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quant-ph9511004.txt |@word consider:2 results:1 controversial:1 gk:1 whose:1 inverse:2 quasi:6 under:2 very:1 dell:1 wave:5 hamiltonian:1 guo:2 solution:2 concise:1 rigorous:1 dynamics:1 sum:1 current:2 sokolovski:2 new:1 equivalent:1 edited:1 here:2 consideration:2 extrema:1 obtained:3 sending:1 search:1 incoming:9 institute:1 pellegrini:2 allows:1 reports:1 prior:1 published:1 action:1 symmetrical:2 studi:1 via:1 projection:1 iet:1 addressed:1 1st:1 apply:1 total:1 imaginary:1 continuous:1 classically:1 ψn:8 therefore:6 taken:1 becomes:1 tenerife:1 berlin:1 appendix:3 normalized:2 particular:3 known:1 iv:1 iii:2 derivation:2 account:1 iannaccone:2 leavens:3 equation:6 work:2 values:1 stimulating:1 wang:2 states:17 numbers:1 want:2 verlag:1 s3:1 s2:1 orthogonality:1 write:2 significance:2 may:1 derived:1 elettronica:1 waves:1 righthand:1 derives:1 council:2 element:2 green:3 acknowledges:1 order:1 talk:2 finalized:1 over:1 professors:1 course:1 paper:1 its:2 derive:1 probability:4 la:1 energies:1 interesting:1 τd:11 systems:3 jaworski:1 mention:1 nov:1 now:1 easily:1 dirac:1 university:1 establishing:1 orthonormal:2 by11:1 mode:1 each:2 universit:1 2i:4 characterized:1 mean:1 mesoscopic:2 energy:2 related:1 obtains:1 pollak:1 quantum:2 our:5 special:1 out:1 canada:2 shown:3 matrix:2 space:2 since:1 rev:8 research:3 investigation:1 formula:1 electronics:1 ref:1 correct:1 barrier:2 written:1 diagonal:2 nth:2 informazione:1 ministry:1 times:5 barriers:1 onto:1 manuscript:2 relate:1 wiesendanger:1 number:2 channels:6 multilayered:1 given:7 perturbation:1 publication:1 introduction:1 dipartimento:1 system:9 their:1 dwell:18 exactly:1 uttiker:2 part:1 authors:1 believe:2 clarifying:1 project:1 ingegneria:1 microstructural:1 perturbative:3 tells:1 sciences:2 potential:4 finding:1 so:6 channel:4 unperturbed:1 formulas:3 added:1 denominator:1 most:2 connected:2 connor:1 acknowledgements:1 average:1 typeset:1 feynman:1 phis:1 left:1 physics:1 fact:2 show:2 supported:1 relation:4 substituting:1 find:1 ratio:1 state:4 should:1 only:2 rich:1 postulated:2 local:1 equilibrium:1 peaked:1 his:1 di:2 de:5 straightforwardly:1 dt:2 dr:2 arxiv:1 microscopy:1 approaching:1 scanning:1 set:3 national:2 packet:2 result:3 discussions:1 recently:1 eigenfunctions:1 pisa:2 diverge:1 symmetric:1 outside:2 closed:1 between:6 αn:4 terms:1 august:1 extend:1 gratefully:1 both:1 last:1 many:1 region:11 according:1 propagation:1 connection:2 layered:1 context:1 economou:1 expression:4 mechanics:1 relevant:3 point:1 corresponds:3 dimensional:6 moreover:1 strong:1 basis:7 three:3 been:1 springerverlag:1 workshop:2 ph:2 choose:1 corresponding:2 quantities:1 present:2 case:4 pacs:1 solid:1 evaluated:1 will:2 tunneling:5 chaotic:1 surface:1 equal:1 ii:1 im:1 different:1 italy:2 degenerate:1 author:1 formulations:1 unity:1 quant:2 widely:2 units:2 finite:1 φm:6 φn:33 european:1 used:1 peaks:1 sym:1 normalization:3 recent:1 matters:1 nevertheless:1 well:1 spent:1 bohm:1 materials:1 maxima:1 just:3 obtain:1 baskin:1 shape:1 using:3 density:12 extends:1 location:1 technological:1 untherodt:1 heidelberg:2 real:1 evaluate:1 possible:2 δnm:1 world:2 accepted:2 helpful:1 particle:3 reduces:1 yields:2 arbitrary:3 stationary:3 italian:1 right:1 searching:1 pω:1 provided:1 vol:1 cnr:2 comments:2 recami:1 tends:1 prof:1 object:1 scientific:1 informatica:1 agreement:1 step:1 substituted:1 revtex:1 substitution:1 relating:1 properties:1 numerator:1 side:1 peak:2 into:1 within:1 integral:1 bound:6 appropriate:1 because:1 references:1 operator:2 proportional:1 statistics:3 degli:1 springer:2 laguna:1 way:1 series:1 was:3 function:4 but:2 delta:2 devices:1 k1a:1 limit:2 demonstrate:1 strongly:1 associated:2 defined:1 abstract:1 problem1:1 general:2 physical:2 phantom:1 functions:5 us:6 nn:1 vanishes:1 field:1 spatial:1 a1:1 a3:2 a2:3 a5:3 a4:1 a7:1 a6:1 assume:1 ottawa:2 time:20
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quant-ph9511006.txt |@word limited:1 consider:1 magnetic:2 results:2 leads:1 eds:1 scalar:4 localized:3 compact:5 looking:1 inverse:1 yngvason:5 nonlocal:1 charge:4 th:2 p2:3 wave:3 interpreting:1 hamiltonian:4 supports:1 notes:1 t2:1 t0:13 solved:1 originally:1 consistent:1 arnold:1 concludes:1 haag:2 even:2 established:1 nonlinear:1 appear:2 section:1 current:1 consistently:1 above:1 reply:1 satisfy:2 never:1 desired:1 simon:1 alone:1 november:1 equations:4 interpret:1 institute:1 allows:1 controversy:1 fourier:5 settled:1 criticism:1 inducing:1 apply:1 resolutions:1 causal:6 derivatives:2 hegerfeldt:18 takes:1 positive:2 properties:2 call:1 m2:9 separated:2 berlin:2 known:1 foundations:1 iii:1 must:1 springer:2 ma:1 deformed:1 equation:9 theories:1 proof:1 aqft:2 kosi:1 relativistic:4 purposes:1 states:7 assumptions:1 want:1 sense:2 occur:1 end:1 notation:1 logunov:1 delay:1 located:3 symposium:1 may:2 earlier:1 applications:1 physik:2 data:1 response:1 short:1 light:1 lines:1 allow:1 representation:1 acausal:2 constituents:1 pointed:1 expects:1 interpreted:2 through:2 looks:1 argued:1 existence:1 its:3 itp:1 buchholz:5 probability:2 interesting:1 82a:1 exhibits:1 absence:1 systems:3 mail:1 non:1 framework:4 tails:1 nov:1 dirac:4 always:2 applied:1 conflict:1 inherent:2 universit:1 spinor:2 adjointness:1 there:1 energy:3 related:3 frequency:2 measurement:1 quantum:9 beyond:1 out:2 shown:1 space:3 since:5 rev:6 projected:1 particles:1 contained:1 induction:2 occurs:1 math:1 shows:1 benjamin:2 theory:14 causally:1 localization:1 inapplicable:1 free:3 york:2 carl:1 ruijsenaars:1 times:1 gordon:5 hence:2 onto:1 exhibited:1 first:4 already:1 render:1 precisely:1 given:1 needed:1 introduction:1 system:5 their:2 assumption:1 fermions:1 observable:1 x2:1 x3:1 x1:1 distance:1 cimento:1 preparation:1 matter:1 xi2:1 interrelated:1 nouvo:1 modern:1 any:2 latter:1 note:1 caesar:1 forces:1 new:2 spectral:3 electric:2 axiomatic:3 algebraic:3 germany:2 considered:2 order:3 proceedings:1 points:1 velocity:1 physics:3 notion:2 quantity:3 phenomenon:1 violation:1 atom:9 multicomponent:1 relation:1 solutions:5 d4:1 ground:1 causality:7 analytic:2 only:4 employed:1 local:5 do:1 his:1 goes:1 klein:5 get:1 de:1 joint:2 cannot:7 international:1 evolution:2 fields:5 arxiv:1 wightman:1 whether:2 contain:1 london:1 implication:1 clausthal:1 dobrev:1 exists:1 see:4 sec:1 result:1 oldenburg:3 interacting:2 doebner:1 positivity:3 state:7 between:2 comparable:1 august:1 nature:1 article:1 configuration:1 problem:4 restrictions:2 pertain:1 compton:1 propagation:1 hψ:2 uni:1 experimental:2 grounds:1 comment:1 relevant:1 point:1 dimensional:1 pct:1 moreover:1 speak:1 described:1 basis:2 three:1 cauchy:1 ph:1 lett:3 nattermann:1 corresponding:1 both:2 sufficient:1 photon:1 external:1 spin:1 present:1 case:3 p0:2 exponential:1 nski:1 value:1 will:2 while:1 behavior:1 ix:4 coupled:1 vol:1 ii:1 il:1 fermion:1 lengths:2 quant:1 arguments:1 finite:3 uncharged:1 used:1 singapore:1 recent:1 whereby:1 locality:1 well:3 analysis:1 academic:1 todorov:1 without:1 components:5 model:1 self:1 charged:1 distances:1 density:4 photons:1 conclude:2 transformed:2 questioned:1 versa:1 mod:1 excited:3 gave:1 identical:1 bogolubov:1 possible:1 press:1 world:1 like:1 particle:3 lost:1 signal:1 fully:1 mathematical:3 methods:1 classical:4 some:1 tempered:1 understood:1 respect:3 slanka:1 nonzero:1 electromagnetic:1 overlap:2 behave:2 provides:1 scientific:1 standpoint:1 hilbert:2 about:1 extension:1 considerations:1 raised:1 maxwell:2 into:1 references:1 einstein:1 operator:1 argumentation:1 statistics:1 shells:1 assumed:2 support:13 initial:1 question:2 transform:1 forward:1 propagator:1 form:1 but:3 reed:1 delta:1 irreversible:1 supp:2 characteristic:1 fermi:6 lightcones:1 distribution:2 similar:1 defined:1 proven:1 general:4 single:1 exist:1 physical:2 functions:2 paradox:3 no:2 when:1 streater:1 field:11 test:2 conclusion:1 thaller:3 excitation:3 time:7 problems:2 structure:1 vice:1 governed:1 mass:1 fachbereich:1 observables:1 backward:1 original:1
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quant-ph9511008.txt |@word represent:3 consider:6 remarkable:1 squared:1 focus:1 leads:1 roy:3 computation:2 edu:1 operationally:1 involved:1 contributions:1 issues:1 inverse:1 terms:1 re:2 ects:1 waveplate:1 ts:3 interactions:2 shall:1 environment:1 does:1 analogous:1 unit:1 ta:7 skepticism:1 supported:2 amplitudes:2 g2:3 6p3:1 orthogonal:3 frequencies:1 connects:1 wave:1 veri:2 experimentally:3 condition:1 interferometry:1 num:1 incoherent:1 pbs:1 level:4 transmission:6 cause:1 mirror:2 make:1 t0:3 large:5 discrete:1 small:2 optics:1 noted:1 possibility:1 upper:1 expanded:1 deutsch:5 direct:1 aip:2 approximation:2 rate:6 displays:1 steadystate:1 rigorous:1 further:2 dynamics:6 implemented:1 theory:3 established:1 what:1 nonlinear:8 appear:2 apparatus:4 ned:1 axes:1 brief:1 current:4 experiment:2 above:2 susceptibility:1 new:4 3g:1 method:1 edited:1 full:2 explosion:1 behavior:1 degree:1 lange:2 here:3 atoms:6 reported:1 explore:1 operating:1 ansatz:2 separation:1 strategies:3 alone:2 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quant-ph9511009.txt |@word monte:8 gt:3 results:4 illustrated:1 grateful:1 involved:1 shevchenko:2 calculate:2 shrinkage:1 nonlocal:1 th:3 stochastic:2 nodes:2 fermionic:3 case:9 random:6 very:2 alder:1 wave:16 sons:1 difference:2 exact:5 leads:1 basics:1 immediately:1 hamiltonian:6 positions:1 itep:2 solution:3 vector:3 small:4 employing:1 force:1 oscillator:4 direct:1 sign:1 zero:2 xf1:5 implemented:1 carlo:8 even:1 employ:1 errors:1 const:1 sum:1 3n:1 above:2 nine:8 method:13 xfk:1 xfl:1 component:1 here:6 hundreds:1 promoted:1 spinless:2 operating:1 sinh:2 represented:2 slater:1 equations:1 change:3 obtained:3 convert:1 items:1 study:2 studied:3 allows:2 trial:9 action:3 explain:1 plotted:1 members:1 figure:1 decrease:1 total:2 propagators:1 linearly:1 use:8 takes:1 would:1 prove:1 remains:1 positive:1 negative:1 e0:6 calculation:1 nucl:1 explicitly:1 ψn:4 taken:2 iteratively:1 type:1 ψg:14 more:4 bakker:1 started:1 initial:5 pairs:1 appendix:5 koonin:2 particular:1 known:6 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quant-ph9511010.txt |@word concept:1 partial:5 consider:3 results:1 leads:2 schatten:1 commute:8 consists:1 research:1 eigenbasis:1 equivalence:1 tr:29 gρ1:3 those:2 under:4 exposition:1 sent:2 advantage:1 orthogonal:6 rise:1 noncommuting:4 summarized:1 difference:1 condition:1 school:1 conjugating:1 presented:1 tra:6 trc:3 trb:5 solution:1 noninvertible:1 couched:1 eigenvalues:3 application:1 work:1 consistent:3 direct:2 maintain:1 second:2 pl4:1 further:1 spectral:2 what:2 abc:1 stands:2 invertible:11 sum:2 expressed:1 above:1 new:2 method:1 exercise:1 satisfy:4 notions:1 meb:1 respectively:2 equals:1 answers:1 diagonal:1 ranges:1 mermin:1 address:2 along:1 strong:1 equations:2 obtained:1 naval:1 receive:1 vectors:1 hughes:1 simultaneous:1 schumacher:1 action:1 studies:1 composed:1 useful:2 claim:1 marginal:3 namely:1 highly:1 ask:1 decrease:1 glance:1 use:1 projector:1 would:1 prove:2 positive:9 properties:1 call:1 therefore:3 taken:3 noisy:1 marginally:1 more:4 formally:1 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quant-ph9511011.txt |@word represent:1 partial:3 consider:1 rev:2 equalities:1 illustrated:1 rˆ:1 expressions:1 localized:1 compact:1 simon:3 depend:1 concerned:2 tn:1 finally:1 under:2 analogous:1 norm:1 supported:1 straightforward:1 far:2 conjectured:2 dell:1 unchen:3 corollary:1 difference:1 fakult:1 condition:1 treating:1 riemann:1 hamiltonian:2 enss:1 t2:8 t3:1 t1:6 large:3 vector:1 anal:1 der:1 second:4 rigorous:2 further:3 click:1 scientific:1 even:2 established:1 what:1 section:3 xφ:1 expressed:1 find:2 above:1 sup:7 new:2 acknowledgments:1 body:1 outgoing:1 chose:1 equals:2 here:1 along:1 strong:1 observing:1 remark:7 incoming:1 fourier:2 point:1 appropriately:1 via:1 useful:1 limr:1 integrations:2 limt:3 rσ:4 apply:1 total:2 brc:2 unit:2 readily:2 use:3 asymptotic:6 usa:1 prove:3 sake:1 uniformly:1 tends:2 ψt:35 calculation:1 noting:1 undivided:1 brunswick:1 more:2 operators:5 odinger:3 controlling:1 proceed:1 known:1 hold:2 iii:1 ontological:1 evolves:1 crosses:3 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quant-ph9511012.txt |@word consider:4 ωs2:2 magnetic:4 results:1 leads:4 grateful:1 consists:1 fawcett:1 issues:1 whose:1 calculate:1 finally:1 tm:1 under:2 maryland:2 te:1 worth:2 norm:2 straightforward:1 orthogonal:2 wave:4 sons:1 summarized:3 bringing:1 condition:12 entire:1 hamiltonian:7 applicable:1 vector:14 indices:1 tem:3 consistent:1 surrounding:1 second:3 enclosed:1 further:1 substitute:1 zs:2 even:1 established:1 plays:2 section:4 above:4 new:5 change:1 method:1 satisfy:12 edited:1 ibid:2 respectively:4 component:12 here:5 okinawa:1 cylindrical:14 active:1 equations:14 kakazu:2 z2:2 obtained:3 study:1 vectors:1 allows:1 reports:1 periodic:4 walther:1 poisson:2 fourier:1 χs1:5 χs2:5 useful:1 scaler:1 compare:1 apply:2 unit:1 derivatives:2 use:3 would:1 prove:3 covariant:1 ψs:12 contains:3 next:5 eϕ:3 more:1 becomes:6 operators:4 factor:1 emission:2 particular:2 known:2 must:8 account:1 quantized:10 equation:12 asσ:14 obvious:1 us2:4 us1:6 mr:1 following:5 arrive:3 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quant-ph9511013.txt |@word represent:1 u0:4 qian:2 rev:18 riesenfeld:3 kanai:2 p02:1 follow:1 research:3 gk:1 worked:1 consider:1 whose:3 pˆc:3 inverse:7 technique:2 finally:2 does:1 preserved:1 th:1 timedependent:3 anharmonic:37 applied:1 global:1 ermakov:6 g0:13 far:1 wave:2 exact:18 brihaye:1 condition:1 hamiltonian:7 did:1 irreducible:1 solution:2 t0:34 sang:1 vector:1 manifestly:1 eigenvalues:4 optics:1 noted:2 work:1 force:3 coordinate:1 second:3 zz:1 further:4 odd:1 canonical:2 even:4 index:4 nonlinear:1 morse:1 section:1 expressed:1 agrees:1 cheng:1 lifshitz:1 new:4 falling:1 ˆk:1 method:23 contrast:2 coefficient:1 q1:3 ibid:3 preserves:1 korsch:1 groups:3 aid:1 path:1 standard:2 equations:3 change:1 differential:2 obtained:4 search:1 algebra:26 institute:1 ˆq:3 elaborate:1 studied:2 soliani:1 approaches:1 p2:1 uniquely:1 eˆ:2 regardless:1 elaborated:1 substitution:1 order:3 decrease:1 univ:1 unit:1 use:4 intensively:2 positive:1 uniqueness:1 cho:1 few:1 bases:2 therefore:3 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quant-ph9511014.txt |@word consider:7 illustrates:1 rev:6 magnetic:1 comparatively:2 desirable:2 results:1 leads:2 scalar:5 commute:4 edu:1 go:1 amplified:1 hole:6 localized:6 whose:3 certainly:1 repetition:2 depend:1 simplify:1 seriously:1 passage:1 quasi:2 behave:2 present:2 under:3 subtleties:2 supported:1 attribution:1 straightforward:2 boucher:2 very:3 induce:1 every:1 experimentally:3 emphasized:1 parameter:1 condition:2 chapel:1 treating:1 osi:1 differentiated:1 obvious:2 immediately:1 level:1 cause:1 solution:4 correct:1 large:3 convenience:1 small:2 configurations:1 smaller:4 illustrating:1 destroys:1 consistent:1 approximation:7 likely:2 evaluated:1 reply:1 further:5 dynamics:2 implemented:1 expressions:2 linear:1 even:2 what:9 appear:4 apparatus:1 brackets:4 sum:3 brief:1 expressed:2 centers:1 experiment:3 abt:3 above:5 new:1 consisting:1 satisfy:2 edited:1 full:3 backreaction:5 evaluating:1 degree:2 applies:1 component:2 preserves:1 here:3 desired:1 appropriate:1 strong:1 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quant-ph9511015.txt |@word represent:1 partial:2 consider:1 meson:1 interference:2 interpret:2 entropy:9 grateful:1 expressions:1 gk:2 issues:1 gr:1 whose:1 inverse:1 const:1 calculate:1 graph:1 deterministic:3 tr:4 environment:4 those:1 stable:5 stochastic:3 include:2 tc:1 norm:2 ingredient:1 induce:2 wave:4 difference:1 condition:3 ochanomizu:1 hamiltonian:31 did:1 turns:2 try:1 solved:3 differential:1 science:1 manifestly:2 lˆ:3 upper:1 ocha:2 force:2 pragmatic:1 renormalized:3 consistent:1 sign:1 approximation:5 zero:1 further:4 dynamics:8 spontaneously:1 odd:2 linear:3 even:5 arimitsu:3 what:1 appear:1 section:2 anniversary:1 expressed:5 consistently:4 poles:1 above:6 destroyed:1 new:4 increasing:1 method:6 suppress:1 full:2 lee:15 exchange:2 respectively:3 sint:2 never:1 here:2 understanding:1 following:1 separation:2 others:2 represented:1 equations:2 implicit:1 change:1 suggest:1 obtained:2 property:1 colored:1 thirty:1 institute:1 spontaneous:1 study:3 larger:1 experience:1 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quant-ph9511016.txt |@word magnetic:8 four:1 consists:1 localized:1 whose:5 whatsoever:1 under:7 ontological:1 worth:1 digit:1 dell:1 every:3 govern:1 vastly:1 school:1 vector:3 guiding:8 markov:1 force:8 construed:2 consistent:2 approximation:2 second:6 implemented:1 even:25 established:2 specification:1 consequent:1 above:2 supplies:1 increasing:1 ever:1 notions:5 here:10 governing:2 represented:3 obtained:5 derivable:1 elaborate:1 completely:10 controversy:1 karin:1 stressed:1 suitable:3 changes:3 york:3 attractor:1 divide:1 classification:1 explained:1 plenum:1 highly:2 stern:4 derivatives:1 would:24 achieve:1 negative:2 inevitable:3 maes:1 noting:1 m1:1 therefore:3 ip:3 type:1 composite:11 naive:6 odinger:20 aware:1 separates:1 must:14 me:2 word:1 room:2 leavens:1 mn:1 mk:8 theories:2 macroscopically:3 mv:1 transparency:1 concepts:3 example:18 indicated:1 give:1 relativistic:2 involve:1 want:1 crystallized:1 absolute:4 hoc:1 turn:2 provide:3 feature:2 how:6 nontrivial:1 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quant-ph9511019.txt |@word proposition:2 concept:1 partial:2 consider:2 remarkable:1 particular:6 results:5 leads:1 commute:2 entropy:33 broader:1 edu:2 follow:2 issues:1 alq:1 whose:7 preserves:1 concerned:2 tr:35 acting:1 finally:1 lanford:1 under:6 tr1:1 stochastic:3 analogous:1 tr2:1 presentation:2 sent:2 jensen:1 straightforward:1 orthogonal:16 far:1 translations:1 haag:1 splitting:3 every:4 entries:1 difference:1 matrices:13 condition:6 χd:4 tri:1 entire:1 presented:1 noiseless:4 discrete:3 convenience:1 vector:1 min:1 science:1 small:6 eigenvalues:2 optics:1 upper:3 smaller:1 computation:1 consistent:4 estimates:1 direct:2 approximation:1 fold:1 second:2 equal:5 rigorous:1 further:3 cfs:3 linear:3 even:1 established:1 what:2 plays:1 advantageous:1 section:9 agrees:1 current:2 version:1 above:7 new:2 net:1 neu:1 consisting:3 implementable:1 satisfy:1 enh:1 l1:6 equals:2 here:3 understanding:1 desired:1 others:1 represented:1 ψj1:2 along:1 ensembles:1 obtained:3 remark:3 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quant-ph9511020.txt |@word limited:1 since:5 consider:1 rev:4 results:1 leads:2 roy:1 scalar:2 generalize:1 go:5 gn:8 certainly:1 calculate:1 providence:1 pˆi:1 equivalence:5 tr:4 finally:1 under:2 106a:1 γb:15 γa:2 confirmation:1 amplitudes:3 dϕn:1 very:1 wave:1 lecture:1 telling:1 difference:2 bringing:1 treating:1 four:1 mc:1 hamiltonian:5 turns:2 proposals:2 solution:4 solved:4 a120:1 math:4 indices:1 eigenvalues:2 der:1 inconsistent:1 expanded:1 det:4 arnimallee:1 sign:2 matrices:1 second:2 value:2 canonical:2 subscripts:1 what:2 gavazzi:1 adds:1 sub:1 brackets:1 trivial:1 sum:2 while:1 expressed:2 agrees:1 consistently:1 above:8 new:10 order:7 parametrization:1 movement:1 condensed:1 led:1 even:1 here:5 mev:2 tangent:1 possibility:1 others:1 path:41 change:2 contraction:1 obtained:3 antisymmetric:1 vectors:1 pˆµ:1 action:12 complicated:1 changes:2 involves:2 york:1 via:1 raise:1 extra:1 explained:2 replace:1 sliced:14 b224:1 total:1 unit:1 use:2 proceed:1 would:6 positive:1 m1:1 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quant-ph9511022.txt |@word consider:1 results:3 localized:1 inverse:1 const:2 technique:1 quasi:1 th:1 under:1 case:5 belonging:1 choice:1 difference:1 condition:1 solution:2 large:1 discrete:1 eigenvalues:1 noted:1 sukhatme:1 sin4:2 sin2:7 even:1 established:1 contributed:1 agrees:1 poles:2 above:3 new:2 method:2 coefficient:1 2kr:6 here:1 atoms:1 behaviour:6 simon:2 depend:1 logarithmic:1 institute:1 allows:1 reports:1 ctg:2 usually:1 opinion:1 suitable:1 makes:1 cancellation:2 decrease:4 use:1 asymptotic:6 would:1 positive:3 negative:1 next:1 therefore:4 type:3 more:3 zeroes:1 transcendental:1 becomes:1 odinger:2 validity:2 excellent:1 known:2 must:3 high:1 rβ:3 equation:2 modified:1 publications:1 following:2 making:1 example:1 sense:1 states:7 want:1 allowed:1 evidently:1 guarantee:1 provide:1 feature:1 pure:1 instead:1 ordinary:1 sin:9 after:1 derived:1 applications:1 produce:1 waves:1 wave:12 rather:1 so:3 fundamental:1 decreasing:2 tbilisi:2 wigner:5 satisfied:1 years:1 course:1 mentioned:1 its:3 decay:3 ln:3 solving:1 decreases:1 choose:1 derivative:1 main:1 correspondence:4 them:1 they:1 nov:1 now:2 term:1 fully:1 university:1 radial:1 2m:1 2i:2 2k:1 square:4 series:1 energy:2 books:1 obtains:1 quantum:1 our:2 eq:3 rev:1 denotes:1 studying:1 dominate:1 correct:1 free:2 extraordinary:1 approaches:1 khare:1 york:1 substantiation:1 generate:1 care:1 exponentially:1 hence:1 first:1 origin:2 xa:2 dominating:1 law:2 checked:1 leading:1 eqs:1 behaves:1 their:1 1e:1 gives:2 authors:2 representing:1 than:1 zβ:1 oscillate:1 wide:1 kind:1 finiteness:2 limiting:1 2kφ:1 rǫ:2 powers:3 collecting:1 modulating:5 san:1 modern:1 stillinger:1 say:1 manner:1 any:2 relatively:1 convenient:1 latter:1 isolated:1 sound:1 potential:6 generalized:1 destroy:1 investigations:1 aexp:2 most:2 class:1 considered:1 kr:23 exp:2 kz:4 physics:4 bateman:1 incomplete:1 phenomenon:1 probe:1 discovered:1 solutions:2 substituting:1 find:1 principal:1 slow:1 spite:1 enough:1 only:6 molecules:1 employed:1 do:2 2mu:1 ones:1 dz:5 integrable:2 2me:1 dr:1 normalizable:3 continuum:6 arxiv:1 yield:1 view:1 set:1 achieved:1 depends:1 radius:2 differentiable:1 review:1 state:3 various:1 correctly:1 between:5 boundary:2 approach:1 recently:1 ln2:1 last:2 many:1 taking:1 according:2 comment:1 ci:4 point:1 corresponds:1 consideration:1 moreover:2 considering:1 due:1 strategy:1 cosine:1 asymptotics:5 interest:2 collected:1 ph:1 hardly:1 define:1 corresponding:3 2ir:5 observe:1 systematic:1 general:3 former:1 present:1 applied:1 k2:1 georgia:1 exponential:1 will:3 dept:1 while:2 vol:1 von:5 ave:1 vanish:2 make:1 same:1 quant:1 modification:1 erdelyi:1 higher:2 used:2 infinity:3 see:2 levels:2 potentials:11 recent:1 schr:2 lim:1 usual:1 distances:1 moments:1 obtain:1 underlying:1 unifies:1 yet:1 previous:1 rapid:1 conclusions:1 conclude:1 theorem:3 solvable:1 excited:1 euler:1 take:6 press:1 immediately:1 like:6 follows:1 separately:1 arbitrary:1 mathematical:2 because:2 neumann:5 namely:1 some:1 examples:1 oscillations:2 ourselves:1 cooper:1 dimensions:1 lead:1 does:2 tends:1 power:2 slight:1 expansion:1 found:2 takes:1 o:4 slightly:1 gamma:1 into:1 integral:1 bound:7 acad:1 references:1 isospectral:1 methods:1 hep:1 u4:1 there:5 fast:1 u2:1 atkinson:1 lot:1 was:3 function:12 form:2 denoting:1 but:2 construction:1 reed:2 embedded:1 characteristic:1 us:4 below:1 limit:2 anew:1 demonstrate:1 problem:1 called:2 constant:2 abstract:1 convergent:1 xiii:1 exist:1 together:2 constructed:2 functions:11 no:2 vanishes:1 setting:1 spatial:2 confine:1 conclusion:1 francisco:1 a11:1 a2:1 variable:1 ago:1 coulomb:1 rule:1 volumes:1
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quant-ph9511023.txt |@word measurements:1 allowed:1 consider:7 remarkable:3 depends:2 rev:1 lack:4 edn:1 results:2 leads:1 quadrature:1 subtle:1 broader:1 anticorrelated:15 hole:1 lkn:3 whose:2 preserves:1 violate:2 spin:6 technique:1 nonlocal:10 effort:1 certain:1 present:3 under:2 analogous:2 presumed:2 p2:1 outside:1 far:4 plausibility:1 wave:4 electron:22 every:4 interpreting:1 twice:1 telling:2 affect:2 uwa:1 difference:1 exact:1 condition:1 look:1 entire:5 immediately:1 hamiltonian:4 transmission:4 positions:4 integrating:2 michael:1 applicable:1 occurs:3 large:3 solved:2 convenience:1 phase:1 succession:1 small:1 eigenvalues:1 lk3:7 upper:3 unexpected:1 force:1 tem:1 harder:1 consistent:4 edu:1 measurable:1 dimensional:1 modified:1 approximation:1 zero:14 apparently:1 evaluated:1 realistic:1 further:2 eik2:4 imposing:1 even:7 established:1 what:3 appear:4 incompatible:1 sun:1 sum:3 intimate:1 near:2 current:1 remembered:1 experiment:8 above:5 new:4 appeal:1 body:45 full:3 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quant-ph9511024.txt |@word dewitt:2 consider:6 remarkable:1 rev:1 primed:1 four:1 eds:1 scalar:11 localized:1 whose:1 subjected:1 equivalence:1 tn:4 finally:1 does:1 p2:10 casadio:2 wave:1 leads:6 hamiltonian:1 x0c:7 list:1 solution:1 large:1 discrete:1 convenience:1 math:1 force:1 oscillation:1 deutsch:1 zc:14 approximation:2 zero:1 evaluated:1 further:5 dynamics:1 even:1 what:2 section:1 near:2 uniform:1 annals:1 poles:1 above:3 suppose:1 method:1 evolving:1 respectively:1 desired:1 sinh:15 directions:1 path:4 along:3 z0:6 logarithmic:1 obtained:4 involved:1 study:1 studied:1 suggests:1 survey:1 action:1 changes:1 examining:1 followed:1 integrations:1 replace:1 put:1 total:3 planck:2 linearly:1 use:1 takes:2 next:1 nucl:1 compensate:1 therefore:1 taken:1 more:1 flat:1 israel:1 giovanni:1 emission:1 particular:2 hole:4 iii:1 evolves:1 ma:5 pursue:1 decouples:3 inertial:2 rohrlich:1 oscillator:5 remain:1 example:1 thermally:1 lϕ:3 candelas:1 allowed:2 sharp:1 rather:5 discussion:1 write:1 acta:1 sin:2 may:6 residues:1 plane:1 waves:1 response:1 remember:1 effective:1 yielding:1 accelerated:4 green:1 order:1 indeed:2 over:1 cosh:15 course:1 through:3 hypersurface:1 existence:1 still:1 its:3 before:1 ima:1 x1c:1 coordinates:3 absence:1 systems:1 omitted:2 mail:2 lz:3 lx:2 ly:2 centenary:1 return:1 yc:1 introduce:1 effects:2 they:1 half:1 nov:1 now:4 represents:1 term:1 university:3 level:2 barton:1 each:1 found:2 2h:3 england:2 independent:1 energy:2 ea:2 gaussian:3 related:1 inverted:4 unprimed:1 frequency:1 obtains:1 quantum:12 infinity:1 eq:10 event:2 space:3 furthermore:1 since:4 lagrangian:8 particles:2 replacing:1 istituto:1 interchanging:1 sinh2:2 theory:5 divergence:1 fisica:1 free:1 quite:1 complicated:1 ask:2 interaction:1 derivation:1 r2:1 could:1 transition:5 length:1 place:1 exhibited:1 first:4 simplifies:1 probability:5 xc:1 armitage:1 another:3 given:6 perturbation:1 temperature:2 introduction:1 bologna:4 eqs:1 unruh:3 final:1 recovered:1 schwarzschild:1 x2:3 x3:3 x0:3 x1:1 than:3 begins:1 roberto:1 birrel:1 venturi:1 exhibit:1 hz:1 generality:1 electrodynamics:1 curved:2 orders:1 acceleration:10 convenient:2 self:1 davies:2 note:3 potential:2 analogy:1 so:1 detector:24 subject:1 austr:1 shall:5 evaporate:1 boltzmann:1 brout:2 xµ:4 surprising:2 considered:5 clear:1 later:1 detectors:3 sciama:1 principle:1 exp:16 mechanical:2 physics:2 sum:1 fact:1 probe:1 evaporation:1 purely:1 keywords:1 eliminated:1 ground:1 implying:1 aτ:2 should:1 black:5 factor:1 local:1 hope:2 di:2 dependent:1 familiar:1 dz:5 dx:4 dy:4 dv:1 dt:7 du:5 dr:5 ds:1 dp:5 dq:1 evolution:1 fields:1 arxiv:1 wightman:1 set:3 observer:5 our:1 undergoes:1 frame:1 observed:1 see:4 result:4 close:1 contour:2 encouraged:1 mechanically:3 away:1 tend:2 state:4 approach:2 discovery:1 terms:3 reproduced:1 nature:1 spindel:1 however:4 vanishing:1 comm:1 extent:1 essentially:1 limits:1 compton:2 equal:2 x2c:1 context:1 disappears:1 otherwise:1 pre:1 relativity:1 point:15 lagrangians:1 harmonic:5 dimensional:3 pole:2 exhibits:1 constant:7 considers:3 considering:2 described:2 trajectory:2 due:4 been:1 ottewill:1 hawking:4 ph:2 define:1 direction:2 corresponding:6 quantities:1 sufficient:1 excite:1 observe:1 general:1 case:4 bπ:1 appearance:1 value:1 transformation:1 will:10 while:2 replaced:1 situation:1 nonrelativistic:1 vectors:1 examines:1 coupled:3 metric:1 wkb:1 thus:4 non:1 according:1 ii:1 itself:1 disappear:1 different:1 italy:1 make:2 any:1 unity:1 parts:1 quant:1 wavepacket:4 largest:1 units:1 finite:5 higher:1 evolve:3 extended:4 a2t:2 effect:3 usually:1 moment:2 uses:1 infinite:1 lower:1 nucleare:1 expression:2 nonetheless:1 without:1 lim:8 coordinate:1 model:2 dimension:1 usual:5 cosh2:7 just:2 rindler:2 obtain:3 sriramkumar:1 using:1 eigenstates:1 previous:1 adv:1 enters:1 singularity:1 integer:1 density:3 absorption:1 z02:1 had:1 add:1 internal:1 excited:2 real:1 evaluate:1 results:2 possible:1 corresponds:1 vacuum:4 press:2 world:1 loss:1 pertinent:1 like:4 particle:9 follows:1 performing:1 serves:2 integrals:3 become:1 replacement:1 therein:1 because:1 classical:9 backgrounds:1 b4:6 accelerating:1 b2:10 respect:1 proper:3 happens:1 describing:1 lead:1 integration:2 per:2 x3c:2 behave:1 unit:2 run:1 sezione:1 agreement:1 expansion:1 padmanabhan:1 2m:1 grotch:1 horizon:2 other:1 cambridge:4 into:1 integral:5 three:1 references:2 einstein:1 frames:1 assumed:1 question:1 transform:1 u2:17 quanta:1 was:1 naturally:1 function:4 considerably:1 elsewhere:1 form:2 but:1 idealized:1 line:1 coupling:1 infn:2 whether:1 minkowski:6 2πin:1 us:2 2πn:3 grove:1 limit:16 distribution:2 monopole:6 similar:1 mechanics:1 associated:5 defined:1 abstract:1 contribute:1 denote:1 wavelength:2 nazionale:1 defines:1 again:1 stationarity:1 field:14 setting:2 becomes:1 department:1 massless:3 concerning:2 conclusion:1 oneself:1 uniformly:1 a2:6 variable:1 implies:1 factorized:1 dτ:5 interval:1 holes:1 mass:2 time:12 4b:1 once:1
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quant-ph9511025.txt |@word limited:1 ui:2 sci:1 consider:8 priori:1 rev:9 forbidden:1 desirable:1 results:18 holevo:2 leads:2 commute:1 generalize:1 comments:1 computation:1 edu:2 go:1 follow:1 remarkably:1 conservative:1 whose:1 certainly:2 amplification:3 depend:1 doe:1 iii:3 concerned:1 equivalence:1 vs:1 environment:1 sigart:1 finally:1 critical:1 protocols:2 th:1 under:4 kwong:1 eliminate:1 case:7 random:8 oblivious:1 orthogonal:14 very:1 ρr:3 ρc:2 choice:2 knapsack:1 vastly:3 difference:1 securely:1 timely:1 four:2 school:1 dominate:1 publicly:6 level:2 transmission:7 suffices:1 notes:2 eve:25 wait:1 ri:3 noiseless:4 vector:2 minimal:2 affect:1 science:2 small:18 entropy:10 noted:1 upper:5 unexpected:1 commitment:1 vertical:2 deutsch:2 consistent:3 feasibility:1 consists:1 rate:31 design:1 comforting:1 pass:6 incidentally:1 further:2 leakage:1 linear:2 even:13 what:6 errors:8 giving:1 section:8 axes:9 pleased:1 paragraph:2 goes:3 shared:3 learned:1 public:5 heuristically:1 full:1 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quant-ph9511027.txt |@word epeau:2 partial:1 results:1 bob:10 roy:1 entropy:8 montr:2 fout:4 consists:1 particles:6 amplification:1 violate:1 containing:2 environment:1 williamstown:1 under:2 analogous:1 resources:1 division:1 random:8 orthogonal:2 choice:1 affect:1 entire:2 transmission:9 trb:1 noiseless:2 small:1 optics:1 round:2 trw:1 ville:1 smaller:1 tel:2 deutsch:1 direct:2 second:2 design:1 maurer:1 odd:1 targets:3 even:5 errors:4 xor:2 appear:2 apparatus:1 3p:1 expressed:4 agrees:1 henceforth:1 above:4 new:2 method:9 full:1 submitted:1 whose:2 respectively:2 component:1 teleportation:6 gilles:1 diagonal:2 desired:3 alone:1 along:3 change:1 ensembles:1 obtained:1 convert:1 sender:4 leaves:2 larger:1 allows:1 leaving:2 prior:1 resulting:1 schumacher:4 action:1 formation:4 conveniently:1 changes:1 uniquely:1 via:2 followed:1 besides:2 9a:1 private:1 outcomes:1 viz:1 recurrence:5 use:5 asymptotic:4 would:3 probabilities:1 positive:5 properties:1 ψi:5 call:2 therefore:2 centre:1 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quant-ph9511028.txt |@word concept:1 φn2:1 φn1:1 results:4 go:3 follow:1 expressions:1 devoted:1 content:1 baym:1 program:1 applied:2 straightforward:1 very:1 sons:1 difference:1 hamiltonian:5 t0:2 phase:9 dealt:1 infinities:1 q1n:1 consists:1 second:13 pass:1 further:1 substitute:1 canonical:6 aim:1 section:3 axes:1 δq1:9 reconstruction:1 new:4 method:1 supporting:1 led:1 here:1 diagonal:5 canonically:1 q12:1 directions:1 equations:11 obtained:2 spite:1 involved:1 study:7 action:1 iet:6 apply:2 total:1 use:3 working:1 sake:1 next:1 therefore:1 taken:1 means:3 more:3 knows:1 operators:10 odinger:5 normalized:1 fermionic:2 language:1 quantized:3 equation:19 work:1 oscillator:6 infinitesimal:7 following:3 making:2 2mr:2 indicates:1 sense:2 tan:2 s3:2 s2:6 s1:2 s0:8 write:1 how:1 ordinary:1 parameter:1 sin:2 product:1 transforming:1 after:1 derived:2 imply:1 si:2 so:3 definitions:1 order:1 interpretation:5 help:1 indeed:1 paper:7 statistical:1 derive:3 hq1:1 fix:1 h2:4 systems:4 might:4 them:1 within:2 integral:6 ωr2:1 introduce:1 hamilton:3 identically:1 nov:1 now:8 eigenvalue:1 february:1 dirac:1 2e:1 each:1 2m:4 2i:2 differential:1 retrieve:1 series:1 energy:1 related:3 used:3 quantum:13 our:10 shown:3 space:8 since:2 particles:4 may:15 shows:1 benjamin:1 wiley:1 theory:5 retrieved:1 mω:19 fisica:1 departamento:1 base:1 york:1 put:2 beginning:1 definition:1 derivation:2 r2:7 turn:1 first:4 already:1 xy:1 done:1 precisely:3 angular:1 given:1 rewritten:1 introduction:1 system:1 fermions:1 calculations:2 john:1 final:1 gives:2 exactly:1 zeroth:1 x2:2 than:1 third:1 double:1 zero:2 annihilation:1 future:2 rederiving:1 amplitude:2 were:1 rewrite:1 any:1 angle:1 built:1 ypx:1 deexcitation:1 take:1 lectures:1 begin:2 normal:2 clearer:1 cummings:1 pair:2 considered:1 mechanical:2 physics:1 fact:1 show:6 purely:1 solutions:1 wigner:6 find:1 q1:36 q2:8 based:1 dp1:2 state:1 only:1 attained:1 hope:1 continuity:1 normalizations:1 above:4 get:8 df:1 de:2 2me:1 report:1 dt:7 procedures:1 dp:3 dq:2 prime:1 arxiv:1 yield:1 aec:1 signify:1 imposing:1 ωq1:5 relative:1 p21:1 result:2 p22:1 brazil:1 said:1 tensor:1 written:5 identification:1 between:1 approach:2 terms:4 interchangeably:1 einθ:1 attention:1 however:1 moyal:6 p2y:2 suggested:1 both:3 cos:2 last:2 density:4 equal:1 quantization:9 unb:1 hω:3 expression:6 relevant:1 co:1 conclude:1 ca:1 harmonic:6 publishing:1 px:3 py:3 ai:1 much:2 expected:1 ph:6 choose:1 field:3 understand:1 spin:3 those:1 p2:6 p1:12 brasilia:2 value:1 will:7 suppose:1 viii:1 thus:1 encountered:1 quantize:1 movements:1 develop:2 perform:2 make:8 same:10 complex:1 quant:6 defines:1 φn:3 development:1 literature:3 upon:3 usually:1 realm:1 pδq:1 eigenvectors:2 task:1 schr:5 modes:2 approached:1 solve:1 sets:1 coordinate:1 left:1 proposed:1 half:4 obtain:2 ideas:1 identify:1 using:5 conclusions:2 interested:1 transformed:2 occurring:1 transformation:12 momentum:1 generalized:1 real:2 format:1 showing:2 possible:3 vacuum:1 immediately:1 apart:1 like:1 serves:1 δq:8 continue:1 steps:1 arbitrary:1 spins:1 mathematical:2 because:1 methods:3 classical:15 creation:1 q22:1 ourselves:1 eiθ:1 equivalent:1 conventional:1 step:1 found:2 imaginary:1 deriving:1 about:1 important:1 act:1 considerations:2 previously:1 into:2 h1:1 obtaining:1 nothing:1 everyone:1 references:1 operator:7 ei:2 bosonic:1 ellipse:1 intention:2 xpy:1 bosons:1 was:2 function:7 but:1 made:1 instructive:1 wish:1 ωt:2 us:2 liouville:3 retaining:1 problem:3 define:2 similar:1 called:1 touchstone:1 mechanics:6 constant:2 defined:7 abstract:1 formalism:5 universidade:1 physical:1 again:2 functions:7 completeness:1 when:4 schwinger:1 application:1 other:1 ambitious:1 papers:1 acceptable:1 picture:1 excitation:1 dq1:1 a1:5 a2:5 variable:1 implies:1 together:1 n1:1 n2:1
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quant-ph9511043.txt |@word partial:1 consider:1 brownian:6 leads:2 scalar:1 entropy:7 go:1 remarkably:1 preserves:1 calculate:1 deterministic:3 tr:1 environment:8 quasi:1 th:8 include:1 presently:1 desirable:1 wave:2 electron:1 four:1 presented:1 hartle:1 small:1 generalize:1 programme:2 employing:1 measurable:1 approximation:4 zero:2 dynamics:1 requiring:2 spectral:1 what:1 nonlinear:4 sub:1 blum:2 section:2 interactions:2 above:1 international:1 degree:1 respectively:1 concepts:1 here:1 behaviour:1 reported:2 separation:1 strong:2 equations:3 cern:4 study:2 studied:1 experience:1 published:1 action:1 jackiw:1 inducing:1 polonica:1 collaborating:1 apply:1 univ:1 standing:1 superpositions:1 working:1 suppl:1 next:1 classically:3 nucl:2 therefore:1 type:1 von:1 today:1 becomes:1 odinger:1 cases:1 high:2 quantized:1 work:2 oscillator:3 fock:1 tracing:1 following:1 states:1 effectively:2 purity:1 regions:1 pure:1 instead:2 may:1 derived:1 tied:1 reflect:1 produce:1 physik:2 short:1 attempt:1 dynamical:1 effective:2 higgs:1 correlation:1 zakopane:1 order:2 tomboulis:1 over:1 experiments:2 including:2 pointer:1 thank:1 ln:1 tori:1 coordinates:1 production:3 degrees:1 systems:7 mail:2 spreading:1 non:2 landau:1 effects:2 acta:1 nov:1 university:4 traced:1 sufficiently:2 universit:2 d47:1 subsystem:1 energy:4 gaussian:5 related:4 frequency:1 expect:1 quantum:25 our:1 transitions:2 es:1 out:1 matrix:2 rev:2 chaos:12 induced:5 39b:1 arizona:4 theory:5 barrier:1 localization:1 trˆ:1 necessarily:1 hep:2 transition:2 decohering:1 motion:8 impure:2 exponentially:1 corrections:2 configurations:1 first:2 initial:1 iht:1 theoretische:2 nonperturbative:1 directly:1 open:2 long:2 temperature:1 introduction:1 nondissipative:1 behaves:1 system:7 their:1 intermediate:1 brevity:1 variational:3 final:1 twopoint:1 cornwall:1 part:3 representing:1 regensburg:5 third:1 double:3 fm3:1 matter:1 contrary:1 self:1 potential:2 resembling:1 heisenberg:2 begin:1 towards:1 kam:1 regular:3 connected:1 phase:1 dens:1 flow:1 physica:1 irregularity:1 feynman:2 principle:1 exp:1 mechanical:3 physics:2 thomas:2 phenomenon:4 show:2 supported:2 friction:1 infrared:2 find:1 tdhf:5 slow:1 based:1 situations:1 explicitly:1 integrate:1 equilibrium:2 regularly:2 gev:1 dependent:3 zurek:1 dyn:1 cannot:1 new:4 report:1 evolution:2 fields:4 arxiv:1 wightman:1 tuned:1 underlying:1 gell:1 lny:1 observed:3 enhanced:1 mechanically:1 interacting:2 functionals:1 state:4 closed:1 between:1 fermi:1 approach:2 terms:2 however:4 omn:1 vernon:2 extent:1 observable:1 dates:1 according:1 energies:1 mann:1 otherwise:1 minima:1 presumably:1 relevant:2 nonrelativistic:1 simple:1 coexistence:1 dimensional:3 semiquantum:9 considers:1 conference:1 decohere:1 described:2 due:1 been:1 elze:7 ph:3 prototype:1 dots:1 corresponding:1 both:2 sufficient:1 coherent:1 observe:1 understand:2 renormalizable:1 solid:1 near:1 behavior:1 drives:1 tunneling:1 unitary:1 coupled:3 chaotic:2 refs:1 thus:1 formalism:1 make:1 radiation:1 poincar:2 complex:3 quant:2 higher:1 literature:1 trajectories:1 effect:3 hans:2 hartree:1 schr:1 modes:2 poland:1 well:3 claims:1 model:3 puzzle:1 obtain:1 ch:2 previous:1 rapid:1 density:4 irradiated:1 lett:1 theorem:1 breaks:1 cf:1 test:1 vacuum:1 mod:1 semiclassical:2 like:1 particle:6 follows:1 reduces:1 yields:1 neumann:1 classical:7 back:1 scale:1 lead:1 electromagnetic:1 behave:2 proc:1 refer:1 properties:1 freedom:2 introduces:1 involving:1 extensions:1 germany:2 homogeneous:1 into:2 functional:4 down:1 references:2 institut:2 additional:2 there:1 fast:2 analyze:1 sections:1 naturally:1 function:1 trying:1 vne:3 october:1 whether:1 ur:2 tucson:2 limit:3 fluctuations:2 autonomous:1 b436:1 fluence:1 associated:1 abstract:2 influence:1 chao:1 general:1 single:2 exist:1 wavelength:1 az:2 regime:2 functions:2 no:2 amounts:1 detail:1 field:15 department:2 tpr:2 picture:1 excitation:1 in2:1 generated:1 important:1 coupling:1 thermalization:1 packets:1 together:2 time:5 observables:1 decoherence:11 requires:1
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quant-ph9512002.txt |@word proposition:2 monte:4 unavoidable:1 partial:1 consider:7 penrose:1 maximum:1 global:2 blanchard:5 integration:2 switches:1 eds:1 mild:1 concept:1 generalize:1 foundations:2 go:1 sci:1 theorems:1 gj:1 gi:7 scr:1 compact:3 whose:6 preserves:1 careful:2 depend:1 tx:12 re:1 tt:26 deterministic:11 tr:16 posteriori:1 preprint:4 environment:3 uniqueness:13 program:1 infinitesimally:1 manifolds:1 th:4 under:4 stochastic:18 eβ:13 worth:1 norm:3 conservation:1 ty:4 finkelstein:1 comm:1 ψt1:12 g1:1 very:1 brownian:2 schur:1 percival:1 compacts:2 wave:5 every:17 should:2 entries:2 cook:2 experimentally:1 emphasized:1 difference:1 matrices:7 condition:2 paz:1 dim:3 induced:1 hamiltonian:4 did:2 knight:3 notes:1 t2:2 prolonged:1 t1:1 try:1 discrete:1 differential:5 recall:1 markov:5 optics:8 der:1 martingale:6 zn:3 aρa:1 zi:2 miller:1 htm:1 measurable:1 sign:2 jump:9 consists:2 second:2 evaluated:1 pass:1 rigorous:3 invariant:4 qmc:1 radon:2 carlo:4 canonical:1 even:2 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quant-ph9512005.txt |@word scl:15 consider:4 similarity:1 hats:1 results:1 gy:1 generalize:1 localized:4 simon:1 calculate:1 a19:1 corrections:1 pˆt:1 under:4 anharmonic:3 belonging:1 far:1 wave:9 electron:1 perelman:1 nieto:4 difference:1 condition:3 hamiltonian:5 solution:7 large:5 discrete:1 vector:2 indices:1 zk:2 iexp:1 rigorous:1 dynamics:3 zr:1 appear:1 expressed:2 3c:1 subtracting:1 filled:1 here:1 along:2 equations:2 change:2 differential:1 obtained:2 search:1 generalizing:1 institute:1 vectors:1 action:2 jackiw:1 uniquely:1 danger:1 imaginary:4 conventional:2 remains:2 negative:3 hilbert:1 explicitly:1 usp:1 theoretical:1 more:1 operators:4 normalized:1 particular:1 known:3 me:1 deformed:1 equation:8 oscillator:4 ik:4 values:1 dec:1 root:1 example:1 claim:1 dxt:1 states:7 assumptions:1 degenerate:1 sense:1 iφ:1 hydrogen:2 requirements:1 discussion:1 recovers:1 write:1 acta:1 fourdimensional:1 oscillators:3 after:1 hence:3 plane:1 dynamical:1 sh:3 negligible:1 representation:1 order:6 helv:1 interpretation:2 ith:1 over:1 nauenberg:1 its:4 group:1 symmetry:2 coordinates:1 complex:3 systems:4 jacobi:3 ours:1 averbukh:1 maximal:1 non:7 hamilton:3 multidimensional:1 now:3 eigenvalue:3 2v:1 equality:1 university:1 2x:1 sufficiently:1 2g:1 2m:6 2i:1 mean:2 domain:1 square:1 energy:3 related:2 constitute:1 frequency:1 quantum:7 our:5 eq:20 rez:2 space:2 restricted:1 furthermore:1 rev:6 re:2 acting:1 rn:1 ref:3 math:4 i2:3 linear:5 localization:1 ecl:9 mω:4 quasiperiodicity:1 estimate:3 definition:4 omit:1 times:1 motion:1 georgescu:1 consequence:2 first:1 there:2 probability:3 variables:4 number:2 restrict:1 utilized:1 simplified:2 least:1 mostowski:1 xr:2 xt:8 guess:1 glauber:1 leading:2 eqs:2 system:2 approximately:1 their:1 2ωk:1 gives:2 exactly:1 part:1 authors:1 specify:1 iωt:4 iωr:1 iteration:1 second:1 annihilation:2 determined:3 a40:1 ruelle:1 iωk:2 rewrite:1 ann:1 argument:1 seen:2 any:1 angle:1 depending:1 note:1 potential:3 generalized:2 so:3 coincide:1 heisenberg:1 pexp:2 twodimensional:1 ht:1 letter:3 formulae:1 torus:1 later:1 coincides:1 feynman:1 exp:21 physics:1 fact:1 show:1 find:2 ground:5 q1:1 q2:2 parameters:1 state:13 should:1 analytic:3 going:1 molecules:1 integrable:3 do:3 2mv:3 dyy:1 notation:1 means:1 carruthers:1 cannot:1 dy:3 during:1 dt:7 evolution:6 qr:2 arxiv:1 rotationally:1 investigate:1 qk:11 set:1 cimento:1 packet:4 namely:1 symmetric:1 outside:1 between:1 αk:4 conditions:1 terms:3 i12:1 confusion:1 weak:1 however:1 jr:2 distinguish:1 configuration:1 concentrated:2 observable:1 region:1 uncertainty:2 equal:1 hχ:2 con:1 arbitrarily:1 conclude:1 simple:2 harmonic:1 cy:2 moreover:1 amrein:1 basis:1 trajectory:4 been:2 mark:1 ph:1 define:1 cx2:2 multiplicatively:1 corresponding:1 subspace:1 spectrum:1 coherent:11 ˇt:1 general:1 applied:1 hωr:2 exponential:1 value:1 behavior:3 hωk:1 wroclaw:2 unitary:1 refs:1 them:1 ii:2 reads:3 property:1 eigenfunction:1 suggest:1 make:1 parts:1 quant:1 regime:1 see:5 i1:4 trajectories:2 purpose:1 onedimensional:1 poland:1 xˆt:2 without:1 position:2 obtain:2 shape:3 λk:2 eigenstates:2 density:3 point:1 concerns:1 transformed:2 lett:3 mod:1 hat:1 transformation:1 momentum:2 dqk:2 real:3 iθ:1 around:2 sums:1 term:2 simmons:2 using:1 formal:1 necessary:1 particle:1 follows:8 specific:1 arbitrary:1 fulfil:1 because:2 classical:11 some:1 a61:1 growth:1 examples:1 proper:1 pω:1 neglecting:1 ourselves:2 shapes:1 dense:1 avoid:1 does:2 minimal:2 rezk:1 uniformly:1 lose:1 relating:1 properties:1 haba:3 comparison:1 dˆ:2 discussed:2 dependence:1 o:7 ψr:2 ensure:1 into:2 integral:2 bound:1 references:1 sov:1 operator:2 support:1 initial:1 transform:1 way:2 function:6 form:2 but:1 construction:3 atom:2 ωx:1 fulfilling:1 ut:7 us:5 ωk:3 limit:10 problem:2 d22:1 defined:4 certain:3 abstract:1 describe:1 denote:1 dξ:1 pˆ:1 periods:1 formulation:1 moves:2 constructed:2 integrability:1 no:2 when:2 setting:1 papers:1 generates:1 ξr:2 ξt:2 generated:1 bounded:2 variable:1 coupling:1 assume:2 d20:1 interval:1 packets:4 dρ:3 time:7 nuovo:1
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quant-ph9512006.txt |@word villeurbanne:1 consider:1 chinese:1 gupta:1 particular:3 results:3 eds:1 ge:2 entropy:1 eη:5 devoted:1 arik:1 montonen:1 concerned:1 tr:4 presents:1 finally:4 monteiro:1 fermionic:1 tb:4 ın:1 p2:2 returning:1 conditions:1 choice:2 deformations:1 riemann:1 hamiltonian:2 turns:1 eigenvalues:2 degeneracy:1 prevent:1 employing:1 dealing:1 second:5 even:1 nonlinear:1 developed:1 deeply:1 section:2 expressed:1 above:1 new:2 satisfy:1 condensed:1 jagannathan:1 degree:1 respectively:4 here:3 illustration:1 obtained:1 study:2 studied:1 published:1 action:1 symmetrical:1 makes:1 useful:1 9a:1 9b:1 viz:1 total:1 use:4 takes:4 would:5 prove:1 monomode:3 quasi:1 france:1 therefore:2 m2:1 eϕ:4 associated:2 meyer:2 type:2 more:2 introducing:1 hermitean:1 operators:3 aware:1 eξ:13 varying:1 known:1 cases:7 iii:1 must:3 states:1 chaichian:1 quantized:1 deformed:8 equation:3 work:2 oscillator:1 fock:2 values:5 temperatures:1 following:3 rodrigues:1 give:1 high:2 vlachos:1 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quant-ph9512007.txt |@word represent:1 concept:7 evidence:3 consider:2 remarkable:1 similarity:1 reaction:1 roc:1 brownian:1 results:2 existing:1 eds:1 experiments:1 entropy:6 comments:1 expressions:1 denotes:1 contributions:1 reasoning:1 issues:1 sch:1 increase:1 const:1 calculate:1 financial:1 equivalence:1 containing:1 charge:2 does:1 those:1 whatsoever:1 hermann:2 stochastic:19 applied:3 far:2 wave:2 every:1 electromagn:1 summarized:1 instruments:1 experimentally:2 genesis:1 bringing:1 treating:1 entire:1 presented:1 did:3 louis:1 solution:2 large:4 discrete:1 vector:1 small:1 manchester:1 optics:1 commented:1 ver:1 century:1 loi:1 past:2 surrounding:1 second:3 cost:1 enclosed:1 further:1 linear:1 spectral:8 index:1 what:3 anton:1 section:1 expressed:1 looking:1 version:1 reproduction:1 above:1 new:4 consisting:1 temperatures:1 2kt:2 edited:1 full:1 exchange:1 never:1 lange:2 here:5 understanding:1 reported:1 free:1 groups:1 others:2 ratio:3 november:1 equations:5 appears:2 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quant-ph9512008.txt |@word concept:1 consider:5 squared:1 magnetic:19 alternatives:1 results:7 illustrated:1 localized:1 relationships:1 adelberger:1 depend:2 calculate:1 graph:1 subjected:1 rf:7 former:2 environment:1 finally:2 critical:1 tj:3 wmn:1 th:1 under:2 analogous:1 tb:4 tc:4 norm:1 ta:4 very:1 choice:1 orientations:1 ui:1 emphasized:1 difference:2 squids:3 immediately:1 level:3 leave:1 small:1 eigenvalues:1 measuring:1 smaller:1 periodicity:3 sin2:1 sign:2 feasibility:1 zero:1 evaluated:2 zz:1 qualitatively:1 even:4 will:2 intersection:2 errors:1 apparatus:2 incompatible:1 remain:2 expressed:2 current:5 experiment:2 new:2 order:1 contrast:3 paradoxical:1 edited:2 condensed:1 simultaneously:1 ibid:1 presilla:2 respectively:3 unobserved:1 understanding:1 behaviour:1 sandberg:1 objects:1 cos2:2 φmin:11 directions:1 path:1 along:1 strong:1 observing:1 galilei:1 obtained:3 zones:2 study:2 larger:1 allows:1 contradiction:1 polarimeter:1 simultaneous:1 stimulating:1 permit:1 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quant-ph9512009.txt |@word consider:3 varying:1 results:5 illustrated:1 entropy:7 edu:2 iu1:1 wholly:2 reasoning:1 issues:2 whose:3 certainly:1 depend:2 graph:2 environment:1 finally:1 program:4 device:1 elliptic:4 ti:1 supported:1 string:9 advantage:1 very:2 springer:3 induce:1 focus:1 affect:1 condition:1 hamiltonian:2 xyz:2 t2:2 solution:1 t1:2 large:1 convenience:1 vector:1 dealt:2 optics:2 related:2 upper:1 zn:3 approximation:2 rate:14 noise:1 dordrecht:1 algorithmic:11 dynamics:5 linear:2 even:1 what:1 iu2:1 appear:1 yakobson:1 sum:1 brief:1 experiment:4 above:1 sup:3 new:6 ever:2 consisting:1 contrast:1 edited:1 kicked:9 led:1 degree:2 respectively:1 never:1 component:1 here:1 understanding:2 behaviour:1 experimentalist:1 asymmetry:1 address:2 represented:2 z1:3 trans:1 rigorously:1 technical:1 studied:1 allows:1 completely:1 thoroughly:1 twamley:1 usually:1 history:1 studies:1 plotted:1 prints:2 schack:7 useful:1 projection:2 extra:1 castin:1 outcomes:1 unit:4 use:1 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quant-ph9512010.txt |@word gv:1 since:2 sci:1 rev:3 dynamic:4 results:7 gy:1 leads:1 incommensurable:2 expressions:6 compact:2 whose:2 dimensionality:1 re:3 paris:1 recurrence:3 quasi:1 does:1 under:4 amplitudes:3 very:1 wave:3 ginv:5 condition:5 unlike:2 hamiltonian:6 irreducible:3 discrete:1 leninsky:1 math:2 eigenvalues:3 anal:1 optics:1 upper:1 zd:4 sin2:3 direct:4 cosh:2 approximation:8 zero:1 masson:1 further:2 dynamics:5 fonction:1 spectral:8 established:1 nonlinear:4 essence:1 brackets:1 section:3 expressed:5 find:2 version:4 subspaces:6 new:3 3a:4 acknowledged:1 revealing:1 evolving:1 degree:2 fiz:1 respectively:1 even:1 here:1 chumakov:1 cos2:2 groups:2 represented:2 consideration:1 along:2 equations:11 change:1 obtained:4 search:1 institute:1 study:2 vectors:1 ay0:1 trial:5 products:1 poisson:1 action:3 suitable:3 studies:1 via:3 useful:1 9a:1 9b:2 unitarity:1 analyzing:1 apply:2 working:1 sake:1 finally:1 substitutions:1 msk:1 therefore:5 memory:1 taken:1 type:4 bethe:2 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