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quant-ph9708044.txt |@word sci:1 consider:5 vattay:1 results:4 gy:1 leads:1 controversial:1 whose:2 certainly:4 calculate:2 aug:1 finally:1 present:3 th:7 stable:3 analogous:1 include:1 p2:29 outside:1 very:1 rise:1 account:1 wave:3 reinterpret:1 every:2 experimentally:1 continued:1 disturb:1 immediately:1 did:1 turns:2 leave:1 eigenvalues:1 der:1 consistent:1 prediction:2 past:3 second:3 further:2 dynamics:1 mj:9 belief:1 even:1 what:2 ˆt:2 stands:2 giving:1 brief:1 consistently:1 above:5 lifshitz:1 new:6 consisting:1 satisfy:2 respectively:4 component:2 here:1 grundlagen:1 directions:1 along:1 strong:1 appears:2 change:2 remarks:1 institute:1 changed:1 reason:1 experience:2 simultaneous:1 usually:1 hospitality:1 suitable:4 changes:3 ψp2:8 uniquely:1 inference:4 extra:1 merely:1 explained:1 apply:2 standing:1 conventional:1 would:5 dalibard:1 ψr:10 hilbert:2 few:1 call:4 therefore:5 m2:24 themselves:1 theoretical:2 separated:6 ρˆm:3 becomes:1 under:1 odinger:2 validity:1 berlin:1 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quant-ph9708045.txt |@word concept:4 sci:1 consider:10 vattay:1 φp2:13 results:8 gy:2 existing:1 leads:1 controversial:1 c2:1 consists:1 follow:1 expressions:1 whose:3 certainly:7 depend:2 calculate:2 aug:1 description:1 contained:2 nonlocal:1 german:1 finally:3 otv:1 th:7 stable:3 analogous:2 include:1 applied:1 fax:1 advantage:1 outside:1 very:1 rise:1 springer:1 wave:8 reinterpret:1 tantalizing:1 under:1 fall:1 telling:1 experimentally:3 continued:1 disturb:2 doesn:1 hamiltonian:2 did:1 turns:2 list:1 solution:2 leave:1 solved:1 settle:1 phase:1 succession:1 eigenvalues:1 der:1 20th:1 prevent:1 strongly:1 work:3 tel:1 consistent:2 sin2:4 measurable:2 past:3 imply:3 further:3 dynamics:1 mj:9 quite:2 haake:1 spectral:1 established:2 what:7 errors:1 ˆt:2 stands:9 apparatus:1 giving:2 section:2 probably:1 consistently:1 above:8 lifshitz:1 new:12 satisfy:2 deduces:1 respectively:5 learn:1 component:3 here:4 atoms:2 following:1 cos2:3 grundlagen:1 along:1 strong:2 appears:2 change:6 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quant-ph9708046.txt |@word code:3 consider:5 rev:5 results:1 commute:2 entropy:18 kato:4 consists:1 maxπ:2 optical:1 devoted:1 const:1 aug:1 ohya:4 iii:1 technique:1 tr:7 contained:1 kβ:1 under:3 analogous:1 case:15 conjecture:1 orthogonal:3 far:3 frequencies:1 rise:1 every:1 application:2 condition:2 entire:1 randomness:2 level:1 bn:3 who:1 noiseless:3 vector:4 math:3 small:2 eigenvalues:4 trs:4 optics:1 still:1 upper:6 says:1 estimates:3 direct:3 rate:3 cost:1 infimum:1 further:1 remarkably:1 peredachi:2 linear:1 spectral:1 index:1 plays:1 appear:2 diag:2 section:1 decoding:1 above:1 sup:4 new:8 consisting:1 ibid:2 jointly:1 address:1 represented:1 standard:1 appears:1 deduced:1 obtained:2 sending:3 remark:1 generalizing:1 barnum:4 institute:1 vectors:8 allows:1 amount:1 resulting:2 schumacher:10 proof:10 makes:1 york:6 appropriately:1 equivalence:2 projection:3 family:2 bounds:1 nonseparability:1 plenum:2 decrease:1 pp:21 apply:2 establish:1 unit:4 conventional:1 additive:3 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quant-ph9708047.txt |@word cosines:1 sch:1 rev:3 focus:1 illustrated:1 computation:4 particles:5 aug:1 young:1 factoring:4 those:1 th:1 caused:1 analogous:1 sent:1 applied:1 amplitudes:2 advantage:1 very:1 results:1 electron:1 every:2 difference:2 logarithmically:1 presented:1 experiencing:1 proposals:1 integrated:1 discrete:1 convenience:1 small:1 enhance:1 optics:1 2πmt:2 second:1 further:4 implemented:1 spectral:1 what:1 sum:6 experiment:6 above:1 increasing:1 method:1 coefficient:1 simultaneously:2 respectively:1 never:1 here:3 others:1 path:1 sine:4 change:1 obtained:2 increments:8 suitably:1 shift:10 larger:1 amount:1 periodic:2 products:1 permit:1 proportionality:1 implement:2 fourier:9 useful:1 instr:1 flexibility:1 summation:3 apply:1 total:3 planck:1 linearly:1 readily:1 use:1 figure:1 would:6 probabilities:2 positive:2 contains:1 arms:1 loops:5 ψj:1 nucl:1 ψi:4 therefore:5 jonathan:1 until:2 today:1 more:4 entrance:1 outputs:2 tested:1 needed:2 particular:1 actual:1 must:2 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quant-ph9708048.txt |@word represent:1 partial:1 sch:1 crucial:1 results:5 leads:1 served:1 consists:1 sci:1 unobstructed:1 consider:1 looking:1 certainly:2 aug:1 laid:1 send:1 answered:1 efficiencies:1 those:1 include:1 case:5 amplitudes:1 very:1 sciences:1 wave:2 electron:1 putting:2 difference:1 condition:2 illustrated:1 vibrational:1 level:1 did:1 notes:1 applicable:1 ascertaining:1 laue:1 leave:1 small:2 der:1 concluded:1 upper:2 employing:1 dealing:1 filled:2 zero:2 cost:1 further:1 implemented:1 port:4 even:6 what:1 rate:1 brackets:1 section:3 thickness:1 experiment:11 above:1 cording:1 replaced:1 method:3 slabs:4 full:2 simultaneously:1 ibid:1 whose:2 respectively:1 aten:1 never:1 here:3 hours:1 reported:1 objects:46 groups:9 boron:1 galileo:1 path:8 principle:1 imperfections:2 change:1 obtained:6 institute:1 involved:3 larger:2 reason:1 thicknesses:1 amount:1 resulting:1 loop:1 poisson:1 pick:1 action:1 transmittance:1 diameter:2 useful:1 inducing:1 namely:1 outcomes:3 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quant-ph9708049.txt |@word consider:2 similarity:1 results:2 roy:1 montr:2 grateful:1 expressions:1 aug:1 equivalence:6 young:1 quasi:1 those:2 very:1 witten:1 putting:1 interpreting:1 partitions:1 school:2 level:3 experiencing:1 list:1 hartle:2 mλ:1 degeneracy:1 zn:2 zb:1 second:3 haag:1 canonical:18 even:4 appear:1 sum:1 celebrated:1 brief:1 above:2 new:2 satisfy:1 degree:2 respectively:1 shankar:1 here:2 brooks:1 represented:1 ratio:1 appears:1 obtained:2 studied:1 suggests:1 permutation:5 usually:1 hospitality:1 suitable:1 makes:1 involves:1 schur:4 use:1 positive:1 contains:1 next:1 nucl:1 therefore:1 type:1 definition:1 composite:1 operators:3 constructs:1 berlin:1 particular:1 known:5 cases:1 springer:1 quantized:2 work:4 det:4 following:2 example:1 stated:1 relativistic:1 sps:7 india:1 states:4 degenerate:4 sense:2 sought:1 verlag:1 rather:2 tableau:1 srinivasan:1 coleman:1 parabose:2 algebra:1 may:1 collection:3 doplicher:1 advocated:1 dynamical:1 spectra:1 explicit:4 correspond:2 so:2 polyakov:1 order:2 xj:3 kostka:1 developed:1 interpreted:1 statistical:1 cole:1 excitations:2 its:1 sλ:4 group:6 exclusion:2 energies:2 interesting:1 systems:5 non:5 kamefuchi:1 oxford:1 sχ:1 manybody:1 easily:1 term:1 by7:2 university:2 hamiltonian:1 establishing:1 possibilities:1 turns:1 2m:2 2n:2 mean:1 homogeneous:2 energy:2 mackenzie:1 frequency:1 quantum:5 our:1 out:1 canada:1 shown:4 since:1 rev:11 denotes:3 particles:7 formula:1 ref:3 interchanging:1 theory:4 panigrahi:2 mω:1 possibility:2 completely:1 statistics:26 complicated:1 degeneracies:1 could:1 length:1 first:1 exotic:1 hyderabad:3 xi:10 parastatistics:1 xm:18 variables:1 number:3 another:2 sutherland:1 given:14 system:17 relations:2 indicate:1 california:1 listed:1 fermions:1 completed:1 exactly:1 proving:1 calogero:1 somewhat:1 x2:1 x1:17 than:1 greenberg:2 kind:1 annihilation:1 determined:1 doubly:1 well:2 spectrum:8 conjugate:2 close:1 seen:2 any:1 viewed:1 latter:1 physique:1 ideas:1 note:1 ideal:3 potential:1 green:1 begin:1 shall:1 falls:1 eaire:1 acknowledgements:1 βǫi:1 interacting:5 considered:1 clear:1 later:1 principle:1 exp:3 physics:2 fact:2 show:1 attempts:1 substituting:1 based:6 knowledge:1 monomial:1 only:1 explicitly:3 threefold:1 columns:1 familiar:1 de:2 words:1 prime:1 fields:1 arxiv:1 summary:1 qc:1 coefficient:1 see:1 recently:2 λi:3 best:1 murthy:1 roberts:1 commutation:2 symmetric:4 written:2 αe:7 limit:1 across:1 available:1 terms:2 however:1 comm:2 bose:10 p2y:1 p2x:1 restrictions:5 many:1 3j7:1 hω:19 context:1 expression:2 finds:2 comes:1 conclude:1 simple:3 harmonic:2 dimensional:1 directions:1 taylor:3 math:2 unusual:1 been:2 pf:1 ph:1 differently:1 arises:1 corresponding:6 denote:3 spin:1 present:2 case:9 ǫi:7 while:1 replaced:1 h3c:1 obeying:6 chernsimons:1 different:9 same:1 quant:1 grand:17 literature:2 laboratoire:1 differing:1 levels:1 recent:1 xji:2 messiah:2 thought:2 model:2 dimension:1 realised:1 being:1 alternative:1 λm:2 haldane:3 hall:1 macdonald:1 lett:4 mod:1 identical:2 possible:1 using:2 apart:1 particle:12 follows:1 often:2 creation:1 some:1 pacific:1 specified:1 nonzero:1 dimensions:2 extensively:1 equivalent:2 clarendon:1 hst:2 found:1 universit:1 integers:1 o:2 obeys:2 into:1 appropriate:2 references:1 scherer:1 elementary:2 rows:1 bosons:1 was:2 naturally:1 function:16 eal:2 but:4 sagan:1 made:1 us:1 grove:1 below:1 fermi:2 define:1 called:1 partition:23 defined:1 certain:1 general:1 single:10 formulation:1 functions:8 no:2 fixing:1 field:2 other:3 kinds:1 polynomials:3 a3:1 structure:2 governed:1 having:1 ohnuki:1 2mω:1 original:1 chaturvedi:2
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quant-ph9709013.txt |@word concept:1 consider:2 fa2:3 rev:5 results:1 leads:1 eds:1 devoted:1 alamos:1 th:1 stable:1 amplitudes:1 very:1 frequencies:1 rise:1 springer:1 affect:1 implying:1 solution:1 leninsky:1 small:1 optics:2 rate:2 further:1 eik2:1 eik1:1 theory:2 nonlinear:3 appear:2 brackets:1 expressed:1 ˆa:5 ˆb:15 ˆe:1 above:1 increasing:2 exchange:2 here:2 aˆa:1 free:1 institute:1 study:1 changed:1 domains:1 matos:1 private:1 condensates:3 apply:1 total:2 unit:2 seligman:1 takes:2 would:1 choosen:1 means:4 type:3 los:1 fb2:3 becomes:1 operators:5 under:2 visibility:8 particular:3 account:1 vladimir:1 deformed:7 science:1 equation:3 modified:1 following:2 ions:1 give:2 process:1 states:5 numbers:1 arise:1 sharp:1 tan:1 provide:1 get:1 how:2 varies:1 symposium:1 parameter:1 l873:1 mat:1 may:4 max:2 oscillators:5 after:2 spot:2 containing:1 stefano:1 fa:1 fb:1 produce:2 waves:1 types:1 man:5 maintain:1 correlation:1 interpretation:1 developed:2 over:1 interpreted:1 course:1 through:2 guadalajara:1 existence:2 systems:1 quant:1 might:1 deformation:3 introduce:1 walls:2 effects:4 now:2 discuss:1 term:1 always:1 traced:1 vibrations:2 2a:1 2b:1 each:3 universit:1 mean:2 domain:2 generation:1 energy:1 bradley:1 frequency:2 quantum:3 eq:6 out:1 shown:1 tombesi:1 space:3 interference:10 indipendent:1 attracted:1 istituto:2 induced:1 shows:1 linear:4 gardiner:1 fisica:3 possibility:1 reason:1 interaction:1 eventuality:1 could:7 concrete:1 hence:1 onto:1 interact:1 first:1 there:2 laguerre:1 set:1 another:2 given:2 rewritten:1 revival:1 hyperbolic:1 introduction:2 leading:1 eqs:1 their:3 realization:1 gives:2 collapse:1 trapped:3 moscow:1 july:1 representing:1 than:1 determines:1 second:1 submitted:1 amplitude:1 were:1 russia:1 argument:1 say:1 any:1 min:2 self:2 mechanism:1 k2:2 k1:2 take:4 tool:1 scripta:1 condensate:2 revivals:1 observation:1 nonlinearity:9 ko:5 physica:1 proceedings:1 points:1 principle:2 exp:2 fact:1 lebedev:1 phenomenon:2 intensity:1 show:2 marmo:4 purely:1 solutions:3 wigner:1 should:1 only:2 factor:1 ˆf:1 di:6 de:1 expectation:1 report:1 collisional:4 evolution:2 fields:12 arxiv:1 including:1 ik2:2 ik1:2 multiplying:1 sep:1 physically:1 depends:1 result:2 biedenharn:1 macfarlane:1 phases:1 commutation:1 pattern:6 consequence:1 symmetric:2 enough:1 αe:1 between:3 cancelling:1 terms:1 attention:1 bose:2 atoms:1 both:3 cos:1 according:1 context:1 filho:1 dipartimento:1 atakishiyev:1 considering:1 described:1 aˆ:6 due:2 been:3 cosine:2 interest:1 ph:1 harmonics:1 corresponding:1 coherence:2 coherent:3 case:5 exponential:1 pacs:1 value:1 will:5 suppose:1 property:1 characterizing:1 della:1 vogel:1 mexico:1 characteristics:1 thus:1 iv:1 cond:1 zaccaria:4 different:3 formalism:1 italy:3 anymore:1 generic:2 cross:2 same:1 clearly:2 reachable:1 arguments:1 investigated:1 see:1 singapore:1 sudarshan:2 hand:1 fringes:2 superpose:1 modes:3 nucleare:1 well:2 davis:1 patterns:1 perugia:1 world:1 vibration:1 wright:1 other:5 lett:4 easy:1 heidelberg:1 momentum:1 iφ:1 showing:2 entangled:1 using:3 mod:1 like:1 alternatively:1 camerino:3 specific:3 yields:1 sezione:1 2iκ:1 classical:1 creation:1 phenomena:1 oscillations:1 provided:1 affects:1 does:1 provides:1 beating:1 mode:1 inserting:1 pr:1 noise:1 scientific:1 bb:1 wong:3 properties:3 introduces:1 dependence:2 collett:2 wolf:1 introduced:1 slightly:1 communication:1 into:3 within:2 obtaining:1 appropriate:1 references:1 einstein:2 initial:2 start:1 anderson:1 lot:1 function:7 form:5 some:1 but:3 matematica:1 atom:2 collapses:1 coupling:1 paolo:1 intuitive:1 characteristic:1 inside:1 us:2 called:1 int:1 abstract:1 describe:2 influence:3 ar:1 nazionale:2 hamiltonian:7 physical:3 materia:1 no:2 na:35 nb:18 when:1 field:4 setting:1 conclusion:1 picture:2 superposition:4 time:6 polynomials:1 important:1 structure:1 longer:1 mancini:1 remarked:1
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quant-ph9709014.txt |@word represent:2 concept:1 consider:5 ceases:1 varying:1 results:1 quadrature:1 entropy:1 inverse:1 calculate:1 deterministic:2 tr:7 environment:6 quasi:1 does:1 under:4 stochastic:5 insights:1 orthogonal:2 rise:1 springer:2 entire:1 unlike:1 hamiltonian:5 issue:1 solution:6 large:3 solid:1 vector:1 small:1 optics:3 application:1 smaller:2 aρa:1 det:6 consistent:1 obsolete:2 ornstein:1 jump:2 second:8 enclosed:1 further:1 linear:1 even:2 index:1 what:2 nonlinear:3 rate:1 brackets:2 diag:2 axes:1 ρr:2 above:2 new:2 consisting:1 y2:1 edited:2 simultaneously:1 burnett:1 equals:1 here:5 behaviour:1 threads:1 represented:1 along:1 strong:1 equations:9 change:1 increments:1 parameters:1 studied:1 resulting:2 cessation:1 plotted:3 technique:1 useful:1 namely:1 plenum:1 wiu:4 rρ:2 apply:1 planck:1 plot:3 projector:3 would:2 prove:1 remains:5 give:3 properties:1 monotonically:1 call:2 therefore:2 more:2 relax:1 clearly:1 becomes:3 operators:2 stable:1 odinger:1 berlin:2 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quant-ph9709015.txt |@word supersymmetrical:1 consider:4 magnetic:21 results:2 leads:1 commute:1 edt:4 chair:1 depend:2 worth:2 straightforward:1 orthogonal:1 implicitly:1 springer:1 wave:6 electron:7 witten:1 nieto:1 exact:1 condition:1 hamiltonian:10 gebra:1 solution:10 solved:1 vector:2 eigenvalues:2 originally:1 degeneracy:1 wronskian:2 sukhatme:1 fold:2 second:3 further:2 even:1 established:3 tkachuk:4 section:3 uniform:2 axial:1 ukrainian:1 new:6 satisfy:4 eksp:1 component:1 here:1 iσy:1 const:2 along:1 xα:1 equations:3 implicit:2 ukraine:1 studied:2 reports:1 action:1 studies:1 jackiw:1 useful:1 iet:1 total:2 establish:2 linearly:2 eiωt:1 eψ:1 next:1 nucl:2 noting:2 therefore:1 usp:1 theoretical:2 more:3 introducing:1 operators:3 odinger:2 clue:1 berlin:1 varying:2 known:3 iii:1 must:1 account:1 ma:1 equation:36 oscillator:2 remain:1 itself:1 obvious:4 following:9 example:1 f1:15 f2:14 give:1 calculation:1 states:1 junker:1 axis:2 provide:1 samsonov:1 explains:1 algebra:7 may:1 parallel:1 constants:1 man:2 sz:11 dynamical:2 explicit:1 darboux:1 so:1 representation:1 order:1 help:2 indeed:2 paper:5 statistical:1 satisfies:5 before:1 group:1 malkin:1 fiz:3 solving:1 parts:1 choose:3 mail:1 lz:10 supersymmetry:9 non:1 obtaining:1 introduce:3 franko:2 equidistant:1 they:3 now:1 easily:1 term:2 2s:1 university:1 2f:1 2eb:3 2i:13 arxiv:1 ei:3 ed:5 energy:1 ea:8 related:1 eb:3 inhomogeneous:1 extended:1 ey:1 ex:1 quantum:5 our:1 shown:3 rev:2 linear:1 moskow:1 khare:2 motion:26 isotropic:1 teor:1 first:3 symmetry:4 variables:2 number:1 angular:1 surveys:1 introduction:1 unknown:1 system:1 relations:6 their:1 iay:1 bagrov:1 πx:1 gives:2 exactly:1 supercharges:26 solenoidal:1 iωt:1 zero:3 annihilation:2 str:1 were:2 ktf:1 treated:1 maharana:1 ann:1 generalization:1 rittenberg:1 convenient:2 note:8 potential:3 take:1 degenerated:1 electric:10 opposite:1 systems:1 connected:3 commutation:4 χs:1 considered:3 ef2:1 ko:2 exp:1 mechanical:2 physics:2 fact:1 relation:2 solutions:5 substituting:2 superalgebra:1 ground:3 state:4 only:2 generators:1 do:2 notation:1 dependent:6 de:1 lviv:4 aim:1 dt:2 fields:7 differential:1 factorization:1 nauk:1 contain:1 fixed:1 set:2 constructing:2 sep:1 see:5 result:1 eaα:1 satisfying:1 axially:1 currently:1 symmetric:1 written:7 timevarying:1 recently:1 reproduced:1 ikz:2 attention:1 p2z:1 both:3 ua:2 taking:1 equal:1 σz:1 hψ:1 σx:1 expression:1 simple:2 corresponds:1 dimensional:12 pole:1 cs:3 considering:1 basis:3 pz:1 three:1 pb:1 much:1 ph:1 define:1 obtained:6 direction:1 supersymmetric:3 commutes:1 concerning:1 coherent:1 c2:4 c1:4 spin:2 present:3 case:23 look:1 pacs:1 truax:1 value:1 will:1 nonstationary:23 iy:1 vi:1 thus:6 them:1 iv:1 ii:1 eigensolutions:1 examined:1 πx2:2 susy:8 ib:1 ie:4 pis:1 pauly:1 same:1 complex:2 quant:1 pauli:14 independent:4 used:2 moment:1 levels:1 purpose:1 potentials:1 normalization:1 schr:2 well:2 analysis:1 without:2 components:2 usual:1 obtain:5 eigenstates:2 except:1 iω:6 conjugated:1 lett:2 easy:1 nicolai:1 solvable:1 transformation:1 momentum:2 eigenvalue:2 read:1 february:1 harmonic:2 i2ω:4 using:7 unique:1 follows:3 yields:1 integrals:11 arbitrary:1 ivan:1 stationary:9 therein:1 because:1 methods:1 deal:1 creation:3 some:2 choosing:1 scale:1 cooper:1 electromagnetic:4 shall:2 does:1 journal:1 although:1 eiω:2 bx:1 bz:2 about:1 pα:2 extension:1 dependence:1 introduced:4 fulfil:1 into:2 iπy:1 integral:11 krive:1 references:2 operator:2 there:2 question:1 way:4 was:8 function:7 form:6 hp:2 but:1 russian:1 true:1 directed:1 applying:2 consist:1 us:5 problem:3 attaches:1 similar:1 calculated:2 mechanics:1 constant:3 nauka:1 defined:1 certain:1 abstract:1 generating:1 exist:1 formulation:1 ay:4 ax:5 az:1 check:1 physical:2 functions:1 no:1 when:1 field:23 details:1 papers:1 conclusion:2 problems:1 generated:2 variable:1 kostelecky:1 together:1 investigated:1 time:14
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quant-ph9709016.txt |@word monte:1 sci:1 dynamic:1 results:2 eds:2 follow:2 localized:2 particles:2 calculate:1 tail:1 flopping:4 resources:1 division:1 vǫ:2 returned:2 straightforward:2 very:1 stroud:1 wave:38 manipulated:1 experimentally:1 exact:2 condition:1 vibrational:1 accompanying:1 positions:1 sliding:1 large:2 discrete:5 vector:1 eigenvalues:2 optics:2 upper:3 renormalized:1 pulse:7 approximation:3 rate:4 noise:1 displays:1 dynamics:4 carlo:1 spreading:1 linear:1 even:3 trapping:2 dunn:1 goes:1 new:2 ever:1 method:1 multitude:2 outgoing:1 full:1 gathered:1 component:1 here:3 atoms:3 ranges:1 explore:1 address:1 equations:5 appears:1 photochemistry:1 institute:2 involved:1 changed:1 allows:1 zener:2 p2:4 resonance:5 studies:1 emerge:1 useful:1 scales:1 suddenly:1 scaled:1 visible:2 issue:1 linearly:1 franck:2 takes:1 would:1 analytic:2 asta:1 zewail:1 escapes:1 finally:1 ψn:3 ψm:1 type:2 theoretical:2 today:1 more:3 preparation:1 becomes:1 envelope:1 odinger:1 validity:3 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quant-ph9709021.txt |@word consider:6 forbidden:1 results:2 leads:3 roy:2 generalize:1 consists:1 follow:1 gj:1 gi:1 whose:1 acting:1 groundstate:4 those:2 under:3 applied:2 straightforward:1 very:1 rise:2 choice:1 witten:1 nieto:1 condition:8 presented:1 turns:1 solution:7 large:2 discrete:1 science:1 small:1 eigenvalues:4 superalgebras:1 dutra:1 sign:1 second:3 gn:1 odd:1 even:1 will:6 morse:1 section:6 indian:2 en:23 above:8 international:2 method:1 contrast:1 confluent:1 degree:2 respectively:3 nen:1 here:7 ranges:1 ansatz:1 xγ:3 standard:1 xε:1 obtained:5 search:1 roychoudhury:1 institute:1 allows:1 perelomov:1 oschl:1 varshni:1 via:5 useful:1 family:3 hermite:1 tools:2 planck:1 unit:1 plot:1 use:2 asymptotic:1 would:3 remains:2 positive:6 contains:1 properties:7 ψn:32 therefore:2 type:3 theoretical:1 more:1 lowering:2 becomes:4 operators:28 odinger:2 berlin:2 particular:2 known:4 cases:4 must:1 springer:2 tunnel:1 recall:2 equation:4 oscillator:26 regularity:1 remain:1 obvious:2 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quant-ph9709022.txt |@word represent:1 partial:4 priori:1 rev:9 magnetic:3 out:3 results:7 threaded:1 leads:1 eds:2 gd:1 generalize:1 philosopher:1 controversial:1 doted:1 consists:2 excludes:1 compose:1 terms:1 fellowship:1 sharvin:1 technique:1 tr:2 environment:5 charge:3 those:2 under:1 td:45 case:4 random:1 amplitudes:3 very:2 rise:1 wave:7 blockade:2 electron:21 suggests:1 resonant:2 affect:1 difference:3 entire:1 transmission:14 issue:1 evd:7 qpcs:2 small:5 gqd:1 oscillation:1 qubit:1 tec:4 direct:3 rate:5 plenum:1 enclosed:1 pass:1 further:1 approached:1 even:5 what:1 nano:1 interactions:1 dephasing:15 expressed:1 find:4 current:6 experiment:6 gefen:1 above:2 new:2 increasing:1 dwells:1 condensed:2 simultaneously:1 respectively:1 concepts:1 modify:1 here:1 free:1 directions:1 path:15 standard:2 equations:1 change:1 obtained:1 incoming:2 ot:1 institute:1 shift:1 study:5 studied:1 miniature:1 chemical:1 resulting:1 stressed:1 usually:1 resonance:1 changes:1 composed:2 via:3 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quant-ph9709023.txt |@word consider:4 caused:1 forbidden:2 decays:1 bandgap:1 results:3 leads:1 grateful:1 consists:1 contributions:1 centers:1 relationships:1 whose:3 inverse:2 technique:1 contained:2 nonlocal:3 monotonically:1 γn:1 excluded:1 under:2 tg:1 supported:1 string:13 straightforward:1 outside:4 far:1 frequencies:8 images:1 wave:5 emphasized:1 rapidities:9 pumping:1 condition:3 level:3 positions:1 solution:2 large:2 vector:1 small:2 eigenvalues:1 optics:1 upper:1 zh:1 pulse:7 ρl:1 approximation:3 second:2 traveling:1 dκ:1 odd:1 theory:6 even:2 interatomic:2 nonlinear:2 section:1 while:6 current:1 version:1 above:1 lifshitz:1 new:2 consisting:1 contrast:3 body:1 σaz:2 behavior:1 respectively:1 here:3 atoms:14 compose:2 ansatz:4 address:1 represented:1 consideration:1 along:1 quite:3 equations:4 obtained:3 tunneling:1 institute:1 study:2 studied:1 allows:1 periodic:1 resulting:2 lightwave:1 resonance:4 suitable:1 studies:1 9a:1 9b:1 highly:2 sgn:2 reflector:1 use:4 takes:1 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quant-ph9709024.txt |@word evidence:1 consider:12 similarity:1 caused:2 varying:1 dynamic:7 results:7 leads:8 gf:10 foundations:1 sears:12 expressions:4 contributions:7 cases:1 gh:1 devoted:2 whose:6 hv2:3 depend:1 calculate:2 transferred:1 tr:1 bragg:1 including:1 quasi:1 present:3 th:1 under:2 analogous:2 include:1 indicating:3 ingredient:1 case:22 straightforward:3 very:13 brownian:3 implicitly:1 reader:1 translations:1 dell:1 wave:9 sons:1 δgf:1 entries:1 experimentally:1 difference:1 coexistence:1 condition:1 trh:1 propagating:1 incoherent:26 immediately:1 hamiltonian:1 occurs:1 leave:1 evy:1 fourier:3 small:8 eigenvalues:2 optics:11 equation:23 configurations:1 approximately:1 direct:3 understanding:2 sign:1 approximation:9 go:1 second:8 value:5 subcollections:2 rigorous:2 further:5 dynamics:14 implemented:1 ba:1 even:3 index:9 plays:2 appear:1 apparatus:3 ˆx:30 section:10 offsets:1 near:1 wavelike:6 thickness:1 reminiscent:2 consistently:1 paragraph:3 subspaces:2 new:7 net:2 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quant-ph9709025.txt |@word magnetic:7 results:2 four:1 roy:1 scalar:1 computation:11 consists:3 involved:1 preserves:1 violate:1 alamos:3 environment:1 finally:1 th:1 stable:1 applied:2 very:3 frequencies:2 readout:1 manipulated:1 chuang:2 summarized:1 experimentally:4 matrices:1 squares:1 hamiltonian:1 positions:2 t2:5 t1:1 large:2 small:2 eigenvalues:2 p9:1 pulse:2 approximation:1 second:1 run:1 implemented:1 even:2 what:1 abd:1 3s:1 3i:6 experiment:10 above:1 new:2 d1:3 ever:1 consisting:1 paradoxical:1 raymer:1 respectively:1 component:1 desired:1 explore:1 selective:1 separation:1 relaxation:1 along:1 strong:1 observing:1 obtained:3 drx:1 compute:1 shift:2 allows:1 products:1 walther:1 pictorial:3 knill:1 resonance:4 fourier:1 delays:1 involves:1 control:2 useful:2 explained:1 highly:1 turchette:1 analyzing:1 frame:1 should:1 manipulate:1 use:2 takes:1 would:2 predictions:1 comparing:3 live:1 therefore:3 theoretical:3 today:1 more:1 optimizing:1 relax:1 composite:1 operators:2 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quant-ph9709026.txt |@word consider:4 remarkable:1 rev:5 magnetic:1 results:6 four:3 eds:5 manages:1 remarkably:1 preserves:1 violate:5 transferred:1 equivalence:1 nonlocal:20 vigier:4 asking:2 conditions:1 electron:2 every:1 hewlett:1 affect:1 condition:9 school:1 positions:1 button:3 tokyo:2 vector:2 jammers:1 inertial:1 configurations:3 work:1 tel:1 consistent:4 measurable:1 past:1 second:2 pass:1 theo:1 dynamics:2 odd:1 aptly:1 scientific:2 even:2 what:3 appear:1 incompatible:1 sum:7 axes:4 summers:1 ˆb:6 version:1 fractional:1 new:5 acknowledgments:1 contrast:1 satisfy:3 exchange:1 respectively:1 never:1 component:1 here:2 modular:3 others:1 directions:1 along:3 equations:7 nachr:1 deduced:2 box:2 sending:1 institute:2 vectors:1 allows:2 reason:2 later:1 prior:1 permit:1 action:3 bob:12 spacetime:2 involves:1 examining:1 regardless:1 addresses:1 outcomes:2 claredon:1 send:4 apply:1 causal:2 unit:1 use:2 would:5 probabilities:4 term:1 chooses:1 generate:1 definiteness:1 a53:1 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quant-ph9709027.txt |@word limited:1 sci:2 consider:1 rev:15 magnetic:17 asteroids:1 blanchard:1 edo:1 iτn:1 instantaneous:7 contributions:1 causes:1 reynaud:1 extra:1 whose:1 terms:2 equivalence:1 quasi:5 th:1 under:1 analogous:1 must:1 quasienergy:1 cm2:1 letokhov:1 p2:4 belonging:1 global:2 returning:2 very:2 frequencies:3 multi:1 iτ1:1 electron:2 crosses:1 every:3 resonant:1 nieto:1 difference:1 exact:2 condition:1 entire:2 incoherent:2 beam:5 hamiltonian:12 turns:1 t0:3 correct:1 vector:5 small:1 eigenvalues:4 concluded:1 quicker:1 specially:1 oscillation:1 trend:1 penetrates:2 motions:1 pulse:2 sign:1 approximation:1 threshold:1 second:1 cost:1 kaiser:1 rectangular:3 theory:2 even:3 will:3 axes:1 zhang:1 henceforth:1 experiment:3 pulsating:3 new:4 falling:1 method:1 contrast:2 simultaneously:2 excludes:1 respectively:1 nb0:1 spacing:2 adressed:1 slow:7 bogdan:1 observing:1 mex:1 wait:1 obtained:1 institute:1 involved:1 leaves:1 changed:1 leaving:1 suggests:1 periodic:8 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quant-ph9709028.txt |@word consider:4 illustrates:1 magnetic:7 separates:1 edo:1 illustrated:1 ge:2 into:5 amplified:4 scr:1 certainly:1 amplification:1 depend:1 departing:1 squeezing:6 th:1 under:1 maryland:1 eiα:1 case:5 advantage:1 returning:1 images:7 results:5 exact:5 condition:6 dim:1 hamiltonian:4 diverging:2 turns:3 t4:1 t2:1 solution:7 t1:1 discrete:1 vector:2 amplifications:1 eigenvalues:8 optics:1 uncovers:1 sturm:5 specially:1 sin2:4 second:3 realistic:1 further:2 odd:1 canonical:1 even:2 trivial:4 selected:1 zhang:1 henceforth:1 above:1 scientists:1 new:2 net:1 method:5 annalen:1 chaotic:3 focuses:3 simultaneously:1 feng:1 reported:1 simon:1 cos2:3 q12:1 along:1 bogdan:1 equations:2 mex:1 obtained:2 instituto:1 institute:1 studied:1 simultaneous:1 resulting:1 narrow:1 emerge:1 captions:1 yuen:1 coinciding:1 poyatos:1 clockwise:1 linearly:1 figure:1 would:1 positive:3 contains:1 ψu:1 calculation:1 therefore:1 m3:2 taken:1 theoretical:1 introducing:2 becomes:2 operators:1 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quant-ph9709031.txt |@word limited:1 consider:20 hint:1 magnetic:2 iib:3 dynamic:1 results:1 switches:3 eds:1 commute:1 follow:1 amplified:4 research:1 causes:2 rd:2 amplification:3 const:1 calculate:1 re:1 alamos:2 chances:1 finally:5 indicate:1 ti:9 tf:6 proceedings:1 un:1 tc:7 ta:119 division:1 distorting:1 orthogonal:3 far:2 mpo:1 rise:5 translations:1 differently:1 wave:29 under:1 hewlett:1 affect:1 emphasized:1 difference:1 exact:3 condition:7 states:1 four:2 school:1 exponential:3 hamiltonian:24 t6:1 cause:1 integrating:2 t2:2 solution:3 t0:20 t1:3 large:8 observables:1 phase:1 laur:1 eigenvalues:2 optics:1 noted:1 proof:5 locate:1 strongly:2 zo:3 tel:2 occurrence:1 probabilities:1 direct:8 approximation:1 second:4 design:1 halliwell:1 further:1 situated:1 even:3 what:2 errors:1 stands:1 rate:4 clock:93 giving:1 section:15 remain:1 localized:4 above:9 values:1 net:1 increasing:3 boost:2 method:2 mp:1 satisfy:2 wavefunctions:1 led:1 ms:1 degree:2 exchange:3 respectively:4 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