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quant-ph9804023.txt |@word consider:2 chain:3 similarity:1 rev:7 brownian:2 results:1 four:1 entropy:23 edu:1 consists:1 localized:4 whose:2 dimensionality:1 albrecht:2 alamos:1 tr:1 environment:12 permanently:1 xxiv:1 hill:1 overlaps:1 case:8 amplitudes:3 distorting:1 straightforward:1 orthogonal:1 translations:1 wave:7 electron:1 cellular:1 mixing:1 difference:1 exact:3 condition:4 paz:1 preuss:1 leads:1 hamiltonian:1 die:1 t2:5 t1:5 vector:1 small:2 der:1 jeff:1 context:1 smaller:2 slower:1 stochastically:2 direct:1 go:1 rate:1 even:1 what:1 apparatus:1 sun:1 sum:2 while:6 causes:1 goes:1 new:1 increasing:3 consisting:1 contrast:1 evolving:1 degree:1 respectively:2 component:1 here:2 separation:1 eikx:4 represented:1 path:9 along:1 reversals:1 institute:1 studied:2 periodic:1 resulting:1 omar:2 usually:1 proportionality:1 automaton:1 spacetime:1 writes:1 plotted:2 via:1 projection:2 figure:15 apr:1 unitary:1 decrease:4 plot:1 superpositions:2 would:3 remains:1 positive:11 negative:9 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quant-ph9804024.txt |@word represent:1 monte:3 partial:32 consider:11 secondly:1 skip:1 resist:1 results:18 leads:4 scalar:4 entropy:6 lewenstein:2 compatibility:1 go:1 follow:1 expressions:2 denotes:4 localized:1 row:1 compact:3 λij:1 requested:1 maximally:4 depend:1 calculate:2 illustrates:1 tr:16 acting:6 finally:4 monotonically:2 present:2 under:6 eprint:2 maryland:1 include:1 worth:1 norm:7 case:10 conjecture:3 supported:1 straightforward:6 without:2 far:3 dλ1:3 account:1 induce:1 vertex:1 corollary:3 crosses:1 putting:1 summarized:2 matrices:16 condition:20 induced:1 immediately:3 presented:3 tra:1 knight:2 t2:21 t1:1 deals:1 vector:6 cee:1 minimal:3 science:1 small:3 eigenvalues:14 c02:1 vincenzo:2 upper:17 strongly:2 smaller:2 says:1 zi:11 haar:3 summarizing:1 estimates:2 measurable:1 approximation:2 located:1 likely:1 displays:1 rigorous:5 further:2 estimated:4 carlo:3 situated:1 nauki:1 goes:1 spectral:3 established:1 what:3 3x:2 appear:2 section:20 expressed:1 uniform:13 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quant-ph9804028.txt |@word limited:1 sci:1 consider:3 induces:1 magnetic:1 particular:1 results:9 leads:1 ga:1 research:2 cases:5 causes:3 scr:1 whose:1 terms:2 system:9 equivalence:1 those:2 under:1 kλ:1 analogous:1 must:2 crest:1 case:20 adiabatic:1 very:3 frequencies:5 focus:1 electron:1 dispersions:1 experimentally:1 emphasized:1 exact:1 condition:2 quantitatively:1 hamiltonian:5 turns:1 solution:2 large:3 discrete:1 vector:5 quick:1 relation:2 optics:3 attracting:1 upper:3 oscillation:3 foundation:1 pulse:1 past:1 second:2 further:2 canonical:1 even:2 what:1 nonlinear:2 bλ1:2 bλ2:2 section:2 agrees:1 fock:2 ner:1 movement:1 coefficient:1 condensed:5 newyork:1 respectively:7 never:1 component:1 lem:2 here:3 sinh:2 represented:1 depend:1 strong:5 equations:7 change:3 obtained:2 ref:3 institute:1 involved:1 study:1 studied:2 natures:1 usually:3 changes:3 plotted:2 composed:1 discontinuous:3 modulated:1 decrease:1 apply:1 total:1 derivatives:2 conventional:1 takes:3 would:2 jpn:1 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quant-ph9804029.txt |@word concept:2 consider:1 chain:1 caused:1 varying:1 results:5 cheung:1 causes:1 devoted:1 whose:1 essentials:1 nuss:2 charge:2 cne:1 preserved:1 under:3 include:1 cm2:1 case:5 straightforward:1 zhang:1 frequencies:4 induce:4 focus:2 electron:4 refractive:2 difference:1 nor:1 condition:1 hamiltonian:1 transmission:1 applicable:1 large:8 solved:1 rj:2 small:1 chuang:1 drop:1 attracting:1 measuring:1 findings:1 miller:2 pulse:23 second:1 further:1 dynamics:1 estimated:1 kitagawa:2 theory:2 even:1 index:2 what:5 nonlinear:6 appear:1 complexities:1 section:2 supplied:4 thickness:2 current:4 above:1 supplier:3 new:1 net:3 increasing:1 contrast:2 coefficient:2 edited:2 lee:1 ibid:3 respectively:1 modify:3 here:7 understanding:1 mev:1 capacitor:7 address:1 directions:1 consideration:1 κw:1 change:3 obtained:2 almost:1 institute:1 shift:28 larger:2 approaches:2 hiroshima:2 narrow:1 changes:1 via:2 see:1 modulates:1 extra:17 apr:1 semiconductors:1 marked:1 apply:1 total:4 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quant-ph9804030.txt |@word limited:2 footing:1 arrives:1 consider:6 pointing:1 represent:3 eaires:1 global:1 splitting:3 integration:14 leads:1 scalar:1 consists:3 spaced:1 expressions:1 contributions:1 weakly:1 localized:5 devoted:2 whose:1 inverse:1 reformulate:1 illustrates:2 recurrence:1 finally:2 preserved:2 ti:23 analogous:1 include:1 worth:1 norm:1 applied:3 amplitudes:1 straightforward:3 zhang:1 far:2 curves:9 wave:36 summarized:1 tridiagonal:1 difference:6 exact:9 condition:11 presented:2 transmission:1 turns:1 solution:35 t0:41 discrete:17 small:7 inspection:1 lines:2 inserting:1 des:2 neighborhood:1 specially:1 nullity:1 dealing:1 pulse:1 centrifugal:1 past:1 second:4 cost:1 plenum:1 evaluated:3 equal:2 dynamics:6 implemented:1 odd:1 goes:1 even:1 wyatt:3 what:1 rate:1 sum:7 consequent:1 current:1 mv:1 above:4 new:1 increasing:1 method:8 satisfy:1 outgoing:9 wavefunctions:1 respectively:4 component:1 desired:1 dimensionality:1 possibility:2 eiky:1 eikx:1 directions:2 re:1 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quant-ph9804031.txt |@word partial:2 consider:3 helstrom:1 results:4 four:1 entropy:3 consists:1 follow:1 δji:1 whose:2 dimensionality:1 const:3 segments:1 finally:4 investigation:1 th:4 worth:1 eliminate:1 p2:1 conjecture:1 straightforward:1 orthogonal:12 choice:2 matrices:6 condition:2 entire:1 school:1 level:1 transmission:2 turns:1 solution:5 large:2 subdeterminants:1 vector:8 recall:2 small:1 eigenvalues:4 disciplines:1 second:2 design:1 further:2 pmi:1 pmj:2 linear:1 even:3 aim:3 what:1 errors:1 stands:1 section:2 axes:1 jaeger:1 cryptographers:1 above:3 dieks:1 new:1 method:1 exercise:1 satisfy:1 respectively:1 never:1 here:1 diagonal:2 highly:1 tangent:1 address:2 represented:1 quite:1 observing:2 obtained:5 dividing:1 institute:1 larger:3 drt:1 prior:3 amount:1 resulting:3 usually:1 york:1 projection:1 family:1 apr:1 explained:1 convexity:2 outcomes:4 decrease:2 planes:3 unit:1 readily:1 use:3 lose:1 probabilities:7 positive:8 negative:3 next:1 chapt:1 therefore:3 taken:1 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quant-ph9804032.txt |@word represent:1 sci:1 consider:7 chain:14 desirable:1 leads:1 proposition:2 spiridonov:1 expressions:2 inverse:3 const:1 analytic:1 paris:2 technique:3 tn:5 th:1 dressing:2 vladislav:1 worth:1 applied:1 erale:1 springer:3 dokl:1 wave:2 corollary:1 every:4 difference:4 condition:1 illustrated:1 hamiltonian:8 ref:1 solution:21 t0:9 t1:4 discrete:17 anal:1 noted:1 application:2 wronskian:6 sturm:2 direct:2 cosh:7 second:6 arizona:1 dedonder:1 odd:7 linear:3 spectral:9 established:2 stands:2 sum:1 calcul:1 expressed:2 current:1 poles:1 sur:1 above:2 new:8 method:2 coefficient:1 full:5 notions:1 fiz:7 respectively:1 equals:1 here:2 les:1 sinh:3 concluding:1 along:1 marchenko:2 equations:5 εn:7 logarithmic:1 obtained:5 quart:1 remark:5 institute:1 study:2 studied:4 completely:2 resulting:3 usually:2 opinion:1 appropriately:1 formulated:1 f1:2 apr:1 jap:1 summation:1 apply:2 des:1 linearly:4 readily:2 eψ:1 prove:1 sake:1 give:6 call:2 therefore:1 usp:1 taken:1 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quant-ph9804033.txt |@word measurements:6 customary:1 consider:3 results:4 leads:2 eds:1 ge:1 commute:1 entropy:1 overlap:10 expressions:5 compact:1 inverse:1 depend:1 superpositions:1 passage:5 γk:4 finally:1 under:3 γb:8 γa:7 tc:1 sent:2 amplitudes:1 broadly:1 orthogonal:1 far:1 frequencies:1 maali:1 trough:1 resonant:3 emphasized:1 matrices:4 condition:1 level:4 suffices:1 solution:2 damped:1 large:1 solved:1 small:8 eigenvalues:19 optics:1 equation:5 hindered:1 ueg:5 sin2:1 direct:1 sign:1 approximation:2 zero:3 cost:1 dynamics:5 bilinear:1 what:2 nonlinear:1 stands:1 apparatus:3 giving:1 sum:2 dephasing:1 expressed:3 experiment:4 above:5 consisting:2 full:1 simultaneously:3 respectively:4 never:1 here:3 atoms:6 reported:4 ramsey:1 possibility:1 represented:1 ratio:1 equations:2 appears:1 change:2 obtained:3 instituto:1 davidovich:2 involved:4 study:1 allows:2 leaving:1 resulting:3 usually:1 resonance:1 implement:1 studies:1 involves:3 apr:1 namely:1 vii:1 plenum:1 private:1 γt:2 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quant-ph9804035.txt |@word replacing:1 vorticity:9 consider:3 rev:6 results:1 illustrated:1 ginzburg:3 follow:1 gl:1 2n1:3 optical:1 compact:1 increase:2 terms:3 zone:1 alamos:2 deterministic:1 tr:1 ts:3 anglin:2 γk:4 quasi:1 does:5 contours:2 stable:2 analogous:1 eβ:5 tc:7 case:3 supported:2 straightforward:1 orthogonal:1 far:4 rise:1 multi:1 wave:4 axes:2 specific:1 gov:1 obvious:2 solves:1 level:3 did:1 turns:1 tanh:2 integrated:1 large:2 solved:1 annihilates:1 small:3 equation:13 configurations:1 strongly:2 smaller:2 slower:2 disordered:2 estimates:2 prediction:2 past:1 surrounding:1 second:3 enhancement:2 pass:1 further:1 theories:1 linear:5 even:5 established:1 what:2 nonlinear:1 appear:1 rate:1 giving:1 evaporative:2 while:3 agrees:1 current:1 above:5 new:2 net:2 ˆk:1 respectively:1 spacing:2 here:1 atoms:2 ansatz:1 quenches:6 relaxation:1 along:1 strong:2 appears:2 change:1 obtained:1 γn1:1 leaves:1 larger:2 allows:1 completely:1 suggests:1 resulting:1 formation:1 fourier:2 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quant-ph9804036.txt |@word concept:1 partial:2 consider:1 schatten:5 entropy:33 computation:1 ohya:8 tr:1 tk:1 stochastic:1 norm:1 applied:4 provides:1 wave:1 every:1 resonant:1 exact:1 level:7 proc:1 solution:1 eigenvalues:1 markov:1 optics:2 upper:3 oscillation:1 sin2:1 kodai:1 approximation:1 dynamics:4 what:1 appear:1 expressed:1 above:3 sup:2 new:1 method:1 degree:1 respectively:1 teleportation:1 cos2:1 represented:1 change:7 rigorously:2 study:2 studied:3 reason:1 eberly:2 published:1 plotted:1 uniquely:1 useful:1 projection:1 apr:1 decrease:2 apply:4 use:1 contains:1 cho:1 therefore:5 associated:1 nondegenerated:1 brings:1 operators:1 excellent:2 known:2 hold:1 springer:2 tokyo:2 science:2 equation:3 reviews:1 obvious:1 following:6 trans:1 example:3 give:1 process:2 numbers:1 narozhny:1 verlag:2 information:9 provide:1 means:1 how:2 nontrivial:1 acta:1 parameter:1 description:1 may:1 after:2 derived:1 mapping:4 faculty:1 lifting:5 attempt:1 dynamical:2 computations:1 sr:3 shore:1 so:2 sn:3 correlation:2 sa:6 sf:3 holds:2 eigen:1 reservoir:1 constituents:1 over:1 insight:1 paper:1 through:2 statistical:3 japan:3 yamaguchi:2 jaynes:5 its:2 derive:1 interesting:1 expectations:1 decreases:1 systems:4 rabi:2 image:1 non:3 widely:1 processes:2 investigated:1 often:2 walls:1 compound:5 now:2 eigenvalue:1 february:1 fully:2 university:3 hamiltonian:4 accardi:2 transmitted:2 mode:1 each:2 2n:2 mean:1 em:1 arxiv:1 ei:1 ek:14 ej:1 operator:7 frequency:1 quantum:48 our:2 event:1 shown:1 rep:3 since:4 rev:2 reader:1 ri:1 math:2 theory:5 approaches:1 e1:5 e0:5 milburn:1 definition:1 interaction:6 transition:2 sanchez:1 yamazaki:1 probability:6 number:1 channels:2 another:1 knight:1 open:6 city:2 given:6 revival:1 inoue:1 system:19 master:1 final:9 gives:1 urbanik:1 continuous:3 formulate:1 representing:1 relative:1 ktr:1 annihilation:1 ss:9 determined:1 contrary:1 enables:1 treated:1 kossakowski:1 manner:1 seen:3 note:1 sciences:3 take:3 hs:3 davies:1 degenerated:2 channel:11 trace:2 mondragon:1 most:1 cummings:5 letter:2 revivals:1 why:1 especially:2 considered:2 physica:1 order:3 points:1 exp:7 mechanical:13 quantity:1 rotating:1 relation:2 decompositions:1 trivial:1 find:1 based:1 ith:1 irreversible:4 state:34 only:1 local:1 equilibrium:3 goes:1 get:1 dependent:1 between:6 joint:3 gea:2 ones:1 expresses:1 evolution:2 differential:1 investigate:1 stead:1 view:1 set:1 computed:3 maximum:1 observed:3 see:1 result:1 sem:1 forthcoming:1 interacting:2 ieee:2 written:2 various:2 correctly:1 simplest:1 approach:1 petz:1 publishers:1 however:2 banacloche:2 many:2 taking:1 σe:9 σz:2 connection:1 whole:1 among:1 cn:3 point:1 simple:1 dimensional:1 pol:1 respect:1 hω0:1 described:1 transformations:1 been:5 springerverlag:1 reduction:1 describes:3 combined:1 interest:1 ph:1 fig:3 θl:1 photon:3 coherent:1 spin:2 case:1 pacs:1 engineering:1 will:1 optimization:1 suppose:5 behavior:2 ku:1 unitary:2 von:4 itself:1 different:1 quant:1 pauli:1 φi:2 φj:10 several:1 development:1 used:1 effect:1 purpose:1 entanglement:1 identity:1 lower:3 expression:2 well:1 academic:2 model:6 arising:1 researchers:1 composed:1 onoda:1 being:2 generally:1 obtain:3 atomic:1 λk:7 λn:1 chiba:3 kluwer:1 density:1 photons:1 conclude:1 mathematically:1 lett:2 gave:1 represents:1 decomposed:1 inversion:1 department:2 mathematics:1 press:1 using:3 unique:1 mod:1 loss:1 like:1 follows:7 completely:1 reduced:2 mathematical:1 methods:1 classical:4 creation:1 phenomena:1 ideals:1 moreover:4 describing:2 electromagnetic:1 does:1 decomposition:5 expressing:2 chains:1 refer:1 problems:1 journal:1 about:1 carried:1 concretely:1 introduced:1 communication:3 h0:3 h1:3 en:3 elementary:1 neumann:3 log:7 h01:8 initial:12 much:1 analyze:1 was:4 treat:3 function:1 irreversibility:1 form:2 hr:4 some:3 but:2 atom:19 dissipative:2 collapses:1 compute:2 evident:1 ut:13 ωt:2 us:2 limit:1 problem:5 called:4 mechanics:3 constant:2 defined:6 certain:2 general:1 single:2 exist:1 inf:1 explains:1 identities:1 physical:3 yoo:1 mutual:29 dressed:1 when:1 detail:1 field:3 details:1 becomes:1 hove:1 jcm:14 electrodynamical:1 noda:1 superposition:2 uniformly:1 includes:1 important:2 suited:1 coupling:2 pseudo:1 time:11
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quant-ph9804037.txt |@word since:1 consider:1 rev:3 results:1 leads:1 roy:3 computation:1 2r2:2 replacements:2 depend:1 arthurs:2 technique:1 finally:1 does:3 infinitesimally:2 th:3 te:1 p2:8 choice:1 summarized:1 trouble:1 exact:1 school:1 hamiltonian:39 t2:12 t0:8 t1:11 math:2 small:4 shows:1 noted:1 rθ:4 q1i:1 zero:1 further:1 canonical:8 even:1 will:4 iterating:1 giving:1 dr0:4 section:1 selected:1 consistently:1 goes:1 new:2 net:1 method:3 contrast:1 satisfy:1 full:1 respectively:1 modify:2 here:1 desired:1 path:39 along:3 appears:1 rr0:1 obtained:3 studied:1 allows:1 reports:1 drk:1 drj:2 resulting:2 erj:3 action:2 midway:1 useful:1 apr:1 integrations:6 propagators:1 select:1 use:2 working:1 positive:1 next:3 nucl:1 therefore:1 taken:1 more:1 becomes:5 operators:2 odinger:13 known:2 must:1 account:1 βr:3 permits:1 recall:2 equation:16 det:5 modified:2 values:1 following:1 arrive:4 example:1 def:2 dn:2 f2:1 give:3 calculation:1 india:2 sharan:3 βr0:5 needs:2 end:1 hoc:3 feature:2 write:1 necessary:1 answer:1 revs:1 product:1 replacing:1 earlier:2 respective:1 plane:5 summarize:1 wave:1 realized:1 short:11 natural:2 dσk:1 dββ:3 explicit:1 summing:1 sj:7 so:1 representation:3 order:3 xk:9 over:3 soon:1 paper:2 london:3 mentioned:1 satisfies:3 still:1 its:1 pj2:3 derive:1 chosen:1 coordinates:24 actually:1 distinguishing:1 degrees:2 systems:1 non:2 thereby:1 introduce:2 scaling:11 framework:1 transparent:1 2t:1 easily:2 term:3 finite:3 2r:1 2s:1 university:1 each:2 2m:26 2n:21 side:1 2k:18 schemes:2 energy:1 idea:3 measure:1 quantum:2 our:2 eq:6 er:1 kapoor:5 rp:1 factors:2 pk2:2 dewitt:4 lagrangian:7 may:1 denoted:2 rn:8 evaluation:1 correct:11 rj:24 rk:15 after:2 free:7 pur:1 definition:3 r0:39 r1:7 r2:5 route:1 omit:1 times:3 isj:1 first:7 hyderabad:2 already:1 variables:4 number:1 done:4 illustrate:1 given:7 cartesian:3 similarly:1 introduction:1 needed:1 too:2 scheme:18 final:2 gives:3 q0j:1 exactly:1 jamia:2 part:1 because:1 than:2 second:1 gij:2 stp:2 topics:1 generalization:2 dθ0:4 conjugate:2 need:1 seen:2 any:5 built:1 lim:6 note:3 potential:3 take:3 mit:1 2mr2:1 added:1 shall:5 who:1 most:1 propagate:1 dθj:2 calculated:1 coincides:1 feynman:1 points:1 exp:19 mechanical:2 rθ0:1 physics:2 fact:2 joining:1 marinov:1 show:2 purely:1 trivial:1 find:1 q1:11 q0:13 q2:11 just:1 dp0:12 b110:1 iet:2 should:1 failed:1 only:5 generators:3 factor:1 integrable:1 local:4 hope:1 2mr:2 do:2 legendre:1 above:5 get:2 de:2 overall:1 propagated:1 dp:4 evolution:3 qt:8 arxiv:1 inomata:4 contain:1 qk:2 qj:4 dpj:4 view:1 set:6 computed:3 unpublished:2 see:1 sec:2 result:1 fail:1 close:1 kinetic:1 incorporating:3 between:1 invariant:1 boundary:1 available:1 terms:10 however:3 p2j:3 suppressed:1 suggested:2 σj:3 last:1 σn:1 resides:1 many:1 equal:2 quantization:16 expression:3 lagrangians:1 d30:1 writing:1 described:1 addition:3 trajectory:3 been:3 mark:1 expected:1 pk:2 ph:1 pi:1 fk:3 define:4 θj:15 θk:4 corresponding:3 sufficient:2 6r:2 general:1 θt:1 case:2 exponential:1 laplace:1 expanded:1 employ:1 replaced:1 procedure:1 thus:3 ij:5 2rn:1 k0:2 different:1 dβ:2 make:1 same:1 quant:1 arguments:2 pauli:3 several:1 used:1 trajectories:2 hand:1 uses:1 purpose:1 potentials:1 normalization:1 slicing:1 schr:13 mention:1 well:1 without:2 fk2:1 dimension:1 87a:1 r02:3 proposed:1 being:2 obtain:3 transforms:1 immediately:1 momenta:6 yet:1 generator:1 had:1 except:1 bench:1 add:2 interested:2 lett:2 solvable:1 transformation:1 momentum:1 dqk:2 real:1 delhi:1 possible:2 grid:1 press:1 using:3 sakita:1 mod:1 appearing:1 particle:10 identifying:2 follows:2 velocities:1 renamed:1 steps:2 integrals:2 arbitrary:6 beltrami:1 right:2 methods:2 classical:14 nagar:1 pτ:8 dimensions:5 lead:1 kr0:1 integration:4 pankaj:3 proc:3 demonstrated:2 q2i:1 pose:1 step:3 found:1 relating:1 stage:1 deriving:1 carried:1 getting:1 freedom:2 dependence:1 o:7 practical:1 carries:1 mixed:1 dθk:1 soc:3 cambridge:1 h2:10 into:1 within:1 integral:34 appropriate:1 square:1 references:1 operator:5 hep:2 strictly:1 quadratic:1 way:1 was:7 propagator:23 function:5 form:1 but:3 hj:7 pj:19 construction:1 ho:1 delta:1 true:1 absent:1 compute:1 2πi:1 inside:1 2πm:1 up:6 us:5 placed:1 below:1 limit:2 problem:1 called:1 detailed:1 interval:1 ad:3 defined:4 abstract:1 describe:1 denote:1 pˆ:2 formulation:1 θn:4 formalism:2 commuting:1 functions:4 edwards:2 when:1 field:1 other:2 papers:1 department:1 out:1 polar:8 briefly:1 kt:7 problems:2 shown:1 helping:1 qσ:1 important:2 tackle:1 generalized:1 gets:1 d29:1 required:2 pseudo:4 dσ:1 time:22 starting:1 original:1
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quant-ph9804038.txt |@word limited:2 logarithms:1 jason:1 consider:4 represent:6 caused:1 particular:1 results:11 four:4 computation:17 edu:1 consists:1 causes:2 whose:1 calculate:2 graph:1 concerned:1 factoring:15 environment:1 behave:2 under:1 include:2 norm:1 supported:1 string:2 very:5 implicitly:1 amplifies:1 sons:1 putting:1 matrices:1 entire:2 solves:1 level:4 evaluation:1 notes:1 applicable:1 correct:4 discrete:1 vector:7 small:3 optics:1 round:2 upper:2 focs:1 occurrence:1 deutsch:1 renormalized:1 pulse:6 l3:1 jump:1 go:1 rate:26 evaluated:1 further:1 implemented:3 theory:1 even:5 index:2 errors:76 apparatus:1 sum:1 selected:1 brief:1 expressed:1 current:2 version:1 above:1 new:4 method:5 simultaneously:2 relates:1 never:1 here:1 represented:1 november:2 principle:1 observing:1 mult:3 search:10 drops:1 institute:1 shift:2 study:2 larger:2 amount:8 knill:1 implement:3 studies:6 cancellation:4 sat:1 extra:1 apr:1 engineering:1 decrease:1 inverses:1 total:1 establish:1 unit:3 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quant-ph9804039.txt |@word limited:1 logarithms:1 code:2 jason:1 represent:12 scratch:1 dynamic:9 results:5 four:8 computation:16 foundations:2 consists:9 causes:3 soc:1 whose:2 fits:1 calculate:10 iii:1 tt:3 exponentiation:2 factoring:18 environment:1 swap:1 include:6 tb:3 dramatically:1 resources:4 allocate:7 division:2 amplitudes:3 advantage:3 very:7 could:1 later:3 mpi:3 putting:2 affect:1 difference:2 matrices:3 vast:1 severely:1 redistribute:3 level:17 positions:1 applicable:1 fewer:2 large:4 discrete:1 vector:30 small:2 accumulation:4 still:1 smaller:3 occurrence:1 f21:15 grover:1 feasibility:4 zero:13 mega:2 picked:1 replicated:1 dynamics:1 implemented:2 machines:1 theory:2 even:3 employ:2 errors:11 adds:1 trapping:1 apparatus:1 clock:1 giving:1 section:9 selected:1 brief:1 3t:2 current:4 sequential:2 redistributes:2 3n:2 3m:4 new:7 increasing:4 public:4 contrast:1 full:1 simultaneously:4 submitted:1 degree:2 respectively:1 gathered:1 realizations:1 lange:2 hours:1 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quant-ph9804040.txt |@word represent:1 concept:4 semantic:8 consider:11 springer:1 rev:1 magnetic:1 results:6 monti:2 chaos:2 leads:1 eds:2 proposition:9 consists:1 follow:1 expressions:3 reasoning:1 issues:1 raven:1 devoted:1 whose:1 amplification:1 paris:1 concerned:1 yngvason:1 languages:7 uniqueness:1 behave:3 those:5 under:3 analogous:1 circumstances:1 worth:6 horgan:1 interacting:1 already:5 straightforward:1 far:1 implicitly:2 rise:2 emphasizes:1 geometrical:1 electron:7 wishes:1 every:6 decide:1 lecture:2 affect:1 emphasized:2 difference:6 continued:1 collett:2 condition:3 common:1 entire:1 randomness:1 presented:1 positions:1 list:7 solved:3 settle:2 phase:1 science:5 small:4 study:1 path:3 unsharp:1 noted:3 prevent:2 strongly:1 says:3 miller:1 consistent:5 komar:2 direct:4 sign:1 approximation:1 second:4 link:3 further:3 copenhagen:1 obstacle:1 avoiding:2 even:11 employ:1 what:17 appear:2 section:1 expressed:1 find:9 current:1 birkhoff:2 tarski:8 experiment:13 paradoxes:2 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quant-ph9804041.txt |@word operations:2 consider:2 rev:2 over:3 results:1 uℓ:3 converge:1 leads:2 paper:1 existence:1 satisfies:1 whose:1 now:2 cm:1 dr:1 cavalcanti:3 nacional:1 ıa:4 potential:1 aut:1 th:2 factor:1 derivative:1 do:2 his:1 closed:1 survival:1 de:2 evolution:1 corresponds:1 resonant:5 using:1 postal:1 exact:2 moshinsky:3 prime:1 term:3 approach:1 arxiv:1 expansions:3 solution:1 yields:2 arbitrary:1 cℓ:4 concluded:1 because:1 dealing:1 kℓ:10 see:1 result:1 substituting:1 our:3 beyond:1 eq:9 stands:1 lead:2 sum:2 squared:1 integration:3 state:1 does:1 above:2 reply:1 boundary:2 conditions:2 shows:2 coefficient:1 multiplied:1 terms:1 uniformly:1 ısica:1 expansion:2 vanishing:2 calder:4 onoma:1 equations:1 ikn:1 definition:1 instituto:1 ref:1 similar:1 taking:1 allows:2 according:1 times:1 resulting:1 obeys:1 universidad:1 opinion:1 consequently:1 first:1 comment:2 cn:4 probability:2 follows:1 apr:1 into:1 integral:2 garc:4 inverse:1 should:1 interchange:3 given:1 asymptotic:1 probabilities:1 leading:3 eqs:1 long:7 nucl:1 ph:1 lett:2 function:3 form:1 odinger:1 repect:1 case:1 inl:1 integrating:1 equation:1 mateos:3 um:1 below:1 un:14 limit:6 following:1 powers:1 precede:1 procedure:1 peierls:1 defined:1 ann:1 concludes:1 argument:1 proven:1 states:1 reads:1 km:1 apartado:1 ikℓ:1 functions:1 perform:1 proportional:1 vanishes:2 same:1 write:2 complex:2 quant:1 take:1 instead:1 kn2:3 preceding:1 derived:1 different:1 substract:1 multiply:1 exico:3 schr:1 expression:4 spectra:1 kn:8 rule:2 provide:1 so:1 time:7 order:1 wavenumber:1
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quant-ph9804042.txt |@word stegun:1 2c:1 obtain:3 years:1 uzbekistan:1 x2:2 ge:1 paper:1 farther:1 jetp:1 spheroidal:4 λk:2 substituting:1 find:3 inverse:1 number:2 knowledge:1 sciences:1 ln:2 concerned:1 solving:2 coordinates:2 sδ:1 recurrence:2 h2:11 only:1 other:1 systems:3 extensive:1 into:6 take:1 2t:3 r12:1 nat:1 get:2 washington:1 rise:1 conditions:2 bound:1 sω:1 inserting:1 insert:1 press:1 using:1 now:2 yu:4 condition:3 aξ:1 treating:1 leads:1 term:2 φk:1 2p:1 2r:1 particle:1 follows:2 university:1 arxiv:1 expansions:4 solution:6 2z:2 oppenheimer:1 large:3 solved:1 2z0:2 analytical:1 eigenvalues:4 2n:1 reduced:2 system:1 heavy:4 hλ:1 requirement:1 differential:1 leningrad:1 zk:1 2x:1 energy:8 hypergeometric:1 related:1 2y:1 approximation:1 born:1 namely:1 us:2 quantum:3 our:1 eq:7 2e0:3 subject:1 2h4:1 mukherjee:1 richard:1 2e:2 ponomarev:1 quarks:2 sanyal:1 expressed:1 mesons:2 particles:1 e12:1 written:2 investigation:1 various:1 hill:1 boundary:3 approach:1 method:5 body:1 confluent:1 terms:2 theory:1 rep:2 multipole:1 flavoured:1 2h3:1 2h2:1 however:1 expansion:6 quark:2 2kz:1 separation:3 substitution:3 t2:2 8e:1 equations:6 z1:3 z2:2 e2:3 obtained:3 asymptotical:7 r1:5 r2:12 mcgraw:1 taking:1 o:4 quantization:1 motion:1 plus:7 stand:1 usually:1 connected:1 estimation:1 expression:2 whittaker:1 numerical:1 separable:1 mathematical:1 βln:1 useful:1 2kβ:1 nonrelativistic:2 apr:1 morii:1 variables:1 waves:1 moscow:1 harmonic:5 h4:7 coincidence:1 dimensional:1 1e0:1 antiquark:1 gluon:1 another:1 nag:1 should:1 angular:2 equating:1 schrodinger:1 given:1 quasi:2 described:1 eψ:1 start:1 z0:4 eqs:1 there:1 three:1 approximately:1 substitutions:1 few:1 describes:1 handbook:1 asymptotics:3 interest:2 m2:10 ph:1 molecular:2 type:1 prolate:2 pl:1 2zr:3 function:1 r4:3 e0:5 calculations:1 form:10 bur:1 academy:1 becoming:1 odinger:12 modelling:1 heat:1 confinement:2 known:1 last:1 6z:1 considerable:2 cosθ:1 applied:1 distance:1 account:1 applying:1 co:1 pacs:1 pn:1 equation:24 equs:1 oscillator:5 zero:1 mk:2 will:2 following:7 problem:1 gives:1 powers:1 2kω:1 komarov:3 references:1 give:2 defined:1 well:1 abstract:1 radial:1 thus:1 states:1 properties:1 numbers:1 want:1 arise:1 need:1 coeficients:1 seek:2 r22:1 functions:10 tashkent:1 derived:1 nauka:1 erdelyi:1 note:1 field:2 potential:10 quant:1 details:1 widely:1 baryon:1 department:1 solve:1 ordinary:1 canonical:1 4s2:2 4z:1 higher:1 formulas:1 qqg:1 used:1 book:1 sαγ:1 abramowitz:1 after:4 problems:1 containing:1 hand:1 hence:1 regular:1 qqq:2 allowing:1 comparing:1 potentials:1 pair:1 baryons:2 wave:6 constants:1 e1:4 sy:1 morishita:1 schr:12 center:10 coulomb:10 4y:1 light:2 spectra:1 separations:1 st:1 4n:1 16k:2 points:1 so:1 kz:1 region:1 physics:3 order:2 choose:1
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quant-ph9804045.txt |@word limited:1 partial:12 consider:5 chain:1 similarity:1 results:5 four:1 entropy:1 montr:1 computation:1 shimony:1 research:1 violate:5 finally:2 th:1 under:4 presentation:1 applied:1 conjecture:2 supported:1 straightforward:2 orthogonal:3 sons:1 surprise:1 matrices:2 condition:2 entire:1 kaszlikowski:1 presented:6 did:1 fragile:8 list:1 large:1 vector:2 science:2 eigenvalues:2 upper:1 smaller:2 fragility:5 b22:1 second:5 zz:1 concludes:1 greenberger:1 odd:3 theory:2 even:3 index:2 sub:2 indep:2 section:8 brief:2 expressed:2 version:1 3n:1 above:7 consisting:1 satisfy:3 respectively:2 component:1 equals:1 address:1 directions:1 change:1 obtained:4 generalizing:1 study:1 larger:5 contradiction:1 ourself:1 simultaneous:1 products:3 suitable:1 klyshko:9 via:1 spatially:1 f1:1 apr:1 outcomes:6 mor:1 total:1 linearly:1 use:1 prove:1 probabilities:1 contains:1 properties:2 bases:2 criteria:19 ardehali:3 type:2 more:7 separated:1 clearly:2 holt:1 appendix:6 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quant-ph9804046.txt |@word villeurbanne:1 consider:1 leads:1 eds:1 scalar:2 generalize:1 spiridonov:1 intricate:1 follow:1 reasoning:1 devoted:2 arik:1 hold:1 concerned:1 equivalence:1 finally:2 does:1 th:1 presentation:1 very:1 zachos:2 every:1 emphasized:1 deformations:2 hussin:1 accompanying:1 vector:1 interpolating:1 zn:3 employing:1 zk:1 second:1 further:1 zs:3 aim:1 what:1 plays:1 stands:1 section:4 goes:1 overcomplete:1 international:2 journal:1 satisfy:5 chose:2 ranged:1 respectively:4 here:2 objects:1 concluding:1 consideration:1 gruber:1 vectors:1 suggests:1 products:1 published:1 action:3 makes:1 involves:1 via:1 useful:1 diffeomorphisms:1 apr:1 plenum:1 summation:1 derivatives:1 use:3 would:1 france:1 nucl:2 therefore:3 type:2 reflects:1 more:3 introducing:1 hermitean:1 operators:17 berlin:1 particular:2 known:1 given:2 fermionic:12 states:19 springer:1 isomorphism:1 ibn:1 deformed:5 science:1 equation:1 des:1 oscillator:1 glauber:1 ere:1 fock:1 values:1 minimisation:1 following:3 making:1 arrive:1 root:2 give:1 process:3 organized:1 high:1 numbers:1 sense:2 sharp:2 rodr:2 clair:1 end:1 rather:1 means:1 far:1 ordinary:5 quon:4 product:4 algebra:15 may:2 applications:1 plane:1 representations:1 rubakov:1 sq:1 provide:1 switch:1 so:2 representation:2 developed:1 years:1 mathematicians:1 paper:5 through:2 statistical:1 still:1 avenue:1 its:1 roots:1 derive:1 group:1 exclusion:2 interesting:1 boson:3 coon:1 main:1 defining:2 deformation:1 non:2 factorial:1 questions:1 material:1 introduce:3 framework:1 now:1 discuss:1 easily:1 term:1 several:1 theory:1 in2p3:1 inherent:2 universit:1 arxiv:1 bueno:1 chung:1 expansions:1 displacement:1 measure:1 eq:16 braided:1 space:3 furthermore:1 rev:4 print:1 ref:4 math:4 rk:9 linear:1 8b:1 8a:1 guess:1 standard:1 york:1 arraga:1 dubna:2 card:1 dunne:1 derivation:1 fractional:6 first:4 twodimensional:1 xn:1 symmetry:3 variables:4 symbolic:1 number:3 isaev:1 precisely:1 open:1 ser:8 little:1 boulevard:1 checked:1 reference:2 anyons:2 similarly:1 introduction:1 eqs:3 relations:2 1a:2 their:2 1c:1 1b:1 1e:2 1d:3 realization:4 scheme:1 fermions:12 mentioning:1 relationship:1 myrheim:1 nieto:1 authors:2 july:1 than:2 coefficients:1 cimento:1 limiting:3 annihilation:3 filippov:1 future:1 russia:1 pre:1 symmetries:2 rewrite:2 conjugate:1 occupied:1 clearly:3 facult:1 lim:6 latter:1 physique:2 note:1 instance:2 k1:1 generalized:12 formulas:1 cnrs:1 shall:2 object:1 eaire:1 involving:1 connected:1 remarks:1 appear:1 especially:1 considered:1 rabat:2 proceedings:2 principle:2 exp:4 occasion:1 physics:5 notion:1 sector:2 show:1 purely:1 relation:1 fletcher:2 find:2 based:1 ıguez:2 parameters:1 state:13 should:1 only:1 factor:1 preliminaries:1 notation:1 get:1 de:5 cannot:1 dz:4 new:1 du:1 qx:1 qz:2 mohammed:1 acknowledgments:1 qa:1 cf:1 kibler:2 view:2 set:1 αr:3 exists:1 see:3 result:4 close:1 lyon:1 invoked:1 erez:1 nuclear:1 written:1 between:6 conditions:1 terms:1 august:1 novembre:1 adjoint:2 interpolate:2 le:1 jr:1 thank:1 goldin:3 many:2 uncertainty:1 connection:1 σq:10 expression:1 point:1 simple:1 harmonic:1 community:1 dimensional:2 respect:1 quons:1 conference:3 described:1 fairlie:2 addition:1 three:2 been:2 int:2 interest:1 ph:1 algebras:3 define:2 corresponding:3 coherence:1 coherent:24 observe:1 berezin:1 spin:1 present:2 case:11 macfarlane:1 exponential:2 value:1 remaining:1 will:1 while:2 viii:2 situation:1 property:2 majid:2 unitary:1 vol:17 refs:1 thus:3 fermion:5 same:1 any:1 unity:3 complex:4 quant:1 pauli:2 finite:2 investigated:1 laboratoire:1 sudarshan:1 usually:1 infinite:2 recent:1 eigenvectors:1 matters:1 well:1 sets:1 exponentials:1 arising:1 dimension:1 usual:1 being:1 obtain:2 correspondences:1 leinaas:1 sciences:1 regarded:1 transformed:1 lett:6 mod:4 eigenstate:2 identical:1 eigenvalue:1 spanned:2 corresponds:6 eorique:1 simmons:1 five:1 vacuum:1 press:1 bit:1 formal:1 like:4 particle:1 follows:2 reduces:1 specific:1 integrals:2 arbitrary:3 works:3 therein:1 methods:5 creation:2 some:2 lead:1 integration:2 comments:1 behave:1 assembly:1 bn:2 super:9 plaza:2 act:1 introduced:3 consequently:1 perelomov:1 into:1 obtaining:1 references:2 determine:1 operator:9 bosonic:7 statistics:1 institut:1 daoud:3 vafa:1 there:2 bosons:4 physicists:1 way:1 jinr:1 function:1 form:1 cedex:1 construction:1 grassmannian:2 russian:1 line:1 2πi:4 azc:1 up:1 us:1 morocco:1 limit:3 called:2 associated:3 defined:5 certain:1 abstract:1 aq:3 work:1 commuting:2 check:1 fizika:1 constructed:1 grassmann:7 functions:1 na:4 when:3 field:3 role:1 nq:2 calculating:1 symbol:1 generated:1 important:1 variable:5 assume:2 overcompleteness:1 time:1 starting:1 nuovo:1
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quant-ph9804048.txt |@word consider:2 results:4 steve:1 roy:1 computation:3 expressions:3 calculate:1 alamos:2 technique:1 charge:1 th:6 analogous:2 circumstances:1 γe:4 division:1 string:3 very:4 dispense:1 implicitly:1 hughes:2 wave:2 sons:1 incoherent:4 vibrational:1 hamiltonian:2 turns:1 fragile:1 t2:1 t3:1 t0:3 standards:1 solved:2 laur:1 eigenvalues:1 optics:2 illustrating:1 murao:1 zero:3 value:1 dynamics:1 linear:1 ˆp:2 errors:1 richard:1 sum:1 while:1 current:2 experiment:1 new:1 increasing:1 method:2 edited:1 degree:3 realizations:2 component:1 behaviour:4 plenio:1 free:1 separation:2 relaxation:2 along:2 equations:1 obtained:1 great:2 ultra:1 technical:1 allows:1 exploitation:1 stressed:1 resonance:1 implement:1 suitable:1 via:3 spatially:3 scales:2 apr:1 total:1 planck:1 standing:1 asymptotic:1 would:3 commun:1 classically:1 therefore:3 centre:1 e2:3 theoretical:2 sort:1 populations:1 thus:5 operators:3 potentially:1 emission:1 degrade:1 cases:1 carried:2 evolves:1 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quant-ph9804049.txt |@word sergei:1 since:2 consider:3 represent:1 depends:2 induces:1 global:1 brownian:2 results:4 leads:8 scalar:1 commute:1 follow:1 expressions:1 research:1 issues:3 devoted:1 glimpse:1 depend:6 indices:1 illustrates:1 participants:2 interactions:2 reverting:1 superficially:1 topic:2 program:1 promoting:1 those:1 under:3 stochastic:2 anharmonic:1 must:5 p2:2 workshops:1 straightforward:2 aφ:9 very:3 rise:1 removing:1 focus:1 hosting:1 difference:1 condition:1 illustrated:1 indicate:1 hamiltonian:5 did:1 philippines:1 tokyo:1 applicable:1 hereafter:1 leave:1 discrete:1 convenience:1 vector:1 manifestly:1 gauge:15 dedication:1 noted:1 force:1 disciplines:1 consistent:1 arnimallee:1 literature:1 second:5 further:2 defines:1 quite:1 canonical:8 even:2 what:4 plays:1 appear:2 ambiguities:2 incompatible:1 section:1 selected:2 brief:2 expressed:3 enjoyed:1 version:3 en:2 above:2 new:3 method:2 exercise:1 pioneering:1 compact:3 deemed:1 ensure:2 prescriptions:2 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quant-ph9804050.txt |@word monte:2 partial:2 consider:1 rev:6 results:1 quadrature:1 edu:1 contributions:3 whose:1 inverse:1 technique:2 topic:2 th:1 kν:5 applied:5 supported:2 advantage:1 very:2 bratislava:1 exact:2 condition:3 solution:1 large:1 solved:1 flatter:1 small:1 possibilities:1 warszawa:1 optics:2 upper:1 compensated:1 estimates:2 za:1 past:1 likely:1 cost:1 evaluated:1 pass:1 carlo:2 even:1 what:2 errors:1 appear:1 sum:3 uniform:2 consistently:1 experiment:3 reconstruction:15 method:12 satisfy:1 full:1 led:1 lee:2 fields:1 jointly:1 address:1 teoretycznej:1 quite:1 obtained:6 search:1 institute:1 leaves:1 studied:1 allows:1 suggests:1 amount:1 procedure:2 aνn:4 makes:1 buˇzek:2 formulated:1 family:1 apr:1 marked:1 reflected:1 total:1 linearly:1 derivatives:1 use:2 commun:1 probabilities:5 positive:2 negative:1 next:1 mation:1 markets:1 more:1 becomes:2 hradil:1 sharply:1 particular:1 actual:2 off:1 must:1 sample:1 setup:1 work:2 fock:8 values:2 following:1 example:1 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quant-ph9804051.txt |@word limited:1 customary:1 consider:5 chain:1 represent:4 results:10 illustrated:2 deadline:1 grateful:1 consists:1 vl0:1 expressions:1 gl:12 gk:1 hole:3 layers:3 calculate:4 γr:11 γp:9 finally:2 efficiencies:2 include:2 crest:1 iνl:2 lowfrequency:1 supported:1 zhang:1 frequencies:2 implicitly:2 focus:1 electron:9 sons:1 figs:4 redefinition:1 ǫg:2 difference:5 condition:8 splitter:1 randomness:1 level:13 did:1 supports:1 applicable:5 large:1 minimal:2 small:5 γnr:9 markov:1 ueda:3 optics:5 linearizing:1 smaller:4 oscillation:1 renormalized:3 consistent:1 a34:1 direct:1 literature:1 approximation:6 rate:12 tangential:1 further:2 estimated:1 linear:1 even:5 what:2 nonlinear:1 wavenumbers:1 sub:9 brackets:1 section:6 celebrated:1 corporation:1 expressed:1 agrees:1 current:4 below:5 experiment:1 above:1 new:7 method:2 contrast:1 temperatures:3 body:4 led:9 lee:4 ibid:2 respectively:9 here:5 reported:4 goobar:1 bj:2 aid:1 active:8 quite:2 equations:9 appears:1 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quant-ph9804052.txt |@word sergei:1 partial:1 consider:9 caused:1 particular:5 illustrated:1 commute:1 entropy:3 spaced:1 expressions:1 dimentional:1 devoted:1 whose:4 inverse:5 const:2 iii:1 technique:5 tr:26 finally:4 th:1 under:2 analogous:1 norm:1 applied:2 eigenstate:1 straightforward:2 returning:1 very:1 implicitly:1 assuming:3 conditions:1 choice:4 ρtr:1 zµ:11 matrices:10 condition:7 leads:4 provide:1 level:2 solution:21 solved:3 math:12 indices:1 eigenvalues:10 optics:1 simultaneously:1 degeneracy:6 dealing:1 pulse:1 cosh:14 second:2 perspective:2 incidentally:1 further:3 dynamics:12 theories:2 linear:21 spectral:2 will:14 what:2 nonlinear:27 plays:1 section:1 hereditary:2 current:1 3i:1 version:2 above:7 new:6 satifies:1 method:10 satisfy:6 led:2 behavior:1 exchange:1 respectively:1 here:1 atoms:1 equations:19 z1:3 change:3 z3:1 obtained:5 technical:1 shift:1 study:2 allows:3 completely:1 reports:1 eberly:1 suggests:1 accomplished:1 simultaneous:3 poisson:8 published:1 spin:2 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quant-ph9804054.txt |@word barone:1 partial:1 consider:2 rev:6 brownian:3 resistance:1 leads:1 eds:2 scalar:5 entropy:3 primes:1 research:1 contributions:2 particles:1 inverse:1 calculate:1 re:1 environment:28 quasi:2 preserved:1 th:4 under:4 tegmark:1 divergent:1 infinite:1 presently:2 zhang:1 very:1 frequencies:1 conditions:2 results:4 electron:2 summarized:1 2γt:1 exact:3 hamiltonian:2 lombardo:1 turns:1 nucl:1 tre:1 ferreira:1 large:2 small:1 alternatively:1 application:1 employing:2 force:1 renormalized:1 approximation:4 limǫ:1 rate:1 value:1 further:2 dynamics:1 obey:1 spectral:5 aim:3 nonlinear:1 sub:1 blum:1 section:1 analogously:4 expressed:1 current:1 consistently:1 version:1 above:3 new:2 method:2 body:2 chaotic:1 full:1 nonlinearly:1 evaluating:2 respectively:4 fock:1 here:8 understanding:1 highly:1 stopping:1 bremsstrahlung:1 relaxation:1 represented:1 consideration:1 sine:1 equations:15 appears:1 obtained:5 instituto:1 suitably:2 shift:2 study:4 studied:6 reason:1 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quant-ph9804055.txt |@word consider:4 interference:1 magnetic:4 particular:4 dynamic:1 results:3 leads:3 scalar:1 edu:1 expressions:1 contributions:8 optical:2 whose:6 amplification:2 zone:1 finally:1 monotonically:2 present:3 stable:4 include:1 cm3:1 dramatically:1 di2:1 di3:1 applied:8 supported:1 far:1 frequencies:6 wave:17 wishes:1 difficult:1 summarized:1 difference:3 categories:1 illustrated:5 dominate:1 hamiltonian:2 altering:1 national:1 large:10 vector:2 science:1 small:9 speculation:1 noted:1 inserting:1 milonni:2 smaller:1 force:52 oscillation:2 estimates:1 sign:4 approximation:10 rate:2 enhancement:1 further:4 theory:2 residue:2 index:1 wylie:1 trapping:1 sum:4 expressed:4 d3:3 henceforth:1 poles:2 above:9 lifshitz:2 new:1 net:10 increasing:1 acknowledgments:1 coefficient:3 evanescent:6 γz:2 fmax:3 respectively:2 µm:1 component:5 here:12 perpendicular:2 ranges:1 eii:1 explore:1 separation:3 ǫz:1 dissipated:1 sine:1 equations:2 change:1 ωa2:1 obtained:3 noticeable:1 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quant-ph9804056.txt |@word consider:2 rev:8 magnetic:2 results:3 leads:4 scalar:14 generalize:1 comments:1 edu:1 contributions:1 hole:2 localized:1 gr:23 compact:4 whose:2 dimensionality:1 depend:1 calculate:4 white:1 finally:1 program:1 th:1 include:2 indicating:1 divergent:5 sorkin:1 conjecture:1 jensen:1 g0:5 far:2 frequencies:4 critchley:1 choice:2 figs:1 difference:2 categories:1 arrange:1 identity:1 illustrated:2 hamiltonian:3 evaluation:1 fractality:1 t2:5 large:5 hiscock:1 vector:2 math:2 small:2 gauge:1 equation:1 kz2:1 work:1 boulware:2 deutsch:1 renormalized:14 sin4:1 sin2:1 sin3:2 sign:1 zero:1 evaluated:1 further:2 displacement:1 employ:3 appear:1 diag:1 sum:2 expressed:3 d3:6 poles:1 above:1 new:1 principal:3 satisfy:1 full:1 led:1 respectively:5 here:6 ranges:1 explore:1 objects:1 eikz:8 separation:2 address:1 directions:1 eikt:1 obtained:3 institute:1 leaves:1 tµ:1 completely:1 usually:1 fourier:2 spacetime:8 tµµ:1 plotted:1 reflectivity:1 although:3 lafex:1 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quant-ph9804061.txt |@word consider:2 ron:1 roc:1 fabricated:1 microwave:1 chair:1 research:1 gk:1 layers:2 pointing:1 analogous:1 far:1 frequencies:1 wave:11 electron:4 refractive:1 difference:2 transmission:5 ref:2 michael:1 applicable:1 t0:10 travels:3 convenience:1 vector:1 optics:1 smaller:1 direct:3 pulse:31 tex:1 second:4 spectral:6 index:2 nonlinear:2 appear:1 section:1 thickness:2 experiment:3 above:1 new:1 coefficient:2 evanescent:8 here:7 ionization:1 represented:3 path:6 along:7 calculate:1 remark:1 incoming:1 institute:1 larger:3 allows:1 aka:1 narrow:1 plotted:4 apr:1 stingl:1 franz:1 electromagnetically:1 causal:1 linearly:1 plot:1 use:1 would:4 probabilities:2 positive:2 france:1 few:1 depicted:1 therefore:1 taken:4 more:2 entrance:1 ejected:2 apparent:1 emission:1 cases:1 must:1 ulbrich:1 tunnel:5 setup:2 work:1 following:1 proof:1 control:1 compare:1 figure:2 mirrors:1 sense:2 high:1 titanium:1 numbers:1 past:1 evidently:2 calculated:2 axis:3 end:1 rather:1 verify:1 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quant-ph9804062.txt |@word replacing:1 partial:1 consider:1 global:3 results:4 leads:2 scalar:1 proposition:3 go:1 expressions:1 gl:1 devoted:3 whose:2 inverse:1 calculate:1 disposal:1 mutatis:2 equivalence:2 polynom:2 finally:1 tm:1 tk:2 under:4 mutandis:2 analogous:2 presentation:1 applied:1 straightforward:1 very:4 geometrical:1 denoted:1 corollary:3 every:2 difference:1 matrices:11 condition:1 intersections:2 immediately:1 hamiltonian:25 turns:1 list:1 solution:3 t0:53 t1:3 discrete:3 vector:7 indices:2 eigenvalues:2 referred:1 noted:1 dealing:1 measurable:1 ωab:8 second:3 rigorous:2 further:2 choices:2 substitute:1 linear:12 even:1 index:1 what:2 invertible:1 sum:1 analogously:4 expressed:4 sequential:1 above:10 γab:1 dtγ:5 new:4 t2:2 simultaneously:1 deduces:1 respectively:8 here:14 understanding:1 objects:1 address:1 directions:1 path:1 along:44 principle:1 equations:11 interpret:1 morphisms:16 obtained:4 derivable:1 remark:4 institute:1 items:1 vectors:7 allows:1 completely:1 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quant-ph9804063.txt |@word limited:5 positions:1 concept:7 partial:4 consider:10 incorporate:1 issued:1 results:2 leads:1 consists:1 tenable:1 seemed:1 content:1 terms:2 referring:4 paris:2 iii:1 illustrates:1 posteriori:1 environment:2 finally:4 present:4 th:2 under:3 ontological:3 include:1 worth:1 case:1 fax:1 protective:5 presently:1 laws:2 very:11 implicitly:3 wave:3 balls:4 every:1 interpreting:2 decide:1 fall:1 difference:2 matrices:12 condition:6 level:3 did:3 interpretations:1 solution:1 large:1 couched:1 vector:1 differentiates:1 metaphysics:1 inclination:1 noted:5 strongly:3 trend:2 consistent:2 go:2 second:3 doubt:1 incidentally:1 further:3 obey:1 even:3 aim:2 what:13 sud:1 appear:1 forgetting:1 giving:1 trivial:2 section:15 associate:1 contributed:1 remain:2 expressed:1 debate:2 consistently:2 suspect:1 above:8 scientists:1 new:3 contrast:1 notions:3 respectively:1 gathered:1 never:1 modify:1 here:6 virtues:1 met:1 entertain:1 others:1 represented:2 consideration:1 along:1 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