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quant-ph9804068.txt |@word abstract:1 arxiv:1 paper:1 quant:1 ph:1 dec:1 withdrawn:1
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quant-ph9804070.txt |@word concept:4 consider:1 chinese:1 leads:2 gm:1 certainly:1 under:1 straightforward:1 rise:1 perihelion:1 every:2 decide:1 difference:2 exact:2 solution:1 small:2 venus:1 shows:1 consistent:1 approximation:1 second:2 chee:1 dynamics:2 sun:1 new:1 increasing:1 systematic:1 measurements:2 xθ:1 china:1 others:1 consideration:3 change:2 involved:1 larger:1 gravitationally:1 amount:1 usually:1 changes:3 composed:1 apr:1 decrease:1 unit:2 use:1 takes:2 would:4 contains:1 mediate:1 m1:1 therefore:5 m2:1 theoretical:2 minor:1 more:1 separated:3 successful:1 company:1 corrected:4 effort:1 must:3 springer:1 equation:1 work:1 concepts:1 following:2 example:2 wang:1 figure:1 give:4 calculation:7 arise:1 states:3 indicates:1 sense:3 evidently:1 verlag:1 commutable:1 rather:2 discussion:1 feature:2 how:1 may:6 philosophy:2 law:4 data:1 emperor:1 jiang:1 su:1 so:2 order:2 talk:1 interpreted:1 paper:1 statistical:2 its:4 thank:1 relativity:5 lk:1 coordinates:1 actually:2 better:1 freeman:1 good:2 combination:1 zhen:1 oxford:1 now:1 qhl:1 structural:1 university:2 reasonable:2 each:1 weight:4 independent:1 short:2 liaoning:1 astrophysical:1 measure:1 quantum:19 our:6 out:1 space:6 since:1 formula:1 unifying:1 theory:2 attempt:2 quite:1 interaction:2 length:3 first:2 relate:1 variables:1 done:1 periodical:1 synthesizing:1 mercury:2 observer:2 introduction:1 system:7 least:2 zeros:1 too:1 underlie:1 gives:2 explanation:1 part:1 natural:1 than:2 distance:3 penrose:1 anticipate:1 depends:1 matter:1 were:1 sec:1 dalian:1 correction:3 mind:1 dθ2:1 increment:1 seen:1 tells:1 responsible:1 able:1 k2:4 take:1 though:1 most:2 formulae:1 nothing:1 measured:4 observation:6 calculated:1 points:3 principle:2 physics:11 fact:1 planetary:6 show:1 earth:1 d2:2 paradoxes:1 explain:1 should:4 only:2 employed:1 hope:1 get:2 familiar:1 overall:1 pave:1 famous:1 precession:8 arxiv:1 common:1 ql:13 ignored:1 exists:1 observed:1 intensity:1 radius:2 result:4 closer:1 gravitation:6 purpose:1 distinctive:1 state:4 unable:1 between:2 terms:1 nature:1 ignorance:1 key:1 both:1 cos:1 many:1 uncertainty:4 quantization:1 april:1 expression:1 otherwise:1 point:2 simple:1 period:2 table:1 described:1 due:1 been:1 pc:1 judging:1 ph:1 partly:2 precision:2 observe:1 realms:1 uncertain:1 value:1 will:2 shall:2 error:5 thus:1 itself:2 technology:1 orbital:2 different:2 author:1 make:1 same:1 any:3 quant:1 higher:1 evolve:1 see:4 effect:2 delicate:1 scarcely:1 spacetime:1 well:1 without:1 decimal:1 being:2 newton:7 seems:1 thermodynamics:2 unification:1 know:3 presume:1 press:2 integer:2 like:3 kenneth:1 δb:1 reasonably:1 lager:1 beneficial:1 because:2 methods:1 classical:8 some:3 2ql:1 2nπ:1 prof:1 measuring:2 step:1 about:2 range:1 introduced:1 formerly:1 h2:2 into:4 integral:2 satisfactory:1 references:1 einstein:2 proportional:1 ellipse:1 there:6 u1:1 long:1 quanta:1 physicists:1 way:4 call:1 function:2 form:4 becoming:1 basic:2 but:3 subjective:1 subjectively:1 brick:1 made:1 gravitational:5 up:2 us:1 wipes:1 planet:3 mechanics:3 constant:2 zeno:1 certain:1 abstract:1 measurement:11 influence:1 meaningless:1 general:2 ap:1 single:2 dθ:1 compared:2 paradox:1 no:2 when:5 reality:4 role:2 normal:1 department:1 mass:5 deviation:2 polar:1 zhou:1 constructs:1 meaning:2 lang:1 assume:2 orbit:2 weights:1 time:3 original:1
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quant-ph9804071.txt |@word iǫ2:1 iǫ1:1 iǫ0:2 evidence:1 consider:2 springer:5 switched:1 induces:1 global:4 splitting:16 leads:3 eds:1 eǫ:1 entropy:1 contains:2 during:5 sigmund:1 anggi:11 denotes:4 contributions:4 weakly:1 localized:3 compact:1 diffusive:1 heller:1 inverse:1 superpositions:1 zone:1 umel:2 portraits:1 eα:5 tr:10 ρs:7 spirit:1 environment:3 roncaglia:1 monotonically:1 chaps:1 manifolds:1 th:2 under:11 stochastic:1 suffered:1 include:2 quasienergy:15 plata:1 division:1 provides:1 evolves:1 very:2 frequencies:4 activation:3 rise:1 straße:2 harmonics:1 unfamiliar:1 wave:8 ovsiannikov:1 stabilized:2 figs:5 prof:1 mixing:2 vastly:1 little:1 exact:13 appropriately:1 condition:1 four:1 mild:1 incoherent:9 level:17 altering:1 forth:2 notes:1 trb:2 solution:4 t0:3 occurs:3 leave:1 discrete:1 differential:3 demonstrated:1 affect:1 recall:1 small:3 eigenvalues:2 markov:3 referred:1 intricate:1 challenge:1 configurations:4 inserting:2 smaller:1 force:1 incoherently:1 oscillation:1 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quant-ph9804072.txt |@word represent:1 partial:1 consider:2 results:1 four:3 tricomi:1 go:1 follow:2 gl:1 contributions:2 viceversa:1 devoted:1 inverse:1 calculate:2 γi:2 nodes:4 hill:1 p2:1 springer:1 wave:5 every:1 noninvariant:1 varshalovich:1 continued:1 condition:1 illustrated:1 solution:6 deals:1 miller:1 sin2:1 sign:1 ter:6 odd:1 sum:1 expressed:2 cell:6 goes:1 new:2 method:5 coefficient:1 full:1 fiz:3 respectively:3 here:3 cos2:1 separation:7 represented:2 path:1 fifteen:1 property:1 institute:1 study:2 allows:1 published:1 via:1 useful:1 rodrigues:1 total:1 unit:1 eψ:1 prove:1 positive:3 negative:1 hakobyan:2 nucl:3 ψn:6 therefore:3 vi:3 taken:4 associated:2 type:1 theoretical:1 grosche:1 separated:3 nauka:1 ugge:1 ascribe:1 odinger:6 berlin:1 normalized:1 known:1 must:2 account:1 endpoint:2 equation:14 work:2 oscillator:6 erd:1 itself:1 values:3 following:5 example:1 f1:1 calculation:1 sphere:4 numbers:5 verlag:1 orthogonality:2 write:3 fourth:2 ordinary:1 sin:24 product:3 mat:1 algebra:2 may:4 after:2 diagram:2 coming:1 multiplication:1 fk:1 fl:1 types:3 lines:1 correspond:3 su:6 allow:1 representation:2 sd:2 separable:1 developed:2 over:1 professors:1 paper:4 through:1 signs:1 ld:1 group:1 thsun1:2 chosen:1 coordinates:12 li:5 lr:48 fig:1 jacobi:1 main:1 moskalev:1 yl:5 ya:6 propose:1 ye:2 introduce:1 ls2:2 half:1 bogoliubov:1 now:4 teller:1 represents:1 indeed:1 2q:6 2d:1 2e:1 l2:1 l1:1 found:2 2n:1 2i:2 domain:1 differential:1 energy:3 valiev:1 entering:1 year:1 quantum:13 laboratory:1 gordan:7 eq:4 ru:1 shown:1 matrix:16 space:1 nuovo:3 singular:1 research:1 looking:1 rosochatius:2 orthonormalized:2 oberhettinger:1 constants:7 math:2 theory:1 associate:1 free:4 york:2 dubna:4 e2:1 makarov:1 r2:1 could:2 transition:13 motion:2 isotropic:2 teor:1 crm:1 βi:3 first:3 origin:2 xi:9 evans:2 laguerre:1 variables:4 number:6 xd:1 multiplying:2 done:1 angular:1 ser:2 given:4 cartesian:11 introduction:1 top:1 system:6 construct:5 their:3 2ωl:1 superintegrable:3 smorodinsky:5 final:1 moscow:1 exactly:1 authors:1 eliminated:1 x1:3 coefficients:10 determines:1 tree:14 clebsch:6 1l:2 winternitz:3 determined:1 were:1 toward:1 russia:1 hyperspherical:12 ann:1 spectrum:2 generalization:1 formula:3 vilenkin:2 need:1 any:3 generalizes:2 angle:2 magnus:1 lik:1 note:1 k2:1 k1:4 potential:6 generalized:1 fris:1 systems:2 plan:1 formulae:2 analytically:1 kd:2 considered:3 kj:29 professor:1 later:1 vertices:1 drawing:1 graphs:1 proceedings:1 points:1 exp:2 physics:2 section:3 particularly:1 ki:42 relation:1 solutions:1 d2:3 ns2:2 principal:2 q1:3 q2:1 parameters:1 analytic:2 only:3 bases:5 transcendental:1 factor:1 integrable:1 above:2 dependent:1 joint:1 dx:3 dr:4 a86:1 arxiv:1 expansions:1 qd:3 qi:1 fixed:1 kibler:2 view:1 vr2:1 ωxi:1 constructing:2 cimento:3 2c:1 lnr:1 see:1 result:2 discussions:1 macfarlane:1 αs:4 αr:5 nuclear:1 definite:1 written:2 closed:2 between:5 αi:1 invariant:1 x21:1 x22:1 terms:3 pogosyan:9 wn:1 jr:1 vanishing:1 article:3 come:2 thank:1 both:2 collaborators:1 x2i:4 x2d:1 region:3 according:2 quantization:1 ln:1 connection:1 contribution:3 fnl:6 2ni:3 point:2 continuation:3 ca:2 each:3 dimensional:8 bβ:4 table:8 2nr:1 pq:4 basis:5 addition:1 equations:1 laplacian:1 yad:2 ph:2 ls:40 θk:1 graphical:3 θi:4 corresponding:8 ψni:1 θc:1 cos:27 θd:3 fortschr:1 ψnr:4 kalnins:1 general:3 present:1 case:2 value:1 euclidean:1 lαn:1 endpoints:1 identical:1 vd:1 vol:15 ki2:2 thus:1 equal:1 vr:36 vs:32 fn:6 ig:1 different:2 large:1 realizing:1 lett:1 quant:1 arguments:3 higher:1 investigated:1 upon:2 nj:10 potentials:1 clebsh:1 normalization:1 ellipsoidal:1 schr:6 well:1 solve:1 coordinate:1 dimension:1 left:4 spherical:3 being:1 nd:4 obtain:5 rnr:2 preprint:2 nonrelativistic:1 belongs:1 treatment:1 heidelberg:1 momentum:3 real:3 sums:1 know:1 using:5 helpful:1 systematically:1 follows:1 δn:1 yields:2 integrals:2 arbitrary:2 mcgraw:1 right:4 methods:1 classical:2 calculated:2 nr2:2 describing:1 connecting:1 vs2:2 radial:3 bi:2 expansion:6 khersonskii:1 cγ:4 hypermomentum:1 properties:1 asymptotic:1 integers:2 side:1 practical:1 sissakian:6 ci:2 elyi:1 kuznetsov:2 communication:1 into:2 22d:1 integral:5 because:1 references:1 determine:1 sov:1 elementary:1 leningrad:1 acknowledgements:1 comparing:1 strictly:1 there:3 quadratic:1 jinr:4 call:1 was:1 function:7 form:9 adjusting:1 wnn:3 jul:1 construction:1 atom:1 russian:1 line:5 antonyan:6 cells:8 ωr:1 us:3 called:1 mechanics:1 kh:1 constant:2 ai:2 abstract:1 kn:3 dθ:10 formalism:1 ni:9 functions:4 when:1 θb:1 other:1 nq:5 nr:35 ns:17 conclusion:1 node:1 denote:1 polynomials:3 includes:1 sides:3 opened:1 ago:1 dω:3 harnad:1 vinet:1 together:1 n1:4 n2:2 4b:1 caα:4 4a:1
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quant-ph9804073.txt |@word interpret:1 undivided:1 drastically:1 interpretation:14 proposed:1 show:1 indeed:1 move:1 results:2 interpreted:1 obtains:2 course:2 uwthph:1 paper:1 relation:1 solutions:1 reconstruct:1 differentiation:1 follow:1 analogue:1 d2:2 its:4 roots:1 ground:1 current:1 inverse:5 just:3 tx:2 how:1 chosen:2 exact:2 square:1 solving:1 distributed:1 state:6 uniqueness:1 valid:1 fig:1 easy:1 factor:11 role:1 ontological:1 main:2 presentation:1 excited:1 momentum:4 continuity:3 applied:1 his:1 around:1 means:1 dependent:4 disagreement:1 possible:1 obtain:1 answer:1 cannot:2 hamilton:1 know:1 dx:8 press:1 using:6 dt:4 decomposes:1 chicago:2 condition:3 2t:2 going:1 particle:6 follows:2 university:1 arxiv:1 t2:10 solution:10 t0:8 x20:2 theory:1 differential:1 completely:1 found:1 universit:1 difficult:1 2i:1 view:1 heinz:1 classical:8 achieved:1 2x:3 consistent:1 some:1 idea:1 packet:2 contradictions:1 namely:1 result:12 quantum:12 copenhagen:1 extract:1 tempted:1 transport:2 concern:1 shown:7 visualize:1 proceeding:1 what:1 maintained:1 space:2 literally:1 section:2 since:4 rev:1 integration:1 denotes:1 particles:4 written:1 does:2 connecting:1 reconstruction:3 example:2 new:2 correct:2 shows:1 full:3 amplitude:1 whose:1 use:1 here:2 agreement:2 difficulty:1 shape:5 velocity:1 free:2 references:1 universe:1 described:1 appropriate:1 wanted:1 implicit:2 change:2 suggested:1 definition:2 cos:8 cautious:1 last:2 nevertheless:1 hiley:1 could:1 density:1 discussed:1 according:1 david:1 motion:3 april:1 hψ:1 resulting:1 due:3 trajectory:1 attributes:1 contingency:2 expression:1 first:2 detailed:1 probability:17 point:1 apr:1 requiring:1 4i:1 within:2 numerically:1 harmonic:4 system:4 austria:1 because:1 done:1 determine:1 operator:1 broadening:1 given:11 institut:1 takes:1 introduction:1 wien:2 initial:7 theoretische:1 been:1 next:2 explicitly:1 too:1 way:3 taken:3 applying:1 ph:1 final:2 ψd:1 therefore:5 function:9 obtained:6 london:1 only:3 corresponding:2 complete:2 form:1 both:1 continuous:1 agrees:5 odinger:3 but:7 gaussian:1 expected:1 coherent:4 comparison:1 normalized:3 x2:8 implies:1 x0:52 tx2:1 must:3 case:2 account:1 determines:1 equation:9 oscillator:4 zero:1 value:3 ur:1 will:3 considered:1 determined:1 obvious:1 three:1 historical:2 eigenstates:1 following:3 distribution:20 gives:3 agree:1 procedure:1 examples:2 mechanics:7 fulfills:2 compare:1 constant:1 figure:1 ln:2 defined:2 certain:1 abstract:1 thus:1 general:2 reconstructed:1 imagination:2 contrary:1 itself:1 right:1 ist:1 cushing:1 any:2 absolute:3 routledge:1 again:2 functions:1 moves:1 2ix:1 no:1 whereas:1 responsible:1 when:1 ideas:1 same:1 instance:1 without:4 quant:1 units:1 instead:1 flow:2 subject:1 sin:7 conclusion:1 transferring:1 simplicity:3 used:1 superposition:2 may:5 trajectories:8 different:1 dx0:6 wrong:2 moving:2 peak:1 physik:1 mechanical:4 phase:4 wave:7 normalization:6 times:3 schr:3 lead:1 rules:1 makes:1 into:1 later:1 explicit:1 quite:1 together:1 obviously:2 bohm:11 points:6 solve:1 exp:18 time:23 very:2 position:2 plotted:1 boltzmanngasse:1 dimension:1 usual:4
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quant-ph9804074.txt |@word limited:1 partial:3 rev:13 results:7 perelman:1 eds:2 follow:3 zinn:1 localized:4 heller:1 calculate:2 eigenbasis:1 involve:1 unanswered:1 recurrence:1 finally:1 behave:1 manifolds:3 stable:17 anharmonic:2 case:2 very:6 stroud:6 wave:26 electron:5 every:1 lalo:1 hamiltonian:3 did:1 solution:3 large:3 strayer:1 bellomo:2 small:1 diu:1 optics:2 degeneracy:1 enjoy:2 prevent:1 unexpected:1 sin2:2 approximation:2 imply:1 value:1 further:1 dynamics:12 even:3 appear:1 brackets:1 sum:4 judicious:1 new:3 increasing:1 ever:1 contrast:2 satisfy:2 full:1 lee:1 respectively:1 vol:1 here:1 desired:1 cos2:2 separation:1 along:5 great:1 property:2 institute:1 study:5 larger:2 approaches:2 eberly:2 periodic:1 poisson:2 action:2 changes:1 appropriately:1 equivalence:2 scales:1 apr:1 addressed:2 giannoni:1 standing:1 plot:2 use:1 superpositions:1 usa:1 remains:1 quasi:7 nonnegligible:2 periodically:1 few:3 bialynicki:2 therefore:8 bialynicka:1 more:5 becomes:2 under:3 odinger:3 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quant-ph9804075.txt |@word aided:1 four:4 entropy:38 consists:1 whose:3 violate:5 under:11 rise:3 every:6 govern:1 experimentally:1 disturb:2 crops:1 solution:1 vector:1 deutsch:1 direct:3 approximation:1 elegant:1 second:18 implemented:1 machines:1 even:4 established:1 above:29 conduct:1 new:7 increasing:2 simultaneously:3 never:2 here:17 plenio:11 represented:3 calculate:3 obtained:6 study:1 stressed:1 stipulated:1 settled:1 attractor:1 secure:1 explained:1 total:10 unit:1 would:31 motivate:1 call:3 therefore:23 tell:3 separated:1 successful:2 naive:1 phone:2 reversible:8 circumstances:2 word:1 room:1 work:13 theories:1 ere:1 grover:1 concepts:1 example:12 indicated:1 give:1 bennett:10 implementations:1 want:8 keep:5 end:15 provide:1 feature:1 machine:2 how:16 hot:2 ent:1 answer:7 gate:3 brassard:2 description:1 thermodynamic:3 after:12 wrong:1 summarize:2 law:30 types:1 third:3 summing:1 maintain:1 order:10 operations:39 over:13 london:1 eavesdropping:1 fidelity:7 before:2 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quant-ph9805004.txt |@word wigner:6 similarity:1 being:2 p3:1 quasi:1 results:2 known:1 thermal:6 relation:1 solutions:2 statistical:1 lebedev:1 remarkably:1 compared:1 whose:1 heller:1 worthy:1 ratio:1 density:1 vth:4 complex:1 coordinates:1 actually:1 moments:1 finally:1 permanent:1 location:1 easy:1 marginal:1 role:3 analogous:2 must:1 deformation:2 momentum:2 take:1 opt:1 σxp:1 iǫ:1 miele:2 affected:1 pure:1 rev:1 di:1 could:1 end:1 ko:3 introduce:2 federico:1 beam:7 cannot:2 dz:1 makes:1 dx:1 press:1 using:1 difference:2 coincide:1 states:2 represents:1 term:1 mancini:1 like:17 particle:7 obvious:1 arxiv:1 cells:1 lawson:1 phase:3 schwarz:1 arbitrary:3 small:1 through:1 universit:1 dip:1 reduced:1 possibility:1 view:1 function:4 anharmonic:1 differential:2 old:1 neumann:1 classical:8 ficient:1 there:1 variables:1 some:2 back:1 transition:1 approximation:8 edition:1 second:1 expect:1 configuration:1 positivity:1 quantum:13 contains:1 indistinguishability:2 chem:1 eq:1 violates:1 transport:4 obey:1 even:2 shown:1 fisiche:1 space:7 oxford:1 pictures:1 furthermore:1 since:2 definite:1 while:1 its:2 case:2 acting:1 does:2 above:4 between:1 invariant:1 approach:3 terms:1 linear:3 ps:1 respectively:3 equivalent:1 each:1 however:1 free:2 effect:2 clarendon:1 ansatz:1 references:1 address:1 based:1 imaginary:1 standard:2 change:1 temperature:1 obtained:1 both:1 scienze:1 recovered:1 last:1 suitably:1 institute:1 optics:1 taking:1 emittance:6 numerator:1 according:1 o:2 russia:1 propagation:2 σx:2 place:2 obeys:1 context:1 corrections:2 conveniently:1 σp:2 expression:1 assign:1 plays:3 among:4 relevant:1 features:1 probability:1 point:2 tomography:1 noting:1 spreading:5 within:2 harmonic:1 system:4 semiclassical:4 variable:1 multiplying:1 accounts:1 construct:1 framework:2 xp:2 electronic:8 unit:1 size:1 follows:1 given:5 phasespace:1 described:1 takes:1 would:1 prove:1 positive:3 px:2 give:2 transform:3 been:1 twm:2 definiteness:1 going:1 cimento:1 way:1 ph:1 partial:1 more:1 sort:3 formally:1 form:1 behind:1 concerning:1 odinger:1 but:1 transverse:3 state:1 determination:1 discussed:1 particular:3 x2:4 schr:1 than:1 partially:1 p2:3 infn:1 account:1 evolution:1 evident:1 deformed:3 equation:13 napoli:1 oscillator:1 zero:1 considered:1 liouville:5 replaced:3 temperatures:1 ρw:11 following:4 distribution:4 semiclass:1 called:2 say:2 projections:1 mechanics:2 due:4 uncertainty:3 played:1 defined:1 well:1 von:2 thus:3 denote:1 ii:2 effectively:1 single:2 smaller:1 exist:1 conjugate:1 need:1 aspects:1 transit:1 distributions:1 2nd:1 ray:3 symmetrized:1 information:1 rays:6 italy:1 tombesi:1 means:2 lett:1 regions:1 potential:3 quant:1 arguments:1 analogy:2 contain:1 finding:1 dimensionless:1 finite:7 moscow:1 diffraction:1 picture:1 clear:1 used:1 description:3 may:2 whole:1 denominator:1 neuman:1 lens:2 plane:2 connected:1 iη:7 position:1 remarks:1 fedele:3 wave:1 intrinsic:2 man:3 diffusion:1 lower:1 introduced:2 physical:2 effective:2 smallness:1 assume:2 consequently:4 into:1 paraxial:2 physics:1 exhibited:1 thought:1 nuovo:1 ones:1 principle:1 time:2 coordinate:1 velocity:1 model:1 charged:4 starting:1 order:3 beams:1 typical:1
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quant-ph9805005.txt |@word lack:1 brownian:7 kanai:4 menon:1 edu:1 consists:1 whose:1 γt:4 environment:3 does:2 under:2 stochastic:3 case:3 supported:1 results:3 emphasized:1 e2γt:1 severely:1 hamiltonian:4 solution:1 damped:1 vector:1 barbara:1 noted:1 force:4 10b:1 10a:1 second:1 even:1 what:1 sun:1 experiment:2 above:4 lifshitz:1 new:1 contrast:2 paradoxical:1 satisfy:1 address:1 equations:4 appears:1 change:1 colored:1 institute:1 study:1 allows:1 opinion:1 studies:1 manage:1 conventional:1 would:2 remains:1 ψk:6 therefore:2 taken:1 theoretical:1 more:4 composite:1 becomes:2 operators:1 odinger:2 sharply:1 particular:1 iii:1 must:1 obeying:1 account:2 valued:1 science:1 equation:11 work:1 oscillator:1 labeled:1 values:1 making:1 my:1 f1:3 f2:1 give:1 numbers:1 junctions:1 verify:1 write:1 overbar:1 ensemble:2 may:2 derived:2 microstate:1 plane:1 waves:1 wave:12 short:1 natural:1 effective:1 so:5 correlation:1 definitions:1 order:2 reservoir:6 over:3 interpreted:1 thermal:2 paper:1 through:1 statistical:1 argued:1 satisfies:1 its:5 itp:1 before:1 derive:1 thank:1 if2:2 ln:2 degrees:2 systems:1 into:2 orthodox:1 practice:1 landau:1 hamilton:1 effects:3 they:1 oxford:1 nov:1 yu:1 association:1 represents:1 university:1 2m:6 2k:1 another:1 ed:1 gaussian:4 carvalho:1 obtains:1 quantum:10 eq:6 shown:1 3rd:1 space:3 open:1 nuovo:2 since:2 rev:1 reif:1 particles:1 acting:1 hill:1 ref:1 occurs:1 math:1 predicted:1 foundation:1 lugiato:2 theory:1 davidovich:1 approaches:1 california:1 york:1 definition:1 interaction:1 could:1 times:1 motion:8 turn:1 consequence:1 first:2 initial:4 probability:1 directly:1 precisely:1 electronic:1 illustrate:1 given:4 temperature:2 hasse:1 system:4 relations:1 their:2 assumption:1 master:3 normalization:1 white:3 leggett:2 ehrenfest:1 recovered:1 gives:1 kf1:1 eliminates:1 part:1 somewhat:1 authors:2 x2:4 peaked:1 eγt:2 determines:1 accordance:1 require:1 cimento:2 determined:2 generality:1 fluctuation:2 say:1 need:1 seem:1 viewed:1 studying:1 ideas:1 note:1 k2:1 potential:2 absorbed:1 generalized:1 singh:1 heisenberg:1 electric:1 shall:1 measures:1 most:1 treats:1 average:1 physica:2 typeset:1 points:1 exp:3 mechanical:1 physics:2 fact:1 quantity:1 show:3 random:1 tecnol:1 solutions:2 caldirola:6 based:2 should:3 only:3 diffusion:1 dk:2 dependent:3 de:2 expectation:2 criticized:1 cannot:2 instance:2 dx:2 dp:1 evolution:3 qu:1 arxiv:1 investigate:1 exercise:1 approaching:1 coefficient:1 national:1 packet:5 freeze:1 rmc:1 see:2 sec:1 result:3 caldeira:2 functionals:1 artificial:1 state:4 closed:1 αk:1 reading:1 approach:6 2πiτ:1 however:2 ıfico:1 taking:1 uncertainty:6 according:1 quantization:2 whole:1 finds:1 ck:3 cl:1 ca:1 harmonic:1 weiss:1 respect:1 cavities:1 been:1 phy94:1 cient:1 describes:2 damping:1 electrodynamics:1 pk:1 ph:1 corresponding:1 influence:1 former:1 p2:2 eip:1 josephson:1 pacs:1 value:5 replaced:1 behavior:2 applies:1 tunneling:1 phenomenological:1 averaging:1 discrepancy:1 ii:3 quantize:1 im:1 grant:1 make:1 same:5 iα:1 quant:1 emphasize:1 units:1 finite:2 grows:2 singapore:1 uses:1 identity:1 schr:2 center:3 analysis:1 without:2 solve:1 position:7 model:2 usual:2 proposed:1 generally:1 obtain:1 world:1 ogico:1 4m2:1 density:3 point:1 cavalcanti:1 nacional:1 conselho:1 theorem:2 iτ:1 take:1 fluctuating:1 easily:1 rules:1 possibly:1 know:1 using:3 like:1 particle:14 follows:1 performing:1 arbitrary:1 friar:1 because:2 classical:3 some:1 sight:1 specified:1 provided:2 langevin:4 integration:1 ucsb:1 tends:1 prog:3 noise:6 11a:1 scientific:1 11b:1 revtex:1 santa:1 found:2 hilbert:2 mcgraw:1 freedom:2 am:1 desenvolvimento:1 o:3 2cl:1 2iτ:1 presence:1 pergamon:1 spreading:1 functional:1 dissipation:3 2qu:1 references:2 operator:7 uncertainties:1 criticisms:1 prepare:1 there:1 width:1 low:1 way:2 was:1 propagator:1 naturally:1 function:8 form:1 fundamentals:1 but:3 properly:2 elimination:1 cnpq:1 dissipative:1 us:1 limit:1 critical:1 fluctuations:1 percival:2 gisin:2 mechanics:1 constant:2 defined:1 abstract:1 describe:1 akin:1 denote:1 chap:1 reservoirs:1 dα:1 functions:1 compared:2 no:1 when:7 field:1 interested:2 theor:3 conclusion:1 picture:1 generates:1 variable:1 assume:1 dτ:5 governed:1 2mσ:1 mass:2 time:5 starting:1
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quant-ph9805006.txt |@word consider:2 illustrates:1 equalities:2 results:3 existing:1 leads:2 manager:1 gb:1 computation:10 consists:1 query:8 reasoning:1 increase:1 inverse:1 depend:1 calculate:2 concerned:1 white:1 presents:1 finally:1 critical:1 those:1 under:2 supported:1 amplitudes:6 string:18 straightforward:2 very:1 induce:2 every:5 decide:1 difference:1 exact:2 basics:1 presented:1 did:1 try:1 vector:1 harry:1 small:6 upper:1 focs:2 α2j:1 approximation:1 fold:1 second:1 further:1 hewlett:1 linear:2 even:1 will:24 what:2 rate:2 giving:1 section:4 goldston:1 3n:1 above:5 new:2 full:2 degree:2 respectively:1 component:1 equals:4 here:7 behaviour:1 desired:1 situation:1 november:1 equations:1 change:1 box:10 search:1 institute:1 approaches:1 ourself:1 amount:1 products:1 advertising:1 published:1 changes:1 honor:1 via:2 useful:1 requiring:1 wim:2 explained:1 apply:4 total:1 establish:1 use:3 usa:1 remains:1 give:3 few:1 call:4 therefore:9 more:1 becomes:1 operators:1 corrected:1 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quant-ph9805007.txt |@word concept:1 consider:7 splitting:15 leads:1 consists:2 research:2 factorizing:1 whose:2 violate:2 eα:14 equivalence:1 γj:1 γi:1 preserved:1 under:2 eβ:1 amplitudes:1 zhang:1 wave:2 every:1 dispersions:2 condition:4 identity:2 splitter:1 annihilated:1 hamiltonian:4 irreducible:1 solution:3 leave:1 vector:1 eigenvalues:1 optics:1 direct:3 second:1 dynamics:1 port:1 what:2 giving:1 section:1 analogously:1 expressed:1 current:1 version:1 new:1 consisting:1 nakamura:1 pioneering:1 respectively:1 here:3 diagonal:1 groups:4 address:1 represented:1 along:4 invented:1 equations:1 extreme:1 obtained:4 hbi:1 institute:1 shift:1 contradiction:1 products:1 action:3 65th:1 scaled:1 ecα:7 unit:2 use:1 would:1 prove:2 sake:1 uniqueness:1 properties:9 classically:1 therefore:5 criteria:1 ψb:2 ψc:2 themselves:1 ψa:2 ψg:4 more:2 israel:2 vpr:1 started:1 operators:7 ti:1 odinger:2 ζb:1 berlin:1 normalized:1 particular:5 known:2 cases:2 producing:1 must:3 springer:1 valued:1 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quant-ph9805008.txt |@word secondly:2 footing:1 consider:5 forbidden:1 results:2 four:1 eds:4 commute:3 gc:1 cases:1 ptp:1 whose:1 superspace:1 deterministic:1 experimentally:1 finally:1 those:2 th:1 under:1 stochastic:1 characterised:1 worth:1 applied:1 finkelstein:1 broadly:1 far:1 wave:10 bjorken:1 electron:4 sons:1 affect:1 emphasized:2 encounter:2 leads:7 quantized:1 presented:1 issue:3 permits:1 applicable:1 large:3 discrete:3 coincidences:1 commented:2 solutions:1 upper:1 smaller:2 force:3 consistent:2 direct:1 past:1 zero:3 perspective:2 equal:2 further:3 mπ:1 bilinear:2 reconciliation:1 what:6 nonlinear:1 appear:2 section:2 circumstance:1 expressed:1 reminiscent:1 experiment:2 above:11 new:11 net:1 ever:1 simultaneously:1 equals:1 here:3 behaviour:1 separation:1 granularity:1 directions:1 consideration:3 along:1 strong:1 equations:3 appears:2 deduced:1 obtained:1 clarendon:3 root:1 vectors:1 contradiction:2 bertlmann:1 emerge:1 perspectives:1 scales:9 spooky:5 centenary:2 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quant-ph9805013.txt |@word gw:1 consider:6 leads:5 go:2 gm:2 content:2 dimensionality:4 show:2 charge:5 th:1 under:1 ıj:1 g2:1 very:4 continues:1 wave:1 electron:8 encounter:3 four:2 applicable:1 large:2 small:4 noted:2 louie:1 consistent:3 narlikar:1 perspective:2 further:1 even:1 reconciliation:1 what:1 nonlinear:1 appear:2 rd3:1 giving:1 section:1 near:1 expressed:4 consistently:1 above:8 fractional:5 new:2 net:1 ever:2 method:1 lee:1 respectively:1 component:1 here:2 behaviour:1 strong:2 equations:2 emerge:1 spatially:2 scales:6 brought:1 viz:1 neutrino:3 planck:2 proceed:1 would:5 positive:1 handedness:5 finally:2 m1:2 centre:2 m2:2 taken:1 veltman:1 type:5 refs:1 successful:1 conclusions:1 symptomatic:1 clue:2 proton:1 known:6 hole:4 me:3 springer:1 valued:1 lefthanded:1 shielded:1 science:2 mo:1 protons:1 mw:2 mp:2 choi:1 following:1 fluctuational:1 example:2 geometrized:1 heart:1 perlmutter:1 wang:1 relativistic:2 arise:1 quark:3 verlag:1 rather:1 verify:1 discussion:1 di:1 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quant-ph9805014.txt |@word sergei:1 consider:5 represent:3 crucial:1 brownian:1 results:2 leads:1 commute:1 generalize:1 comments:1 eiλ:7 follow:1 certainly:1 inverse:1 depend:5 calculate:3 paris:1 pˆk:2 eˆ:5 pˆn:3 simplify:2 manifolds:4 under:14 stochastic:7 tyutin:1 coor:1 amplitudes:4 straightforward:1 far:1 desirable:1 construction:2 rise:1 induce:1 choice:2 every:1 eiλj:1 difference:1 condition:15 entire:1 hamiltonian:19 turns:1 solution:10 leave:1 vector:2 indices:1 gauge:34 smaller:1 ϑj:1 grateful:1 consistent:2 arnimallee:1 second:6 rigorous:2 further:1 dynamics:3 canonical:24 even:1 will:6 ˆt:1 stands:2 brackets:1 sum:2 selected:1 batalin:3 expressed:2 constrast:1 above:3 ˆg:1 new:5 ˆj:6 ˆk:5 method:4 satisfy:3 degree:1 respectively:1 component:1 equals:1 here:7 desired:1 tangent:1 represented:3 path:40 along:1 constructive:1 equations:3 appears:1 change:4 violate:2 obtained:3 remark:1 transition:3 institute:1 leaves:1 changed:3 allows:2 akj:2 aki:1 poisson:2 pick:1 action:5 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quant-ph9805015.txt |@word represent:8 code:2 partial:1 consider:6 people:1 results:1 four:10 p01:1 commute:4 computation:4 go:1 row:3 whose:5 inverse:1 alamos:3 technique:3 trivial:1 rightmost:1 program:4 those:1 th:3 applied:4 string:3 orthogonal:3 very:3 λa2:1 entries:6 matrices:33 partitions:1 exponential:1 dij:3 positions:12 deals:2 discrete:6 unrelated:1 simulates:1 3b:3 says:1 reck:1 10b:1 10c:1 10a:1 direct:5 zero:10 manipulating:2 odd:3 even:4 aba:1 what:2 adds:1 sheng:1 diag:7 sum:6 expressed:12 henceforth:2 above:2 3c:2 expresses:1 3a:2 increasing:3 bird:2 satisfy:1 margolus:1 full:1 rudimentary:2 commercial:1 equals:6 here:1 iσy:2 pub:1 groups:1 represented:6 sine:1 z0:14 z1:1 change:3 box:1 algebra:2 institute:1 vectors:1 dublin:1 p2:4 products:1 permutation:10 fourier:6 studies:1 useful:3 projection:4 replace:2 pyramid:1 names:2 apply:6 establish:1 manipulate:2 use:8 eye:2 takes:2 would:2 distinct:1 chi:1 contains:2 next:2 rao:1 few:1 call:4 therefore:1 taken:2 type:2 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quant-ph9805022.txt |@word results:1 computation:5 edu:1 query:3 environment:2 finally:1 umass:1 include:1 string:2 choice:3 solves:1 transmission:2 solution:1 fewer:1 optics:1 deutsch:6 zero:2 7th:1 machines:1 appear:1 assistance:1 supplied:1 suppose:5 method:2 full:1 answers:3 separation:1 address:2 auxiliary:1 obtained:1 increments:1 receive:2 vectors:1 funded:1 amount:1 simultaneous:1 stressed:1 useful:2 amherst:1 conventional:2 takes:1 properties:1 call:1 taken:1 25th:1 type:1 more:3 naive:1 factor:1 reversible:1 hold:1 must:4 science:2 challenge:1 work:1 halts:1 following:1 making:1 example:2 inaccessible:1 states:3 assumptions:1 exclude:2 information:12 end:1 discussion:1 holds:3 utilize:1 machine:4 how:1 answer:2 symposium:1 brassard:3 simplicity:1 product:2 may:11 turing:5 after:1 wave:1 parallel:1 natural:1 computations:1 explicit:1 yielding:1 su:2 complexity:7 so:1 ultimate:1 allow:1 berthiaume:3 differs:2 ieee:1 its:1 mod2:1 interesting:1 mail:1 return:1 evolution:1 effects:1 they:1 half:1 structural:1 easily:1 dirac:1 always:1 university:1 possibilities:2 transmitted:1 2n:1 uninteresting:1 ei:1 doing:1 idea:1 expect:1 measurement:3 quantum:42 operation:2 eq:1 special:2 out:1 shown:1 space:3 restricted:1 research:1 foundation:1 theory:5 contain:1 vazirani:1 reason:3 jozsa:4 care:1 definition:4 interaction:1 counterpart:1 consequence:1 user:1 powerful:1 oracles:3 carry:1 given:6 unitarity:1 system:2 returns:3 assumption:1 normalization:1 calculations:1 realization:1 scheme:3 national:1 gives:1 reversed:1 exactly:1 than:3 unfortunately:1 distinguishes:1 second:1 classes:4 amplitude:1 prospect:2 separations:3 modern:1 generalization:1 need:1 any:2 viewed:1 able:1 note:2 transmit:2 added:1 unless:1 machta:2 simplify:1 device:7 observation:1 later:1 proceedings:2 principle:1 mechanical:1 physics:1 specification:1 show:2 random:1 halting:1 trivial:1 only:1 equipped:2 bernstein:1 do:1 notation:1 runs:1 arxiv:1 investigate:1 queries:2 set:3 relativized:3 relative:3 computer:29 enumerates:1 interacting:1 review:1 state:5 use:2 between:6 available:3 recently:1 however:2 both:1 σn:5 many:2 annual:1 equal:1 receives:1 otherwise:3 dimensional:1 church:1 conference:1 described:2 transformations:1 basis:2 faithfully:1 much:1 ph:1 abstract:3 understand:1 external:1 angles:6 value:1 will:2 rests:1 replaced:1 unitary:2 allows:1 thus:5 defeated:1 helped:1 grant:1 φx:6 make:2 accomplished:1 same:7 quant:1 finite:2 evolve:1 undecidable:1 defeat:1 purpose:1 identity:1 nonetheless:1 solve:2 sources:1 questions:1 using:1 yes:1 rapid:1 transformed:1 transformation:2 represents:2 read:1 possible:1 world:1 bit:3 accepted:2 envisioned:1 steps:1 arbitrary:2 works:1 page:2 because:1 classical:17 provided:2 yields:1 proc:2 journal:1 fed:3 restrictive:1 hilbert:3 certainty:1 acm:1 plus:1 act:1 introduced:3 soc:2 computational:3 phase:20 appropriate:2 references:1 raises:1 determine:1 operator:1 refined:1 assumed:1 there:7 lond:2 inner:2 way:1 was:2 assumes:1 naturally:1 function:2 complete:1 form:3 but:4 encode:1 encoded:2 partially:1 jonathan:1 wish:1 devices:1 dmr:1 submitting:1 problem:1 proved:1 computing:3 defined:1 certain:1 universal:3 general:1 separating:1 single:2 physical:2 again:1 no:5 whereas:2 when:1 other:1 role:2 department:1 conclusion:1 briefly:1 superposition:5 problems:3 prepared:2 massachusetts:2 astronomy:1 structure:1 implies:1 faster:1 factors:1 notion:3 parallelism:4 time:1 oracle:38 strings:4
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quant-ph9805023.txt |@word sci:1 consider:3 rev:1 dynamic:1 results:3 eds:1 scalar:1 computation:2 c2:1 bremsstrahlung:1 flash:3 quasi:1 present:1 conjecture:1 far:2 frequencies:2 rise:1 focus:1 ultraviolet:1 refractive:31 experimentally:2 bubbles:4 difference:2 exact:1 school:1 exponential:2 did:1 louis:1 eigenmodes:1 tanh:1 t2:1 applicable:1 t0:6 viable:2 large:3 adjust:1 small:1 der:2 configurations:2 wronskian:1 edu:1 estimates:2 approximation:8 surrounding:1 zero:3 cost:1 timescales:2 value:2 qualitatively:2 dynamics:1 estimated:2 even:3 index:30 putterman:1 sum:1 brief:1 find:1 above:2 waals:2 international:2 coefficient:3 discontinuity:1 led:1 αij:1 never:1 modify:1 proc:1 here:2 behaviour:3 reported:1 sinh:3 evaluates:1 based:3 strong:1 equations:1 change:13 obtained:2 convert:1 technical:1 yablonovitch:1 changed:1 ourself:1 amount:2 suggestion:1 pick:1 studi:1 suitable:2 studies:1 plotted:3 via:2 while:1 visible:2 total:4 asymptotic:2 usa:1 sake:1 predictions:1 properties:1 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quant-ph9805024.txt |@word concept:1 partial:2 consider:13 remarkable:2 illustrates:1 duplicates:2 squared:1 forbidden:2 varying:1 results:8 four:12 commute:1 entropy:10 grateful:1 follow:1 remarkably:1 denotes:2 reasoning:1 whose:24 depend:1 aug:1 re:5 equivalence:1 tr:1 acting:1 supported:1 answered:1 finally:2 program:1 under:6 worth:1 maximum:2 p2:7 conjecture:2 global:1 amplitudes:10 rb:15 straightforward:1 far:1 rise:4 emphasizes:3 wave:9 ρb:1 every:1 application:1 difference:2 matrices:3 condition:4 partitions:3 entire:3 incoherent:1 implying:8 knight:1 solution:3 large:1 discrete:5 vector:4 elsewhere:1 indices:3 generalize:5 shows:1 noted:2 upper:8 deutsch:1 hillery:6 sign:2 fold:1 second:10 noise:1 substituting:1 incidentally:1 expressions:1 machines:22 linear:1 even:1 index:6 what:1 nonlinear:1 stands:1 giving:2 section:3 3p:2 dephasing:2 expressed:3 ˆb:3 above:2 increasing:1 acknowledgments:1 contrast:3 satisfy:2 simultaneously:8 ρab:4 respectively:6 transmitting:1 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quant-ph9805025.txt |@word represent:1 partial:1 consider:1 switched:2 caused:2 magnetic:43 varying:1 results:11 fluids:2 leads:3 facilities:1 scalar:3 commute:3 generalize:1 ǫm:5 gyration:21 expressions:1 reasoning:1 causes:1 soc:2 compact:2 looking:2 certainly:1 berry:2 depend:11 calculate:1 re:1 pˆi:1 pˆj:4 tr:5 charge:3 indicate:1 those:4 under:3 phil:1 include:1 ki2:1 case:13 expressing:1 advantage:3 very:3 springer:1 dokl:1 geometrical:2 wishes:1 summarized:2 difference:2 condition:1 dok:1 four:1 differentiated:1 gov:1 mc:3 variable:1 hamiltonian:45 bn:5 turns:3 savard:1 leave:2 convenience:1 vector:10 math:3 guiding:96 small:2 relation:4 refer:2 configurations:2 employing:3 occurrence:1 zj:2 direct:3 modified:1 approximation:7 elegant:1 second:9 alfv:1 evaluated:4 follow:2 further:4 dynamics:1 linear:2 even:5 will:15 trapping:1 brackets:5 section:7 lawrence:2 foregoing:1 expressed:4 find:5 current:1 version:2 en:1 above:3 new:10 method:7 contrast:2 temperatures:2 coefficient:5 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quant-ph9805030.txt |@word proposition:10 represent:4 concept:2 partial:1 consider:20 springer:6 funct:1 rev:11 blanchard:1 results:5 four:8 sαj:2 scalar:2 commute:2 lαβ:12 grateful:1 quantites:1 lahti:4 follow:1 expressions:3 contributions:1 localized:1 forget:1 compact:2 rd:1 certainly:1 depend:5 calculate:1 exploited:1 paris:2 spin:3 equivalence:1 canonical:1 extraneous:1 kβ:1 finally:1 tj:2 those:1 th:2 under:11 ebres:2 norm:4 brown:1 belonging:3 abelian:1 outside:2 far:1 collision:1 rise:1 translations:3 dell:1 choice:9 every:1 rm:7 jacob:1 iur:1 matrices:4 wick:1 condition:34 ıas:1 hamiltonian:4 zeit:1 irreducible:2 notes:2 list:1 solution:1 deals:3 discrete:1 vector:7 phase:1 rj:2 indices:9 drop:1 der:4 measuring:1 des:1 neighborhood:4 physikalischen:1 dealing:1 direct:7 riesz:1 zero:5 fredenhagen:1 pass:1 further:2 d4:6 substitute:1 linear:5 spectral:4 index:9 what:1 appear:6 clock:10 section:9 agrees:1 infinitesimal:2 above:6 new:7 reynaud:1 acknowledgments:1 exercise:1 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quant-ph9805031.txt |@word cµ:1 limited:1 sci:7 consider:5 remarkable:1 caused:1 dynamic:5 results:5 leads:5 rapid:1 scalar:5 comments:1 computation:2 c2:3 consists:1 primes:1 gl:1 voids:1 supposes:1 issues:1 compact:1 bassett:1 certainly:1 feeding:1 calculate:1 zone:2 graph:1 concerned:2 flash:1 wish:3 quasi:3 does:1 squeezing:1 those:3 excluded:1 under:2 observations:1 indicating:1 subtleties:1 case:14 updated:1 expressing:1 outside:2 far:4 frequencies:2 pages:1 modes:2 hard:1 keeping:4 geometrical:1 aware:1 wishes:2 ultraviolet:1 2πc2:1 messy:1 refractive:17 experimentally:2 emphasized:1 difference:3 exact:3 condition:3 school:2 exponential:1 wronskians:1 did:1 louis:1 proposals:1 solution:1 damped:1 large:12 solved:1 convenience:1 phase:1 dealt:1 small:4 eigenvalues:3 rk:13 equation:28 configurations:3 still:2 upper:2 smaller:1 eberlein:6 ten:2 dealing:1 φin:1 edu:1 estimates:1 direct:5 approximation:20 surrounding:1 zero:10 ministry:1 timescales:3 reply:1 further:1 dynamics:3 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quant-ph9805032.txt |@word monte:6 switched:1 amplifier:6 results:1 four:1 consists:1 gk:1 row:2 faridani:1 inverse:1 paris:1 tw:1 technique:3 finally:1 compensate:1 present:1 th:1 tb:1 γd:1 g2:1 advantage:1 song:1 far:1 wave:2 impinged:1 entries:1 experimentally:2 matrices:1 leads:1 annihilated:1 smithey:1 hamiltonian:2 proposals:1 try:1 solved:1 vector:1 affect:1 chuang:1 speculation:1 setup:7 bd:1 smaller:1 slower:1 pulse:6 feasibility:2 second:1 plenum:1 traveling:2 cat:1 carlo:6 even:1 index:1 what:1 errors:6 apparatus:1 sum:2 current:1 fock:5 reconstruction:16 new:2 3a:2 increasing:3 method:9 κn:1 full:1 degree:1 respectively:1 tomographically:5 here:5 diagonal:4 beck:1 amplification:1 inversion:2 relaxation:1 along:1 strong:1 obtained:4 leaves:1 vectors:2 allows:1 atom:5 gnm:5 makes:1 anticommutators:1 plotted:2 via:1 compare:1 highly:1 singlephoton:1 annihilator:2 total:3 estimate:1 use:4 takes:1 would:6 sake:1 give:1 comparing:1 depicted:1 raymer:1 theoretical:7 more:3 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quant-ph9805033.txt |@word limited:1 partial:1 consider:2 caused:5 leads:1 consists:1 follow:1 amplified:1 alamos:1 equivalence:1 tr:13 braginsky:1 quadruple:1 grabowski:1 under:1 pˆy:3 pˆx:1 translations:1 wave:2 every:3 difference:1 condition:3 nonselective:2 trk:4 hamiltonian:3 vector:5 small:1 disturbs:3 ueda:1 noted:1 consistent:1 second:2 noise:1 rigorous:1 even:1 established:1 ˆs:1 apparatus:32 ˆa:1 above:3 equivalent:4 satisfy:2 notions:1 respectively:1 selective:6 represented:2 standard:2 change:12 obtained:4 leaves:2 yˆ:5 prior:7 simultaneous:1 usually:1 makes:1 sci:1 uniquely:2 formulated:1 regardless:4 projection:6 family:8 9a:1 9c:2 9b:1 outcomes:2 apply:1 operational:8 univ:1 conventional:1 takes:1 prove:1 positive:5 nagoya:2 properties:1 comparing:1 call:2 therefore:2 taken:1 composite:4 operators:6 odinger:2 validity:1 berlin:2 controlling:2 normalized:4 particular:1 iii:2 ρa:9 kraus:1 springer:2 valued:6 equation:2 ρj:1 ρn:1 ρs:4 following:5 ρx:3 process:3 neglected:1 states:12 numbers:1 counting:1 occur:1 information:1 holds:1 xˆ:8 answer:1 parameter:1 disproves:1 map:9 may:1 after:13 collection:1 inst:1 designed:1 cambridge:2 readout:1 chikusa:1 davies:2 fundamental:1 order:4 operations:1 interpretation:1 over:1 lahti:1 paper:2 statistical:3 japan:1 satisfies:2 its:3 before:3 subensemble:1 khalili:1 detected:1 systems:1 quant:3 thereby:1 richness:1 ya:1 school:1 effects:1 they:3 now:2 represents:2 february:1 university:2 l2:4 disregard:1 found:1 characterized:1 directly:2 related:1 variety:1 measurement:30 quantum:8 out:1 shown:5 space:8 res:1 since:5 rx:1 ry:2 denotes:1 denoted:3 formula:4 gov:1 correct:1 math:4 shows:3 theory:2 free:1 quite:1 completely:4 detecting:1 publ:1 definition:1 interaction:6 derivation:3 hence:2 first:6 probability:10 number:2 another:2 given:10 adjoint:1 system:6 relations:1 assumption:1 postulate:5 gives:1 continuous:1 17b:1 17a:1 than:1 18b:1 18a:1 determines:1 preparation:2 appealing:1 determined:3 were:2 outcome:25 questionable:1 disturb:1 ann:1 turned:2 argument:1 affirmative:1 randomly:1 disjoint:1 any:28 self:1 note:1 sciences:1 k1:4 indexed:1 so:9 strengths:1 spectral:1 trace:3 shall:6 measures:5 said:1 measured:9 class:2 considered:1 partition:1 coincides:1 typeset:1 principle:2 ku:1 physics:1 fact:1 selection:1 show:1 reductions:1 lewis:2 probe:9 spaces:1 relation:1 based:1 assertion:2 should:3 only:1 rich:1 postulated:1 hamiltonians:1 mixture:1 dependent:1 da:8 joint:4 cannot:2 dx:1 dy:2 during:1 dt:2 evolution:3 conditions:2 arxiv:1 yield:1 investigate:1 controlled:1 fixed:1 view:1 apparatuses:1 strengthened:1 requirement:1 set:13 observer:2 detection:6 depends:1 result:1 disturbing:1 satisfying:1 ways:1 subsequent:1 state:61 classes:1 between:3 caves:1 approach:1 statistically:2 however:2 uψ:1 distribution:22 observable:16 realizable:2 uncertainty:2 according:3 arbitrarily:1 point:1 reasons:1 16a:1 16b:1 16c:1 dimensional:2 exploit:1 sequences:1 ogawa:1 cp:3 pr:11 sensible:1 described:2 basis:1 px:2 due:1 been:2 reduction:12 ph:3 define:1 describe:1 corresponding:1 both:1 xxx:1 photon:1 precision:1 spectrum:1 irrelevant:1 present:1 case:2 k2:4 pacs:1 transformation:2 will:3 suppose:7 couplings:1 identical:3 unitary:3 thus:4 surprisingly:1 ii:2 busch:1 suggests:1 same:8 imoto:1 potentially:2 finite:1 independent:1 http:1 upon:3 hand:2 action:1 schr:2 modeled:1 without:4 sets:2 coordinate:1 position:11 model:15 left:3 just:13 less:1 when:2 ozawa:7 using:4 alternative:2 macroscopic:1 eigenstates:1 sampled:1 preprint:2 density:4 conclude:1 mathematically:1 lett:1 easy:1 eigenstate:4 momentum:10 real:4 read:1 possible:2 press:1 immediately:1 follows:5 server:1 arbitrary:10 mathematical:1 because:1 sequence:1 conditional:3 some:2 back:1 born:1 specified:1 total:1 measurements:3 does:3 demonstrated:1 measuring:12 object:27 kyoto:1 eixp:1 revtex:1 informatics:1 hilbert:5 bz:1 stage:6 commun:1 compatible:4 rev:4 perturbing:2 references:1 determine:2 operator:5 statistics:1 there:6 los:1 borel:18 way:1 ixp:1 was:4 function:6 form:1 converse:1 but:5 posterior:8 properly:1 line:2 compute:1 up:1 problem:2 stages:1 similar:1 called:7 mechanics:1 controllability:1 later:1 proved:2 defined:1 abstract:1 measure:5 linearity:1 general:2 examine:1 formulation:1 families:1 commuting:1 check:1 nn:1 no:1 generally:1 other:2 exp:2 prepared:2 ξi:1 ξj:1 bounded:1 ξn:1 variable:4 coupling:2 assume:2 lanl:1 equivalently:1 mass:2 presenting:1 time:25
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quant-ph9805034.txt |@word limited:2 consider:5 lack:1 desirable:1 results:1 leads:3 dbj:1 consists:1 follow:1 research:1 gr:7 depend:1 violate:1 finally:2 does:3 restriction:1 those:1 under:1 worth:4 p2:1 very:5 wave:4 every:1 orientations:4 experimentally:3 emphasized:1 difference:1 school:1 immediately:2 applicable:1 discrete:1 phase:3 small:2 referred:1 optics:2 noted:2 smaller:1 ten:1 consistent:2 approximation:1 imply:1 microphysical:1 copenhagen:1 even:2 what:2 apparatus:4 sum:4 axes:2 nec:1 experiment:16 above:6 new:3 contrast:3 satisfy:2 edited:3 simultaneously:1 here:1 cos2:3 address:1 directions:1 ratio:1 along:17 standard:2 equations:1 change:1 clarify:1 larger:7 gle:1 simultaneous:2 usually:5 der:1 york:1 criticism:1 spatially:2 family:2 merwe:1 vii:1 polarizers:20 highly:1 counts:4 use:2 prove:1 probabilities:18 negative:1 next:6 noting:3 call:2 therefore:4 aperture:3 2y2:30 more:1 separated:2 becomes:4 postulated:1 emission:6 validity:2 tested:2 needed:2 particular:2 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quant-ph9805035.txt |@word r1r:4 caused:1 global:1 leads:1 partial:1 r1l:7 depend:1 pb2:1 technique:1 tr:1 tl:1 aut:1 th:1 stable:1 amplitudes:6 advantage:4 zhang:2 very:3 wave:12 difference:2 continued:1 condition:1 treating:1 four:5 prize:1 level:1 transmission:8 applicable:1 t1:3 discrete:2 minimal:1 small:3 challenge:1 miller:2 second:6 enclosed:1 equal:4 further:1 dynamics:1 chem:7 expressions:1 even:3 transfer:1 errors:3 wavenumbers:3 t2l:3 sum:4 selected:7 reminiscent:1 goes:1 new:7 method:8 satisfy:1 respectively:3 l1:2 here:1 desired:1 free:1 alone:1 equations:2 appears:1 change:1 box:1 solid:7 parameters:4 studied:2 allows:1 products:1 changes:1 problematic:1 translational:1 total:5 manipulate:1 readily:1 use:2 baer:1 levine:1 probabilities:2 positive:1 kα:1 next:2 few:1 approach:2 theoretical:1 more:5 kˆ:1 composite:9 becomes:1 odinger:2 particular:3 cases:3 balakrishnan:1 ıas:2 equation:2 work:2 values:4 example:1 figure:6 chosen:2 purposes:3 collision:2 numbers:1 allowed:1 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quant-ph9805036.txt |@word supersymmetrical:2 sci:2 consider:7 duplicates:1 forbidden:1 moutard:2 leads:1 scalar:8 higher:1 go:2 expressions:3 factorizing:1 inverse:1 paris:1 finally:1 petersburg:1 th:3 equalities:1 applied:1 springer:1 wave:7 every:2 difference:2 exact:1 condition:2 four:1 beginning:1 hamiltonian:14 did:1 solution:3 discrete:6 bq1:2 indices:3 deleting:2 degeneracy:1 sign:1 tex:1 second:1 iσ2:1 odd:1 spectral:3 established:1 appear:1 diag:8 sum:1 reply:1 principal:1 method:1 contrast:1 satisfy:7 simultaneously:2 respectively:2 diagonal:1 met:1 cylindrical:2 hkl:2 address:1 directions:1 consideration:1 equations:1 obtained:1 technical:2 study:1 studied:1 resulting:1 permutation:1 exited:2 rϕ:1 via:1 coinciding:3 decrease:1 use:1 eψ:1 would:2 prove:2 remains:1 positive:3 next:1 therefore:4 ψm:4 taken:1 theoretical:1 more:1 relay:1 solitons:1 operators:16 odinger:2 validity:2 borisov:2 berlin:1 known:2 fermionic:1 account:1 integrating:1 ml:1 equation:9 work:2 ρm:6 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