1 poisson:1 makes:1 followed:1 although:2 explained:1 highly:1 wataghin:1 decrease:1 rσ:1 total:1 readily:1 environment:1 superpositions:1 would:4 sake:1 properties:1 therefore:3 associated:1 jonathan:1 more:1 initial:18 operators:1 odinger:5 particular:1 known:2 iv:2 iii:2 circumstances:1 ρa:2 evolves:1 ıvel:1 ρf:10 work:1 cat:5 sudden:1 obvious:1 evolved:1 mr:1 numbers:1 control:1 organized:1 states:17 purity:5 occur:1 santana:2 s2:3 s1:3 how:2 ρ2f:1 answer:1 instead:2 ordinary:4 parameter:1 sin:6 simplicity:2 product:1 ζf:2 may:2 after:2 confirmed:1 branches:5 dynamical:1 light:1 sp:1 acknowledged:1 purification:8 si:1 so:2 sn:2 representation:1 order:1 over:2 years:1 course:1 paper:2 statistical:10 jaynes:13 its:9 tendency:2 perfect:3 superior:1 thank:1 gleb:1 2λt:5 permanent:1 fig:8 rabi:1 rwa:1 them:1 return:1 pure:10 processes:2 stenholm:1 effects:1 half:9 discuss:1 represents:2 term:1 2r:3 possibilities:2 2a:1 2b:1 each:2 found:4 2n:2 sukumar:2 ifi:3 weighted:1 disentanglement:1 generation:2 energy:1 exatas:1 t3:3 investigated:1 expect:2 quantum:3 eq:5 shown:2 opened:1 space:7 rep:1 closer:1 rev:3 re:1 rf:1 investigation:1 ra:1 occurs:5 ciˆencias:1 shows:2 linear:1 written:1 ısica:1 differ:1 departamento:1 ask:1 interaction:5 regarding:1 transition:2 diminished:1 used:1 times:1 consequence:1 generalizations:2 first:3 already:2 variables:2 number:1 knight:2 illustrate:1 given:3 revival:13 introduction:2 leading:1 system:3 returns:2 inversion:3 collapse:1 para:1 explanation:1 exactly:2 pnm:5 occurring:1 representing:2 peculiar:1 population:2 kind:2 intensity:9 annihilation:1 matter:2 contrary:1 amplitude:1 toward:1 counter:2 ann:1 any:1 relatively:2 realm:1 zero:1 convenient:1 overcoming:1 note:2 instance:2 high:1 subjects:1 pns:1 even:15 what:3 most:3 connected:1 cummings:13 phase:7 intrinsic:2 why:1 clear:1 typeset:1 exp:7 normally:2 fact:2 precise:1 show:3 supported:1 tecnol:1 ground:3 capes:1 partially:1 less:1 state:61 than:2 only:4 going:4 factor:1 nonzero:1 oct:1 mixture:10 means:4 dependent:9 de:9 expectation:1 gea:1 despite:2 during:2 evolution:11 bˇ:1 fields:5 arxiv:1 common:1 view:4 exists:1 achieved:2 freitas:1 flip:1 namely:1 close:1 brazil:4 onto:1 ways:1 ieee:1 initially:6 enough:1 closed:1 between:2 barranco:2 approach:2 αn:2 notice:1 terms:3 importance:1 however:3 banacloche:1 problem:1 both:2 periodically:3 providing:1 ıfico:1 conclusions:1 according:1 σz:2 figures:1 otherwise:1 cn:3 point:4 reasons:1 pessoal:1 moreover:1 considering:1 λtn:1 strong:1 basis:1 invert:1 due:3 been:5 cient:1 ph:1 hardly:1 arises:1 corresponding:1 sufficient:1 coherence:1 photon:3 remark:1 coherent:32 present:1 applied:1 look:1 moya:1 value:1 transformation:3 will:13 neat:1 jaynescummings:1 procedure:2 iy:1 opt:3 almost:2 ir:1 surprisingly:1 equal:2 ii:2 itself:1 im:1 mod:3 demolition:1 different:2 perhaps:1 same:1 iα:14 quant:1 split:1 difficult:1 literature:1 see:5 estadual:2 campinas:2 hand:2 destruction:1 lower:1 schr:5 nevertheless:1 well:4 shore:1 organization:1 model:20 usual:1 λt:12 being:1 commensurability:1 rotated:4 obtain:1 atomic:9 ogico:1 useful:1 collide:1 density:5 nacional:1 conselho:1 lett:2 easy:1 guarantees:1 excited:3 match:1 real:1 easily:1 read:1 iβ:1 possible:5 know:1 using:1 apart:1 loss:1 like:4 follows:2 specific:1 continue:1 either:1 become:3 reduced:1 parity:3 because:9 absolutely:1 creation:1 somehow:1 growth:1 happens:4 clockwise:2 electromagnetic:1 overlap:4 provides:1 propagating:1 ba:1 plot:1 2c:1 oscillating:1 revtex:1 br:3 exciting:1 intense:1 analysing:1 tracing:1 ρˆf:6 aˆ:7 discussed:1 desenvolvimento:1 o:1 2i:1 mixed:4 introduced:1 teven:3 equally:1 into:3 within:1 down:1 revivals:3 references:1 operator:6 coordena:1 nowadays:1 there:7 transform:1 noticed:1 start:3 conservation:2 analyze:1 was:2 function:7 complete:1 form:1 but:3 atom:11 quasiprobability:1 cnpq:1 he:1 up:1 us:1 below:1 limit:1 distribution:2 regimes:1 constant:1 defined:4 certain:1 abstract:1 ao:1 universidade:2 again:1 functions:1 no:1 cos:7 when:2 ne:1 sˆn:3 field:45 other:3 details:1 becomes:3 picture:1 superposition:1 phoenix:1 unicamp:3 nonclassical:1 prepared:5 important:2 dissipation:1 risken:1 reorganization:1 longer:1 assume:1 original:1 time:21 far:1 having:2
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quant-ph9810049.txt |@word consider:4 forbidden:1 results:1 hawaii:1 four:2 eds:1 generalize:2 go:1 perturbations:2 expressions:5 centers:1 naukova:1 looking:2 inverse:1 terms:2 γr:9 technique:5 passage:1 γi:8 kζ:5 stable:3 applied:4 amplitudes:1 2γi:1 keeping:1 dokl:1 wave:5 corollary:2 jack:1 formula:1 resonant:12 difference:5 matrices:3 condition:3 riemann:2 level:14 t2:4 solution:14 t1:4 large:1 solved:1 convenience:1 vector:2 quick:1 refered:1 linearizing:1 degeneracy:2 upper:2 iγi:1 oscillator:2 consistent:1 direct:2 pulse:10 cosh:5 approximation:3 integrability:2 invention:1 invariant:1 substitute:1 zs:3 spectral:5 index:1 nonlinear:6 appear:3 brackets:1 diag:1 section:2 while:2 expressed:1 bdt:2 3h:1 above:1 3c:1 3b:1 3a:1 method:3 3d:1 satisfy:3 κj:2 component:1 here:5 understanding:1 met:1 possibility:2 sinh:4 wfs:4 represented:1 depend:1 along:3 equations:22 change:2 obtained:5 parameters:6 shift:4 larger:2 allows:1 akj:2 periodic:6 published:1 usually:1 resonance:3 cto:1 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quant-ph9810050.txt |@word represent:1 partial:2 dynamic:1 results:2 leads:2 entropy:1 edu:1 gn:1 localized:6 rightmost:3 squeezing:1 under:1 analogous:2 string:10 very:1 choice:1 chuang:1 difference:1 condition:1 entire:1 proc:2 eigenvalues:2 rigorous:2 further:1 dynamics:6 haake:1 even:1 ˆq:1 yakobson:1 near:1 version:1 new:3 method:3 ˆn:6 respectively:1 here:1 groups:1 others:1 represented:1 alicki:1 generalizing:1 shift:14 study:1 stretching:1 reports:1 periodic:1 action:3 resonance:1 fourier:3 studies:1 sci:1 schack:5 useful:1 family:1 unit:7 takes:1 would:1 remains:1 properties:1 classically:2 noting:1 taken:1 becomes:1 operators:2 apparent:1 berlin:1 backwards:1 entangle:1 springer:1 quantized:5 science:1 work:1 following:1 stacking:1 states:7 numbers:1 guarantee:1 information:1 s2:1 s1:1 acts:1 write:2 maps:14 rubin:1 instead:1 displacements:1 map:25 product:4 description:2 produce:1 representations:2 horizontal:1 realized:1 short:1 dynamical:1 fahmy:1 sk:3 algorithms:1 representation:6 gershenfeld:1 s0:1 symbols:1 paper:1 london:1 its:1 symmetry:1 choose:1 mail:2 main:1 defining:1 motivated:2 bernoulli:1 they:1 half:1 now:5 day:1 eigenvalue:1 e2πi:8 university:2 identified:1 crudely:1 orthonormal:1 each:5 2n:8 1an:3 macchiavello:1 square:7 reduce:2 displacement:1 related:2 quantum:41 our:1 eq:8 special:1 shown:1 space:8 since:1 rev:3 chaos:10 similarly:1 acting:1 investigation:1 math:1 benjamin:1 working:1 theory:6 voros:3 albuquerque:1 reason:2 york:2 fixed:1 language:1 widths:1 computers:1 place:1 consequence:1 onto:1 eqs:1 first:1 major:1 initial:1 xn:37 lond:1 xl:2 symbolic:14 tw20:1 given:4 perturbation:1 width:2 top:1 least:3 avez:1 realization:1 egham:1 bits:6 shifted:3 centered:2 part:1 x2:10 x1:39 specify:2 havel:1 structures:1 determined:2 fˆ:3 result:2 sees:1 ann:4 saraceno:3 say:1 enforces:1 close:1 seen:1 latter:1 potential:1 take:1 analogy:1 canonical:1 ˆp:1 towards:2 systems:2 most:1 significant:4 multiply:1 class:4 physica:1 points:3 physics:1 dot:6 dover:1 surrey:1 signatures:2 particularly:1 show:2 labels:2 relation:1 based:1 parameters:2 written:4 only:1 factor:3 notation:5 means:1 udiger:1 closely:1 holloway:1 arxiv:1 expansions:1 hyperbolic:1 investigate:2 contrast:1 through:2 qk:1 qj:7 undergoes:1 see:1 computer:2 geometrically:1 changes:4 recently:1 theoretic:1 subject:1 commutation:1 ways:1 symmetric:1 state:15 boundary:4 caves:3 conditions:5 notice:1 terms:1 spectroscopy:1 vertical:1 complementary:2 qubits:10 incarnation:1 modeling:1 both:1 many:2 region:2 quantization:2 berry:1 context:1 qubit:11 whole:1 unm:1 experimental:1 stretches:1 point:3 simple:2 had:1 dimensional:2 directions:1 quantizations:1 respect:1 cory:1 basis:5 been:4 pk:6 ph:1 define:5 direction:5 arises:1 controlled:4 powerful:1 antiperiodic:3 bulk:1 generalization:1 spin:2 present:3 case:2 unlike:1 ǫd:1 arnold:1 squeezes:1 will:1 while:2 situation:1 revisited:1 unitary:2 mexico:1 chaotic:3 thus:2 quantize:1 itself:1 binary:2 alphabet:1 realizing:1 shifts:4 quant:1 units:1 finite:4 used:1 i1:1 numerical:1 infinite:3 uˆ:4 recent:1 center:1 expression:1 underlies:1 analysis:1 thought:1 consistency:1 position:8 dimension:2 left:6 being:1 followed:2 alternative:1 eigenstates:2 regarded:1 characterization:1 royal:1 except:1 lattice:1 other:1 lett:1 iπ:3 transformation:4 momentum:11 read:1 using:3 advanced:1 semiclassical:1 0ex:1 follows:2 either:2 arbitrary:1 right:3 classical:9 some:1 acad:1 proofs:1 scale:1 does:1 ensemble:1 leftmost:3 chains:1 nmr:2 obey:1 tabor:1 problems:1 equivalent:4 bi:1 eiπ:4 step:2 shifting:2 qˆ:1 hilbert:3 usa:2 dˆ:1 discussed:1 soc:1 within:2 phase:12 carlton:1 weyl:1 references:1 operator:4 statistics:1 vˆ:6 strictly:1 there:3 transform:3 start:1 way:1 naturally:2 form:2 jul:1 fannes:1 versions:1 characteristic:1 us:1 below:1 uk:2 similar:2 brun:1 mechanics:2 ac:1 computing:2 defined:5 likewise:1 abstract:1 ergodic:1 general:1 single:1 pˆ:1 simulations:1 balazs:2 again:2 mosca:1 nm:1 no:1 ekert:1 setting:1 nat:1 department:2 mathematics:1 conclusion:1 june:1 a1:31 important:1 variable:2 astronomy:1 alekseev:1 suffers:1 assume:1 starting:1 baker:22 original:1 equivalently:1 fact:2 time:1 cleve:1 requires:1 strings:2
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quant-ph9810051.txt |@word represent:3 childs:1 consider:6 remarkable:1 rev:15 magnetic:2 excellent:1 desirable:1 results:1 menon:1 four:5 jawaharlal:1 consists:1 causes:1 ahmedabad:1 involve:1 γj:1 finally:1 under:2 include:1 amplitudes:1 2γi:2 g1:6 orthogonal:8 very:1 frequencies:4 rise:2 springer:2 trigonometric:2 sons:1 2γt:2 condition:11 leads:6 europhys:1 level:6 knight:4 dig:2 proposals:1 solution:4 large:2 convenience:1 bypassed:1 a40:1 zero:1 optics:4 dimer:1 upper:2 gg1:7 occurrence:1 oscillation:4 gg2:7 literature:1 supression:1 approximation:2 fold:1 rate:1 go:1 further:6 dynamics:1 leakage:1 ba:1 even:1 established:1 what:2 plays:1 sub:1 imamo:3 section:4 selected:4 near:3 expressed:1 κ2b:2 above:3 berman:2 new:3 satisfy:1 lee:2 ibid:2 respectively:2 never:1 spacing:1 κa:12 here:5 met:1 selective:1 possibility:3 relaxation:1 concluding:1 along:2 standard:1 equations:5 change:1 obtained:3 suitably:1 study:1 vectors:1 eberly:1 suggests:1 resulting:2 resonance:1 suitable:1 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quant-ph9810056.txt |@word consider:1 chinese:1 rev:1 results:1 leads:1 ge:1 research:2 ihep:1 inverse:1 technique:2 anharmonic:5 applied:1 wave:4 affect:1 difference:1 continued:1 solution:7 science:2 pramana:1 sign:1 approximation:1 even:1 section:1 selected:1 method:3 satisfy:1 simultaneously:1 pm1:5 respectively:4 never:1 here:1 china:4 ansatz:7 address:1 equations:3 box:3 institute:2 study:4 studies:1 plotted:2 univ:1 unit:1 readily:1 use:1 eψ:1 positive:1 negative:2 comparing:2 m2:8 today:1 more:1 odinger:9 normalized:4 known:1 hold:1 high:2 ma:1 βr:1 recall:1 equation:13 work:1 oscillator:1 values:4 following:4 14b:1 arrive:2 example:2 numbers:1 beijing:3 compare:1 give:1 relativistic:1 organized:1 states:3 14d:1 14e:1 imϕ:1 14c:1 14a:1 simple:1 write:1 parameter:3 may:1 after:1 cambridge:2 summarize:1 fm:6 constants:2 short:1 natural:2 dynamical:1 secs:1 fundamental:1 order:3 developed:1 insight:1 choose:1 years:1 mathematicians:1 paper:3 signs:2 satisfies:1 ln:2 exact:7 fix:1 actually:1 systems:1 derivative:1 main:2 non:1 they:1 now:2 discuss:1 eigenvalue:3 hereafter:1 advent:1 2d:1 radial:7 constraints:5 another:1 series:1 energy:4 used:1 extended:1 quantum:2 laboratory:1 eq:12 out:1 crucial:1 denotes:1 semiconductor:1 attracted:1 rm:4 math:2 foundation:1 interactions:1 reason:1 khare:1 e1:4 e0:1 r2:1 sextic:1 turn:1 parashar:1 hence:1 retain:1 first:12 origin:2 major:1 already:1 features:1 symmetry:2 dong:1 electronic:1 angular:2 given:5 introduction:1 eqs:3 realization:1 molecular:1 behaved:1 speaking:1 low:1 fraction:1 wellbehaved:1 academy:1 obtained:1 amin:1 attempt:1 undoubtedly:1 varieties:1 distance:1 roles:1 see:1 matter:1 determined:1 7d:2 7c:2 7b:2 7a:2 ann:1 any:1 sciences:1 potential:26 generalized:1 lectures:1 play:1 wells:1 why:1 octic:1 laurent:1 calculated:1 sometimes:1 principle:1 exp:4 constrain:1 physics:4 fact:2 supported:1 spaces:1 relation:2 solutions:5 carefully:1 rough:1 d2:1 find:1 ground:10 based:1 parameters:13 state:18 only:2 employed:1 oct:1 znojil:2 words:1 dr:5 prime:1 arxiv:1 acknowledgments:1 qi:1 shi:1 fixed:1 set:1 national:1 ar2:1 depends:1 sec:2 pm0:4 rmi:1 αr:1 eigenfunctions:9 written:1 closed:1 progress:1 rm0:4 rm1:6 nature:1 attention:1 however:2 unnormalized:3 both:2 last:2 many:1 according:1 chosen:1 hψ:1 figures:2 relevant:1 key:1 appeared:1 dimensional:3 respect:1 throughout:1 considering:1 three:5 been:2 much:1 interest:1 ph:1 fig:2 6a:1 6b:1 corresponding:4 stems:1 spirit:1 those:1 case:1 pacs:1 value:1 choices:1 will:3 almost:1 them:2 converts:1 technology:1 different:2 grant:1 make:2 same:5 quant:1 several:1 higher:1 literature:1 infinity:1 hand:3 arrived:1 potentials:3 frequently:1 recent:1 lower:1 schr:9 center:1 no:1 well:3 relied:1 obtain:6 press:1 atomic:1 world:1 cn:1 hai:1 ny:1 reasons:1 lett:2 easy:3 excited:11 momentum:2 aspects:1 read:2 possible:1 know:1 r0i:1 using:2 advanced:1 like:1 follows:5 become:1 making:1 methods:2 deal:1 people:2 some:4 growth:1 cr:8 dimensions:9 does:1 provides:2 each:1 br:6 properties:1 simpler:1 constrains:2 a1:5 origins:1 constraint:1 discussed:1 15c:1 o:3 a2:7 computational:1 into:2 references:1 there:1 question:1 physicists:1 way:2 was:1 function:3 form:1 energies:1 but:1 intuitive:1 erice:1 us:1 owing:1 problem:1 mechanics:1 ac:7 constant:2 defined:1 abstract:1 denote:1 ar:7 physical:1 functions:4 compared:1 variety:1 zhong:1 when:1 field:1 other:5 republic:2 calculating:2 problems:1 15a:3 a3:7 15b:1 15d:3 variable:1 n0:3 n1:3 4b:2 4c:3 4a:4
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quant-ph9810057.txt |@word measurements:6 consider:8 excepting:2 global:1 results:1 commute:1 depend:1 duction:1 tr:3 send:1 γk:1 meister:1 sent:1 orthogonal:4 very:2 wave:1 print:3 difference:1 exact:1 condition:1 accompanying:2 tra:2 large:3 cas:1 eigenvalues:4 noted:1 sion:2 tem:1 direct:1 elegant:1 subtle:1 further:1 ues:1 sub:1 apparatus:1 exactly:4 sequential:4 replicas:10 ever:1 method:5 mea:4 gener:1 teleportation:1 here:2 separation:1 others:1 obtained:1 institute:1 changed:1 allows:2 resulting:2 stressed:1 usually:1 useful:1 total:3 linearly:2 use:1 takes:3 prove:1 remains:1 positive:1 negative:1 ψk:11 mation:1 therefore:1 taken:1 exhaustive:1 stage:1 type:1 more:12 bennett:2 becomes:1 operators:1 normalized:1 particular:1 known:2 central:1 cases:9 must:4 ρi:2 ρk:5 averaged:1 ρs:1 obvious:1 following:5 trans:1 example:3 control:2 compare:1 stated:1 arise:1 allahverdyan:2 states:13 way:1 performed:1 sense:2 information:6 noises:1 discussion:1 means:1 πk:1 orthogonality:1 how:1 pure:4 optimal:15 simplicity:1 product:1 informa:1 description:1 barnum:1 yamazaki:1 after:4 derived:1 minimized:1 law:1 realized:3 succeeded:1 st:1 si:1 ones:2 so:1 βk:2 se:1 restriction:1 holds:4 interpretation:1 pointed:1 satisfied:2 experiments:1 through:1 statistical:1 jaynes:2 its:1 derive:1 chosen:1 matrices:2 coordinates:1 distinguishing:2 choose:3 ally:1 non:7 practice:1 nonorthogonal:1 mention:1 they:1 now:3 nor:1 eigenvalue:1 transmitter:1 equality:2 always:1 level:2 sufficiently:2 transmitted:1 reasonable:1 each:2 found:1 side:1 mean:8 generation:1 energy:1 measure:3 quantum:16 our:1 eq:1 special:4 out:1 bility:1 shown:1 matrix:2 furthermore:1 induces:1 re:2 investigation:1 alikhanian:1 ble:1 formula:2 ref:1 occurs:3 red:1 nonorthogonality:1 theory:1 ory:2 diagonal:1 standard:1 base:3 bayes:1 forbids:1 pairs:1 interaction:1 place:4 transfer:2 first:4 xk:2 there:3 probability:7 number:3 channels:1 another:1 open:1 given:1 surement:2 unknown:6 eqs:2 sep:1 system:15 πs:3 statement:1 realization:1 scheme:2 final:1 speaking:1 calculations:1 surements:1 proving:1 broadcast:1 quan:1 x2:12 x1:12 than:3 distance:1 wootters:3 showed:1 measured:1 submitted:1 tion:2 outcome:1 distinguished:1 result:2 sees:1 unchanged:1 modern:1 any:2 viewed:1 convenient:1 equipment:2 coincide:3 channel:1 formulas:1 sure:1 shall:2 who:1 most:1 connected:2 drummond:1 pair:1 extremely:1 considered:2 hindrance:1 physics:1 fact:2 quantity:1 saying:1 particularly:3 proba:1 notations:1 brody:1 mitter:1 trivial:1 popescu:1 parameters:1 ment:1 written:1 should:5 only:6 local:4 oct:1 his:2 above:1 get:2 dependent:1 zurek:1 de:1 famous:1 cannot:3 words:1 αk:1 settings:1 arxiv:1 paper:2 ban:1 observer:3 achieved:3 testing:3 detection:1 see:3 num:1 cloning:1 arg:2 uncorrelated:1 acts:1 possi:1 state:18 correctly:1 between:4 neither:1 caves:1 conditions:6 recently:1 reproduced:1 nature:1 however:2 hypothesis:1 tum:1 armenia:1 cor:1 many:3 according:1 against:1 interesting:2 2pe:2 qubit:1 estimation:2 discus:1 among:1 character:2 considers:1 described:2 transformations:1 hypoth:1 due:1 been:3 reduction:4 combined:14 pe:19 ph:4 systems:3 describe:1 corresponding:8 quantities:1 sufficient:1 precision:1 else:1 observers:1 coherent:1 determination:4 bayesian:1 presented:1 spirit:1 present:1 case:13 pacs:1 jointed:1 will:1 brilliant:1 error:9 situation:1 tant:1 opt:11 averaging:1 von:1 thus:10 them:2 equal:2 claimed:1 binary:1 different:4 make:1 same:11 quant:4 products:1 finite:1 independent:4 investigated:1 numerical:1 hand:2 sys:2 entanglement:2 2u1:1 recent:1 eigenvectors:3 minimize:1 well:2 academic:1 usual:1 proposed:1 less:1 generally:1 obtain:1 ozawa:1 previous:1 seems:1 priori:9 lett:5 theorem:1 identical:2 unlimited:1 entangled:4 press:1 using:2 mod:1 loss:1 necessary:1 particle:1 steps:1 arbitrary:2 output:2 yerevan:2 right:1 methods:4 classical:7 some:8 added:1 brothers:1 unavoidable:1 recorded:1 minimal:1 equivalent:2 although:1 post:3 impor:1 bz:1 noisy:1 about:4 actual:1 massar:1 o:1 probabilities:12 tailed:1 mixed:5 introduced:1 automatically:1 rev:9 real:1 communication:1 three:1 because:1 determine:1 registration:1 accumulated:1 neumann:1 assumed:4 initial:2 u1:5 u2:5 abovementioned:1 was:7 ensured:1 function:1 bers:1 but:2 hk:1 construction:1 infor:1 responding:1 tems:1 distinguishability:1 us:5 work:1 problem:4 similar:3 laplace:1 proved:3 conserves:1 defined:1 recognize:1 measurement:16 moved:1 general:4 peres:2 single:1 replica:1 ing:1 physical:1 again:4 mutual:2 rederive:1 when:6 other:3 conclusion:1 helstrom:1 generates:1 calculating:1 preceding:1 problems:2 important:2 prepares:1 equitable:1 correlated:1 practically:1 assume:2 ments:2 hirota:1
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quant-ph9810058.txt |@word limited:1 consider:4 rev:12 bull:1 focus:1 leads:3 consists:2 follow:1 whose:1 certainly:1 depend:1 violate:2 finally:4 present:9 case:16 very:2 wave:1 selleri:3 experimentally:1 trouble:1 four:2 school:1 transmission:9 applicable:1 t0:32 large:1 small:2 noted:1 upper:1 smaller:1 measurable:3 approximation:1 second:11 pass:3 even:1 appear:2 apparatus:2 sum:2 axes:8 nec:1 version:1 above:1 new:5 3e:2 satisfy:1 edited:2 led:1 never:1 here:1 cos2:3 based:2 along:18 standard:1 change:1 extreme:1 larger:5 allows:1 usually:1 emerge:5 spatially:2 family:1 extra:8 vii:1 polarizers:18 use:1 prove:1 distinct:2 predictions:2 next:7 therefore:2 aperture:1 more:1 separated:2 becomes:4 postulated:1 validity:3 tested:2 particular:3 known:1 foundations:1 cases:2 iii:1 must:3 protons:1 theories:5 values:2 following:14 making:1 proof:5 weaker:4 wang:1 high:1 assumptions:2 axis:12 hoc:2 rather:3 s2:1 s1:1 holds:3 far:1 criterion:2 ordinary:17 ensemble:7 simplicity:1 may:5 derived:4 pqm:1 grangier:3 natural:1 exhibited:2 cascade:12 lhs:1 correlation:6 order:2 orientations:2 horne:3 wigner:2 eqs:6 satisfied:2 course:1 experiments:22 through:6 japan:1 its:1 supplemented:1 symmetry:4 chosen:1 interesting:1 imperfection:1 absence:1 according:1 systems:3 covered:1 hidden:1 versus:1 non:7 good:1 maroni:1 enrico:1 xlix:1 they:3 now:6 hall:1 easily:2 2p:8 hereafter:1 always:2 2d:4 realistic:2 inequality:46 each:1 simplified:3 cliffs:1 realism:4 constraints:2 harm:1 energy:1 related:1 extended:1 measurement:2 quantum:25 our:1 summary:1 eq:1 special:2 out:1 emerges:9 shown:1 nuovo:2 since:8 crucial:1 research:1 particles:1 maximized:1 theory:3 quite:2 extraordinary:1 york:1 put:1 pairs:7 correctness:1 feasible:2 place:1 consequence:1 assign:1 first:15 probability:8 number:9 done:1 relations:1 impossible:1 angular:2 passes:1 given:6 similarly:1 introduction:1 interact:1 system:2 approximately:3 their:1 assumption:22 eqm:6 too:1 final:1 prediction:1 tapster:1 butt:1 attempt:1 eliminated:1 than:12 polarized:1 showed:1 double:9 cimento:1 zero:4 rarity:1 depolarization:1 polarizer:17 exhibit:4 symmetries:2 generality:1 argument:1 alley:1 say:1 need:2 seen:3 any:3 viewed:1 wilson:1 angle:5 note:6 ideal:14 absorbed:7 take:4 so:2 detector:1 channel:1 algebraic:1 propagate:1 pair:4 measured:1 sometimes:2 detectors:10 proceedings:1 mechanical:9 physics:2 incomplete:1 3p:2 show:5 violation:8 relation:6 substituting:3 ratio:1 assertion:1 should:2 only:5 experiment:9 ardehali:3 factor:9 local:9 oct:1 do:1 invoke:2 means:1 beams:1 joint:8 agostino:1 international:1 during:1 conjunction:2 freedman:1 podolsky:2 arxiv:1 calling:1 paper:5 roger:3 contrast:1 qm:3 apparatuses:1 2p0:2 requirement:2 set:6 exists:3 violated:3 correlations:1 ullman:1 detection:13 collectively:1 see:2 cim:1 close:1 violates:8 subject:2 inequalities:10 shimony:2 state:7 bruno:1 fermi:1 prentice:1 attention:1 terms:1 emitted:3 weak:2 however:6 efficiency:1 wu:1 analyzed:2 problem:2 faced:1 observable:1 interpretations:2 redefine:1 equal:2 experimental:2 comment:1 bell:18 period:1 moreover:1 considering:1 pp:1 publishing:1 due:1 been:5 much:1 expected:4 ph:1 pi:1 choose:2 direction:2 arises:1 quantities:1 sufficient:2 photon:22 cos:10 refutes:1 those:1 p2:5 p0:13 p1:5 solid:3 value:4 while:2 viii:1 ix:2 orientation:4 vi:1 thus:5 iv:1 ii:1 ij:1 technology:2 make:2 belong:1 same:6 parts:1 quant:1 emphasize:2 used:2 numerical:1 relies:1 locality:11 epr:5 analysis:1 bohm:2 academic:1 solve:1 laboratories:1 grossly:2 spherical:1 less:2 rosen:2 obtain:4 atomic:6 aspect:3 immediately:1 yet:2 previous:5 kanagawa:1 photons:18 coplanar:1 source:6 lett:9 theorem:11 dqm:2 espagnat:1 momentum:2 zou:1 real:12 sagamihara:1 rules:1 implications:1 plenum:1 equality:1 emergence:1 40b:1 englewood:1 reduces:1 unstable:1 arbitrary:4 translated:2 because:2 some:5 supplementary:14 deduce:1 lead:1 sufficiently:2 does:3 assuming:3 demonstrated:2 equivalent:1 references:1 emits:3 rearranging:1 about:2 actual:3 carried:1 anything:1 am:2 discussed:1 o:1 probabilities:19 ou:1 soc:1 into:3 bound:1 three:1 phase:1 accounts:1 einstein:4 statistics:1 assumed:1 there:3 transform:1 long:2 rapisarda:1 start:1 mandel:1 function:6 considerably:6 lowe:1 form:2 but:3 magnitude:6 atom:1 made:1 maximum:3 us:1 limit:1 emissions:1 distribution:2 called:1 mechanics:14 shih:1 proved:1 ad:2 defined:5 certain:1 abstract:1 influence:1 proven:2 general:4 clauser:4 single:8 again:2 nj:1 47a:1 no:5 corporation:2 whereas:1 when:1 detail:1 other:1 test:5 holt:2 important:2 variable:1 implies:1 longer:1 using:8 assume:12 chsh:5 time:4 observables:1 requires:3 original:6
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quant-ph9810059.txt |@word magnetically:2 consider:1 remarkable:1 crucial:1 magnetic:10 lack:1 results:1 illustrated:6 gf:13 ga:1 edu:1 putterman:1 research:1 whose:1 participants:1 preprint:3 charge:9 rokhsar:3 under:1 tc:2 applied:2 random:1 zhang:1 far:1 induce:1 wave:1 electron:1 figs:1 mixing:1 experimentally:2 condition:1 school:1 hamiltonian:2 list:1 large:1 phase:3 barbara:1 setup:4 dilute:1 lewenstein:1 cond:3 estimates:2 direct:1 jump:1 surrounding:1 second:1 rigorous:1 qualitatively:1 petrosyan:1 estimated:2 linear:4 blue:3 index:1 nonlinear:2 trapping:5 fine:1 expressed:2 uniform:1 reminiscent:1 axial:1 experiment:1 above:4 new:4 consisting:1 3d:1 body:1 condensed:2 ibid:1 respectively:1 mr:1 here:3 atoms:10 ansatz:1 groups:2 along:6 z2:1 stark:2 lemmer:1 institute:2 larger:1 piercing:1 amount:1 periodic:1 published:1 hospitality:1 conveniently:1 studies:1 involves:1 santa:1 private:1 addressed:1 condensates:3 total:2 unit:2 franck:2 use:3 takes:2 would:6 contains:1 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quant-ph9810061.txt |@word sergei:1 alm:2 homomorphism:1 consider:2 remarkable:1 desirable:1 results:5 generalize:1 computation:1 go:1 expressions:3 alk:2 whose:1 finally:4 present:3 under:1 anharmonic:2 belonging:1 supported:1 straightforward:1 ll1:1 pressley:1 zachos:1 wave:4 entries:1 mixing:2 deformations:1 condition:1 level:2 irreducible:2 almn:5 tanh:2 large:1 solved:2 vector:1 small:1 eigenvalues:3 optics:5 approximately:1 specially:1 maclaurin:2 consistent:1 cosh:4 approximation:2 second:1 further:1 dynamics:1 substitute:1 scientific:1 what:1 nonlinear:1 section:4 3n:1 above:1 3l:1 new:3 d1:1 method:2 coefficient:1 chose:1 degree:1 here:5 atoms:5 behaviour:1 chumakov:4 groups:4 berkeley:1 deduced:2 obtained:2 averages:1 study:1 studied:1 hospitality:1 useful:1 limq:1 summation:3 apply:1 use:2 takes:1 would:1 commun:1 sake:1 h0:2 jal:1 next:2 comparing:2 m1:5 therefore:2 m2:17 nuelos:1 operators:2 ghandour:1 normalized:4 particular:2 known:3 cases:1 hold:1 analogous:1 high:1 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