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quant-ph9812029.txt |@word our:1 horne:1 consider:1 ith:1 show:6 rev:2 integers:1 results:1 four:2 course:1 experiments:4 identify:1 mentioned:1 arrangement:1 its:1 before:2 derive:1 based:1 golshani:1 relativity:1 seems:1 negligible:1 nonlocal:1 haven:1 forms:1 source:1 only:2 going:3 theorem:5 stochastic:4 momentum:1 identical:1 them:2 dj:1 above:2 notation:1 very:1 db:3 possible:3 preferred:2 da:3 ble:1 cannot:6 know:1 integer:2 now:2 dr:1 condition:11 essential:1 school:1 necessary:1 like:1 particle:1 always:2 university:2 arxiv:1 unnecessary:2 qa:1 realistic:4 private:1 inequality:3 each:4 relation:3 works:1 reduced:1 function:6 requirement:1 set:3 often:1 people:1 imposing:1 violated:1 sin2:2 related:1 deflection:1 relative:1 result:2 quantum:8 escaping:1 satisfied:1 stapp:4 special:2 even:3 index:1 shown:1 runs:1 space:1 since:3 crucial:1 find:1 particles:3 specifications:1 state:2 qb:1 ra:7 rb:7 between:2 denoted:1 hold:1 appeal:1 shows:2 measuring:1 nearest:1 iran:3 theory:5 equivalent:1 arbitrary:1 here:4 am:1 no:2 separation:1 found:1 directions:1 along:1 hand:2 emits:1 bz:1 equated:1 box:3 definition:2 pairs:1 toward:1 equate:1 cqm:1 institute:1 many:1 could:1 impose:2 according:2 o:3 side:1 exemplifies:1 isn:1 usually:1 noticeably:1 suitable:1 studies:1 experimental:4 ch:1 spatially:1 although:1 bell:9 communication:1 variables:1 deals:1 number:3 proton:2 will:2 right:1 references:1 total:2 angular:1 illustrate:1 necessarily:1 working:1 prove:2 introduction:2 there:4 predictions:4 their:1 difference:1 assumption:3 therefore:3 azimuthal:1 ph:1 was:1 theoretical:1 θj:2 obtained:2 direction:3 corresponding:1 form:2 both:1 θb:21 some:1 θa:21 cos:3 but:1 tehran:3 actual:2 role:1 spin:3 experiment:2 rji:1 count:1 pacs:1 whether:2 ignorable:1 work:2 up:3 devices:1 reproduce:3 values:6 rbi:4 error:1 following:4 making:1 problem:1 dec:1 called:2 mechanics:2 separated:1 would:1 orientation:1 almost:1 certain:3 abstract:1 thus:3 denote:1 clauser:1 sense:1 technology:1 different:1 locality:11 large:1 travel:1 generally:1 sharif:1 write:1 sciences:1 other:3 quant:1 take:4 rational:2 department:2 mathematics:1 detector:2 conflict:1 conclusion:1 product:2 used:5 opposite:2 models:2 enter:2 functions:1 singlet:2 important:1 value:3 mechanical:2 pair:5 dichotomic:2 data:1 sides:1 don:1 assume:1 try:1 average:1 possi:1 rai:4 having:1 without:1 so:2 correlation:9 model:10 physics:4 original:1 fact:1
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quant-ph9812030.txt |@word measurements:2 consider:3 rev:5 results:1 four:4 go:1 referring:1 finally:1 present:1 late:1 ingredient:1 very:3 choice:2 putting:1 splitter:2 presented:1 did:1 turns:2 eve:5 leave:1 upper:5 direct:1 second:1 further:1 port:9 linear:19 even:1 what:3 essence:1 analogously:1 version:3 goes:5 new:2 consisting:1 paradoxical:1 simultaneously:2 respectively:1 component:2 here:1 iσx:1 cos2:1 path:10 along:1 obtained:1 sending:2 arrive:1 incoming:2 technical:1 shift:2 inspired:1 reason:1 action:1 bob:10 makes:2 appropriately:2 secure:2 transit:1 unitarity:1 linearly:2 use:1 takes:1 would:4 prove:2 probabilities:1 give:1 chooses:1 properties:1 going:1 therefore:3 type:2 more:2 formally:3 knows:1 becomes:2 labelled:1 particular:2 foundations:1 hold:1 producing:2 must:2 recall:2 originally:1 suggestive:2 itself:1 obvious:1 following:2 dec:1 example:2 proof:1 beautiful:1 compare:1 mirrors:3 bennett:7 india:1 states:10 performed:1 axis:1 information:3 notation:1 rather:1 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quant-ph9812031.txt |@word transitions:1 consider:2 images:6 switched:1 additionally:1 rev:10 forbidden:2 separates:1 focus:8 existing:2 deflector:1 controversial:1 sweep:1 go:1 follow:2 instantaneous:1 localized:1 millisecond:1 increase:1 concerned:1 technique:5 ketterle:1 pfau:1 essentialy:1 supported:2 finally:1 tk:2 th:1 under:3 tf:5 include:1 xtk:1 magnetic:18 indicating:2 random:1 advantage:1 very:6 activation:1 conditions:1 wave:3 axes:1 fall:4 experimentally:2 condition:1 cool:8 xxxvii:1 clouds:3 level:1 preparation:1 positions:3 having:3 applicable:1 t0:3 occurs:1 large:2 tunnel:3 small:4 enhance:1 drop:1 optics:3 application:12 smaller:3 force:8 broader:1 pulse:1 second:1 displays:1 further:5 even:3 what:2 trapping:4 rate:2 section:1 evaporative:1 near:5 current:3 experiment:7 above:1 new:4 falling:2 consisting:1 3d:3 agreement:1 full:1 led:1 promising:1 component:1 residual:1 atoms:91 deposition:1 selective:1 focused:3 andrews:1 separation:1 address:2 directions:2 ratio:7 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quant-ph9812038.txt |@word schumaker:1 consider:6 rev:11 riesenfeld:1 results:7 factorizing:2 whose:1 depend:2 γt:7 timedependent:1 include:1 hill:1 case:1 confirmation:1 hibbs:3 ermakov:3 song:2 rise:1 wave:19 husimi:1 difference:1 exact:6 hamiltonian:16 solution:8 t0:3 damped:1 speculation:2 unaware:1 force:4 haar:1 zero:1 canonical:1 even:1 trivial:1 pandey:2 agrees:1 above:1 new:7 method:6 satisfy:2 lee:3 respectively:1 cos2:1 address:1 path:1 along:2 equations:4 change:2 obtained:6 remark:1 study:1 studied:1 suggests:1 suggestion:1 action:1 changes:2 york:1 classification:1 hermite:1 yuen:1 univ:1 linearly:3 use:4 additive:1 prove:1 positive:7 negative:1 comparing:2 linear:2 m1:1 m0:2 taken:1 formally:1 becomes:1 operators:3 odinger:3 particular:2 known:2 cases:2 iii:1 me:3 account:1 equation:36 oscillator:28 reproduce:1 mw:4 making:3 example:1 νt:1 wang:1 give:7 states:14 numbers:1 βe:1 pure:3 answer:1 instead:1 sin:6 v02:1 may:7 oscillators:6 dx2:1 applications:1 fd:1 choice:3 constants:1 man:1 short:1 explicit:1 so:1 representation:1 order:1 developed:1 over:1 choose:1 interpreted:1 paper:1 through:5 looks:1 mentioned:1 satisfies:2 ln:4 lo:9 li:1 systems:11 mail:1 defining:2 into:1 dae:1 them:1 good:1 serra:1 combination:1 introduce:1 now:2 easily:4 term:3 university:1 level:1 found:6 2n:3 homogeneous:1 differential:1 ed:1 ea:1 w12:1 frequency:18 quantum:19 relates:1 special:1 shown:7 kiev:1 driving:4 cws:3 since:3 lagrangian:2 acting:1 socalled:1 izv:1 formula:1 correct:1 math:11 shows:2 theory:1 quite:1 complicated:1 eiαx:1 driven:14 positiondependent:1 motion:10 equa:1 u20:1 generalizations:3 first:3 probability:1 relate:1 variables:1 xf:2 transform:1 done:1 another:2 xp:17 george:2 given:16 hasse:1 introduction:1 system:41 relations:5 dt2:3 final:1 gives:3 explanation:1 exactly:1 part:2 x2:12 x0:1 than:1 cimento:1 second:2 annihilation:1 determined:1 tion:1 undriven:3 nuovo:1 generalization:2 need:1 any:2 lin:1 instance:1 take:2 finding:3 korean:1 though:2 who:1 jul:1 phase:1 observation:1 considered:2 ko:1 feynman:3 exp:16 physics:1 fact:3 precise:1 show:1 lewis:8 relation:14 solutions:7 substituting:1 d2:2 find:11 ground:1 caldirola:2 parameters:2 title:1 hf:2 state:2 should:3 only:2 explicitly:5 constant:13 do:1 his:1 pulsating:2 dependent:18 satisfied:1 dz:2 combinations:1 dt:3 gen:5 evolution:1 arxiv:1 summary:2 dodonov:1 london:1 kernel:4 set:1 exists:1 our:1 national:1 depends:2 result:3 w1:2 w0:3 discussions:1 kerner:1 mechanically:1 written:3 between:5 invariant:2 approach:1 korea:1 terms:4 however:2 w02:2 ws:7 ji:3 cos:5 taking:2 equal:1 ck:8 among:1 cm:1 point:1 simple:14 ca:1 harmonic:28 ψn0:3 polynomial:1 respect:1 cu:2 pp:1 described:7 transformations:5 addition:1 px:7 been:7 interest:1 ph:2 define:3 dots:1 ψnc:1 arises:1 corresponding:4 oψ:1 kanai:2 coherent:1 systematic:1 denote:1 those:10 p2:8 exponential:1 might:1 mlo:7 evaluated:3 eigenstate:1 will:9 while:1 unitary:21 thus:2 non:2 iv:2 im:2 different:3 inc:1 belong:1 lett:1 same:2 quant:2 constructed:1 iγ:2 independent:3 used:2 v0:3 iv0:1 purpose:1 kim:6 recognized:1 schr:3 well:3 without:3 position:1 model:2 usual:1 unitarily:3 less:1 obtain:1 transforms:1 differentiation:1 eigenstates:2 previous:2 adding:2 conclusions:1 add:1 treatment:2 solvable:1 transformation:21 momentum:1 generalized:1 real:2 showing:1 integer:1 unique:2 necessary:1 reduces:1 abdalla:2 integrals:1 arbitrary:1 mcgraw:1 stationary:1 old:1 classical:16 some:1 examples:5 proper:1 recognition:1 provided:3 eiβ:1 dimensions:1 does:2 unit:14 prog:2 rep:1 equivalent:4 2m:5 simpler:1 o:2 guedes:1 soc:1 hnew:4 soh:1 h0:2 references:1 operator:16 proportional:3 uncertainties:1 there:2 question:3 u0:8 long:3 u2:1 start:1 quadratic:5 way:2 ψn:4 propagator:1 therefore:1 function:5 leach:2 yeon:2 form:1 reduce:1 adjusting:1 but:3 gaussian:3 serie:1 hn:7 hm:1 true:1 he:1 applying:2 annihilate:1 up:3 um:2 distribution:1 uf:5 uc:3 mechanics:3 ac:1 ae:1 defined:5 abstract:1 describe:1 general:4 formulation:2 check:2 physical:1 functions:16 kr:1 mostafazadeh:4 other:2 department:1 theor:2 models:1 problems:1 generated:1 important:1 pedrosa:2 independently:1 implies:2 pion:1 original:1 mass:30 time:21 furthermore:1
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quant-ph9812039.txt |@word consider:1 results:2 eds:1 scalar:1 p00:1 computation:1 zinn:2 whose:1 simon:2 technique:2 corrections:2 tn:1 quasi:1 stable:3 anharmonic:1 divergent:5 case:2 conjecture:1 string:1 hatano:1 very:1 choice:1 exact:1 condition:2 hamiltonian:18 louis:1 solution:1 large:7 discrete:1 herglotz:2 small:1 mo:1 upper:1 milton:2 smaller:1 grateful:1 ten:1 direct:3 sign:5 rate:1 rigorous:1 odd:1 appear:1 agrees:1 above:1 scientists:1 new:2 increasing:3 method:2 lee:1 here:1 behaviour:1 desired:1 along:1 strong:4 appears:1 obtained:2 rigorously:1 study:3 studied:2 periodic:2 action:1 makes:1 merely:1 private:1 replace:1 hardy:1 summation:3 establish:1 use:2 asymptotic:1 usa:2 positive:5 contains:1 negative:4 generate:1 nucl:2 therefore:2 bender:8 type:1 more:2 solitons:1 odinger:6 connecticut:1 excellent:2 hold:1 iii:1 bounces:1 justin:2 quartic:2 recall:2 equation:1 oscillator:2 theories:5 values:6 dec:1 example:1 proof:2 renormalization:1 chosen:1 calculation:2 bessis:2 high:1 numbers:1 sense:1 axis:1 provide:1 discussion:1 breaking:1 answer:1 acta:1 coleman:1 parameter:1 singularities:1 hence:1 plane:5 spectacularly:1 cambridge:1 stress:1 λ2n:1 spectra:1 st:1 so:2 decreasing:1 representation:1 order:12 typical:1 holds:2 dx:1 satisfied:1 approximants:2 paper:2 argued:1 derive:1 rapidly:1 fit:1 decay:2 energies:1 gerald:1 better:1 lt:1 pad:25 into:1 non:4 delocalization:1 p10:1 p11:1 oxford:1 s0:4 easily:1 february:1 university:3 infer:1 magnitude:1 found:1 soc:1 stieltjes:7 financial:1 series:10 energy:38 related:2 toda:1 quantum:3 operation:2 transitions:1 extract:1 shown:3 furthermore:2 rev:11 hill:1 conjectured:1 formula:1 ref:3 math:1 antiunitary:1 theory:10 monotone:2 discontinuity:1 diagonal:14 standard:1 york:1 carl:1 estimate:5 e0:1 dunne:1 consequence:1 first:5 symmetry:4 relate:2 instances:1 given:2 perturbation:19 leading:5 their:1 listed:1 calculations:1 variational:1 boettcher:2 exactly:1 prediction:1 part:8 pnn:5 x2:8 x3:5 than:2 coefficients:11 population:1 holland:1 double:1 distinguishes:1 second:1 were:5 powers:1 perturbative:1 fluctuation:1 summable:7 conventional:2 spectrum:5 studying:2 note:5 extracted:2 potential:2 band:1 accuracy:2 formulas:1 begin:1 who:1 guillou:1 polyakov:1 multiply:1 subtracted:6 surprising:1 considered:2 average:3 phil:1 stronger:1 yang:1 exp:2 camb:1 physics:4 notion:1 fact:2 precise:2 saying:1 b46:1 rayleigh:5 herbst:1 helv:1 relation:4 find:3 ground:19 finally:1 based:1 much:2 state:20 analytic:2 ambiguity:1 factor:1 employed:1 hamiltonians:2 means:2 familiar:1 reversal:1 despite:1 applying:1 dt:1 gen:1 arxiv:1 computed:3 physically:1 see:1 p21:1 result:4 p22:1 discussions:1 recently:1 acts:2 best:2 said:1 inequalities:2 ways:1 positivity:1 symmetric:4 enough:1 various:2 between:2 invariant:1 across:1 terms:1 originated:1 wu:1 rapid:1 jj:1 group:1 last:1 limits:1 condmat:1 many:2 storrs:1 context:1 interesting:1 contribution:1 expression:1 relevant:2 conclude:1 corresponds:1 dimensional:1 simply:1 sequences:4 moreover:1 ct:1 pt:7 addition:1 been:7 strategy:1 describes:1 expected:1 ph:1 pn:3 ann:2 pm:2 schr:6 direction:1 observe:2 determination:1 external:1 p2:8 pacs:1 periwal:1 evaluated:2 while:1 behavior:4 engineers:1 identical:1 averaging:1 wkb:4 thus:2 instantons:2 ii:2 im:4 recursion:1 divergences:1 complex:8 quant:1 several:1 grows:1 higher:3 hermiticity:2 used:2 cubic:1 numerical:9 effect:1 uses:1 potentials:2 kleinert:1 lower:1 off:7 acknowledgement:1 nevertheless:1 well:1 analysis:4 left:1 being:1 accurate:1 superconductors:1 obtain:2 summed:1 previous:1 cut:5 alternate:2 add:1 lett:5 solvable:1 gave:1 real:13 aspects:1 harmonic:1 five:1 press:1 using:5 advanced:1 mod:1 flux:1 vortex:1 yields:1 mcgraw:1 decimal:2 mathematical:1 parity:1 because:3 methods:3 sequence:5 bounce:3 deduce:2 growth:3 hurst:1 choosing:1 table:6 gross:1 lead:1 novelty:1 integration:3 inequality:1 provides:4 unstable:10 proc:1 inserting:1 biology:1 performed:2 bn:13 agreement:4 expansion:5 restrictive:1 orszag:1 depinning:1 although:2 p32:1 imaginary:10 refers:2 properties:4 integers:1 about:2 would:2 shnerb:1 o:2 langer:1 le:1 perturbed:1 rendered:1 h0:2 washington:1 hermitian:4 right:1 amsterdam:1 support:1 there:4 lovett:1 dispersion:4 width:2 borel:8 way:1 was:2 function:11 north:1 form:1 but:3 convergence:2 line:1 true:1 coupling:4 absent:1 compute:2 places:2 us:1 problem:3 constant:1 int:1 determinant:1 evidence:3 chap:1 check:1 analyticity:3 no:2 when:3 vanishes:1 reality:1 field:5 other:2 department:3 kinds:1 thirring:1 meisinger:1 60n:2 implies:1 faster:1 hollowood:1 nelson:2 time:1 requires:1 once:6
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quant-ph9812040.txt |@word concept:1 consider:3 brownian:1 results:6 leads:2 roy:1 commute:1 go:1 subjected:1 deterministic:1 nonlocal:1 th:1 stable:1 stochastic:7 ta:3 case:1 far:1 wave:6 experimentally:1 difference:1 fractal:1 presented:1 t3:5 deals:1 evy:8 differential:2 intermittency:6 work:1 jump:1 second:2 further:1 dynamics:3 even:2 what:1 apparatus:2 giving:1 section:3 a234:1 above:1 fractional:1 new:1 increasing:1 jumps:1 satisfy:1 simultaneously:1 answers:1 tracks:1 departamento:2 along:1 equations:4 obtained:6 instituto:2 generalizing:1 root:1 benatti:1 allows:2 studies:1 pearle:4 useful:1 br:2 apr:1 scaled:1 wataghin:1 causal:1 unit:4 use:3 superpositions:1 working:1 next:3 few:1 therefore:3 usp:1 taken:1 more:3 company:1 odinger:3 particular:1 known:1 cases:1 iii:2 account:2 pursue:1 equation:11 des:1 theories:1 values:1 shlesinger:6 following:2 spontaneous:6 grassi:1 compare:1 give:2 process:7 indicates:1 attain:1 council:1 6m2:2 occur:1 csl:8 noises:1 provide:1 ghirardi:5 feature:1 delay:1 how:1 instead:1 parameter:2 eatoires:1 may:2 different:2 consequence:2 fb:1 law:3 stress:1 attempt:1 lines:1 correspond:1 so:2 fundamental:1 order:1 typical:1 interpretation:12 developed:2 paper:2 london:1 statistical:1 its:1 before:1 kusnezov:2 decay:1 chosen:1 affine:3 gleb:1 exhibits:1 microscopic:2 systems:1 main:1 weber:2 freeman:1 non:6 processes:2 introduce:1 scaling:1 framework:1 tails:1 they:3 cep:2 now:3 term:10 realistic:1 2m:4 ifi:1 mean:9 square:6 prompted:1 energy:4 displacement:4 related:1 solution:1 frequency:1 ey:1 quantum:5 our:3 eq:1 fundamentally:1 space:4 tales:1 rev:8 research:1 induced:1 klafter:1 linear:1 localization:9 ısica:3 free:3 standard:4 besides:1 r2:1 collapsing:1 used:1 length:1 corrections:6 first:1 already:2 probability:2 variables:1 introduction:3 eqs:1 system:3 construct:1 white:7 gpr:4 gives:4 collapse:1 continuous:3 authors:2 x2:3 coefficients:1 diffusion:11 showed:2 zero:1 appealing:1 contrary:2 were:1 dang:1 visited:1 insightful:1 treated:1 rimini:4 fluctuation:1 correction:1 increment:1 studying:1 latter:1 responsible:1 take:1 analogy:6 broglie:1 led:3 involving:1 phase:2 clarifying:1 observation:1 considered:2 coincides:1 face:1 procaccia:1 exp:1 velocity:2 beables:3 fact:1 quantity:1 phenomenon:1 show:1 escobar:3 relation:1 find:1 based:1 parameters:2 should:1 only:1 do:4 his:2 beable:10 localizing:1 df:2 familiar:1 de:8 db:9 fluid:1 da:1 dx:1 dw:10 dt:7 dp:1 evolution:7 continuum:1 arxiv:1 acknowledgments:1 investigate:1 stuff:1 pioneering:1 vink:3 ser:1 reference:2 turbulent:4 observed:1 see:1 enhanced:4 recently:1 brazil:2 exploited:1 nuclear:1 sites:1 between:5 villiers:1 notice:2 terms:2 nature:1 however:1 distinguish:1 both:1 interpretations:1 providing:1 last:2 acknowledge:1 according:2 context:1 comes:1 comment:1 bell:3 character:1 aspect:1 corresponds:2 walk:2 dimensional:1 exploit:1 respect:1 described:1 analogies:1 west:1 due:1 been:2 quickly:1 reduction:1 describes:1 basic:1 degrees:1 ph:3 po:2 flight:4 fokker:1 those:1 p2:5 pacs:1 euclidean:1 while:1 behavior:2 unitary:1 thus:1 iv:1 ii:1 ih:1 santos:2 perform:1 things:1 fractals:1 same:1 paulo:4 quant:3 mixtures:1 finite:1 status:2 independent:2 extended:1 estadual:1 drives:1 campinas:2 hand:1 phy:1 infinite:1 mech:1 schr:3 well:2 analysis:1 bohm:3 without:2 position:5 model:16 dimension:4 usual:2 proposed:2 being:2 mandelbrot:4 obtain:5 assigned:1 identify:2 questions:1 turbulence:10 macroscopic:3 eorie:1 stratonovich:1 cut:1 density:2 point:2 had:2 discontinuous:1 transformed:1 lett:2 input:3 momentum:7 fluctuating:1 possible:1 world:2 vague:1 necessary:1 particle:4 indication:1 conclusion:1 right:1 classical:1 towards:1 moreover:1 transport:2 provided:1 avoid:1 measurements:2 per:4 planck:1 does:1 proc:1 noise:11 rep:1 equivalent:1 revtex:1 although:2 found:2 hilbert:1 bz:1 gauthier:1 about:1 extension:1 instantaneously:1 freedom:1 anomalous:1 dependence:1 o:2 side:1 addition:1 introduced:1 soc:1 own:1 h2:2 into:4 within:1 integral:1 nonsense:1 references:1 presupposes:1 bulgac:1 comparing:1 support:1 there:2 fast:1 noticed:2 conservation:1 way:2 brazilian:1 naturally:1 function:6 medium:2 form:2 memory:1 but:2 cnpq:1 he:1 made:1 dψ:1 wish:1 us:4 hentschel:1 limit:1 problem:1 similar:1 called:1 mechanics:4 associated:1 fokkerplanck:1 defined:1 abstract:1 describe:1 ao:4 single:1 exist:1 typeset:1 universidade:2 physical:3 grw:5 locality:1 when:3 vanishes:1 other:2 nice:1 picture:2 unicamp:1 visits:1 chance:1 richardson:6 variable:1 independently:1 using:1 mass:2 nelson:2 time:5 walker:1 observables:2 laws:1 having:2
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quant-ph9812041.txt |@word concept:1 consider:4 aly:1 disk:1 re:4 finally:1 weyl:1 those:1 under:2 case:9 belonging:1 orthogonal:2 wave:10 tridiagonal:2 nieto:5 matrices:2 obvious:1 exits:1 hamiltonian:6 dxdp:2 solution:1 discrete:2 annihilates:2 truax:1 eigenvalues:1 noted:1 zh:1 sukhatme:3 alhassid:1 past:1 l2s:6 substituting:1 scientific:1 established:2 plays:1 morse:24 giving:1 sum:2 kais:1 above:6 overcomplete:1 new:10 method:3 contrast:1 otka:1 satisfy:3 full:1 respectively:1 here:10 address:2 along:1 strong:1 obtained:2 great:1 shift:2 allows:1 identity:4 inspires:1 bog:2 useful:2 classification:1 ipi:3 unit:1 use:2 additive:2 would:3 levine:1 positive:2 feh:1 hilbert:4 call:2 therefore:5 vi:1 type:1 theoretical:1 introducing:3 operators:18 pisma:1 berlin:1 particular:1 known:2 balantekin:1 iii:1 springer:1 defines:1 equation:3 work:3 oscillator:11 values:4 following:7 rodrigues:1 calculation:1 sense:2 confused:1 states:62 dxn:2 minimum:2 numbers:4 allowed:1 axis:1 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quant-ph9812065.txt |@word code:26 consider:6 chain:1 interference:1 results:2 gx:1 gf:2 entropy:1 consists:1 simon:1 paris:1 finally:2 th:4 conjecture:1 advantage:1 orthogonal:1 gz:1 corollary:1 every:3 matrices:4 condition:1 roy:1 leave:1 vector:4 small:1 upper:3 tel:1 estimates:2 rate:1 further:1 linear:4 even:4 appear:1 section:1 analogously:1 3t:2 above:2 sup:2 new:3 erieure:1 3d:3 satisfy:2 behaviour:1 growing:1 along:1 rue:1 obtained:7 remark:1 trans:6 involved:2 vectors:4 products:1 permutation:1 implement:1 via:2 family:2 f3:1 sloane:3 achievable:1 apply:2 total:1 use:1 additive:1 codewords:4 recalling:1 france:1 few:1 therefore:1 taken:1 duals:1 israel:1 ecole:1 submatrix:1 appendix:2 known:3 enst:1 des:1 mt:1 stabilizer:2 following:4 closing:1 dec:1 example:1 proof:7 f0:2 tau:1 f2:1 weaker:1 f4:1 f5:1 stated:1 vx:2 minimum:11 eng:1 provide:1 how:1 optimal:1 ashikhmin:1 map:1 product:1 fa:1 designed:1 lines:1 yielding:1 indeed:1 over:3 soc:1 paper:1 through:1 existence:2 satisfies:1 ieee:6 derive:1 group:1 fix:2 aviv:2 hzt:1 systems:1 gtx:1 mail:3 gtz:1 norway:1 easier:1 non:5 good:2 combination:1 hxt:1 steane:12 they:3 now:3 2t:2 easily:1 nationale:1 possibilities:1 found:1 2n:4 2h:1 2j:3 2k:4 el:1 weight:16 generation:2 fr:1 quantum:25 shown:1 rq:8 since:4 rev:3 rn:1 helleseth:1 shows:2 log2:5 theory:8 free:1 standard:1 sbe:1 definition:1 pairs:2 asymptotical:3 geometry:1 thing:1 length:4 tempting:1 hence:1 first:1 number:5 nested:1 least:12 open:1 size:2 given:1 introduction:1 leading:1 construct:4 their:5 gilbert:1 commutativity:1 3d2:4 exactly:1 consult:1 than:2 distance:16 second:3 hz:5 cohen:3 argument:3 bitwise:5 say:3 need:1 elsevier:1 clearly:1 lie:2 constructions:3 zero:5 min:2 efficient:1 lim:1 self:1 instance:1 take:1 multiple:1 extending:1 remarks:1 prove:1 analog:1 hamming:4 barrault:1 subgroup:1 notion:1 shor:7 show:1 relation:1 d2:2 d1:1 just:1 parameters:10 eigenspace:1 assertion:1 only:2 sylvia:1 notation:1 di:1 ones:1 words:1 qr:1 arxiv:1 yield:2 quaternary:1 contain:1 fixed:1 remains:1 relative:1 see:5 college:1 terms:1 griesmer:1 best:3 satisfying:3 tensor:1 written:1 geometric:1 approach:2 litsyn:4 recently:1 extend:1 however:1 erard:1 hypothesis:1 improve:2 suggested:1 both:4 equal:2 subcode:2 otherwise:1 point:2 simple:1 dimensional:1 table:4 better:1 pp:9 strong:1 commutative:1 union:2 three:1 pg:1 ph:2 correction:3 define:1 families:6 gap:1 c2:2 c1:2 irrelevant:1 present:3 case:3 chap:1 behavior:1 error:7 vg:3 almost:2 thus:1 them:1 il:1 dual:1 dimacs:1 ready:1 vz:2 binary:11 different:1 macwilliams:1 belong:1 same:3 any:3 quant:1 arguments:1 pauli:1 largest:1 survey:1 several:2 higher:1 fairly:1 extended:1 lower:1 dimension:2 varshamov:1 left:1 distances:1 calderbank:6 proposed:2 less:1 being:1 obtain:1 sabbatical:1 using:3 previous:5 generator:5 wei:2 improvement:2 belongs:3 combine:1 lett:2 easy:1 theorem:16 constant:1 guarantees:1 generalized:13 increases:1 integer:1 bit:1 correcting:4 apart:2 particle:1 follows:4 δq:15 yields:3 university:1 parity:1 sketch:1 classical:1 some:3 examples:1 respect:1 proofs:1 nonzero:1 vol:9 tsfasman:1 steps:1 proc:1 minimal:1 hsh:1 illustration:1 constructive:1 although:2 2m:23 feb:1 chapter:1 most:1 theorems:2 distinct:2 stand:1 introduced:1 primitive:1 inclusion:1 previously:1 bound:7 pair:1 references:1 rows:3 support:2 there:1 lond:1 nonconstructive:1 inner:1 analyze:1 was:2 function:1 hx:5 form:3 construction:5 implies:1 ramat:1 highest:1 info:6 coset:1 applying:1 ux:9 uz:9 bounds:6 us:1 below:2 limit:1 ac:1 proved:2 abstract:1 levenshtein:1 denote:1 engineering:1 exist:2 corresponding:1 inf:1 again:1 codes:40 completeness:1 no:3 rains:2 when:1 interested:1 electrical:1 department:1 generates:3 preceding:1 enlargement:2 generated:1 matrix:3 building:1 bch:2 together:1 weights:4 moreover:1
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quant-ph9812066.txt |@word represent:2 consider:6 similarity:1 magnetic:4 focus:1 leads:1 olive:1 scalar:7 commute:2 go:1 adhere:1 seemed:1 supposedly:1 depend:1 referring:1 subjected:1 presents:1 charge:4 those:10 under:7 kemmer:3 analogous:1 circumstances:1 equalities:1 apparatus:1 g7:5 applied:1 g5:8 confirmation:1 g3:6 g2:8 advantage:1 iǫt:8 very:1 pages:2 g9:8 wave:16 electron:1 emphasized:2 condition:2 generalised:1 hamiltonian:4 zeit:1 notes:1 t2:1 t3:1 t1:2 try:1 discrete:20 vector:5 yong:1 independence:2 relation:7 noted:2 cmp:1 application:1 unexpected:1 10b:1 dealing:1 consistent:1 10a:1 sign:3 translating:1 second:3 ivanenko:3 further:1 conclusion:1 established:2 what:1 nonlinear:1 plays:1 appear:1 tetrad:8 rationalized:1 supplied:1 fock:2 above:12 new:1 net:1 row:1 contrast:5 paradoxical:1 revealing:1 simultaneously:1 relates:1 respectively:5 ǫt:1 certainly:1 here:14 behaviour:2 asymmetry:1 ramsey:1 cart:9 separation:2 consideration:4 standard:1 equations:6 change:1 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quant-ph9812067.txt |@word wµ3:1 wµ2:1 wµ1:1 sci:1 consider:1 pointing:1 similarity:1 rev:16 magnetic:3 results:4 leads:2 roy:2 scalar:3 bais:1 rebbi:1 grateful:1 incorporation:1 expressions:2 gi:1 peshkin:1 relationships:2 content:2 certainly:1 violate:1 technique:1 tain:1 charge:3 arisen:2 under:4 analogous:5 forbidden:1 apparatus:1 applied:1 attempts:1 g4:3 g3:2 g2:3 g1:2 iǫt:3 very:4 rise:1 tacitly:1 wave:19 electron:3 rotational:1 every:4 formula:1 varshalovich:1 condition:4 four:1 presupposed:1 clouds:1 hamiltonian:2 proc:1 t2:1 solution:5 t1:1 try:1 discrete:11 vector:2 phase:1 independence:1 δf3:1 relation:2 noted:2 configurations:1 correct:1 work:3 10b:2 10a:1 sin2:4 direct:1 cosh:2 translating:1 zero:4 ivanenko:2 orthogonal:3 subtle:1 further:5 theory:4 index:2 what:6 nonlinear:2 essence:1 sub:1 tetrad:6 giving:1 section:3 11b:2 foregoing:1 ˆa:18 version:1 localized:1 above:10 values:11 net:1 method:1 contrast:4 satisfy:2 simultaneously:2 degree:1 fiz:1 respectively:4 never:1 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quant-ph9812069.txt |@word rev:20 global:2 results:1 quadrature:1 stochastically:1 γz:2 γy:4 γx:4 depend:1 technique:1 supported:1 squeezing:1 those:5 stochastic:24 case:4 probe:6 lations:1 very:3 frequencies:1 rise:3 replaces:1 sidebands:7 experimentally:3 difference:4 condition:1 level:12 knight:2 ryan:1 damped:2 large:1 dκ2:3 minimal:1 optics:1 equation:8 employing:1 ten:1 insignificant:1 consistent:1 sin2:2 approximation:2 zero:1 enhancement:2 chen:3 manipulating:1 dynamics:2 chem:2 even:1 diffusing:2 current:1 experiment:1 new:1 method:2 ibid:6 respectively:4 never:1 component:4 here:1 atoms:3 ionization:1 reported:1 amplification:2 cos2:1 aid:1 strong:6 observing:1 ρz:2 involved:1 study:1 products:1 real:3 resonance:9 narrow:2 scaled:2 glitch:1 modulated:2 takes:2 would:2 commun:1 remains:1 classically:2 noting:1 therefore:2 widens:1 theoretical:1 possible:1 γn:1 becomes:1 emission:2 transient:2 must:1 stabilized:1 science:1 challenge:1 work:1 values:2 ficek:1 dec:1 spontaneous:2 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quant-ph9812070.txt |@word 1st:1 gu:1 measurements:2 homomorphism:1 consider:2 chain:1 pairing:8 wreath:10 desirable:1 shor:3 leads:2 generalize:1 computation:7 consists:1 gn:3 row:2 simon:5 depend:2 calculate:1 james:1 finally:1 th:3 under:3 summarizes:1 applied:2 amplitudes:1 g1:3 orthogonal:3 very:1 implicitly:1 springer:2 otteler:1 results:1 corollary:2 worst:1 fall:1 exact:4 høyer:3 kerber:1 squares:1 conjugating:1 solves:1 presented:1 irreducible:5 huppert:1 solution:5 t0:8 solved:6 vector:2 science:2 small:1 shows:3 zn:2 smaller:1 occurrence:1 dealing:1 direct:4 suffices:1 matrices:2 fold:1 second:2 cost:1 design:1 evaluated:1 further:1 canonical:1 even:1 index:7 what:1 appear:1 iterating:1 section:7 brief:1 experiment:1 3n:1 subspaces:1 obvious:2 method:2 margolus:1 gruppen:1 component:1 equals:1 here:3 behaviour:1 groups:21 address:1 november:2 observing:1 z1:4 z2:14 box:3 remark:5 institute:2 recursive:2 leaves:1 vectors:1 allows:1 products:9 postprocessing:1 permutation:7 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quant-ph9812073.txt |@word consider:10 illustrates:3 caused:2 magnetic:1 stems:1 hamamoto:1 results:2 extensively:1 leads:2 roy:1 scalar:4 grateful:1 consists:2 spaced:1 contributions:1 c1:3 localized:1 sch:1 excludes:1 calculate:1 concerned:1 technique:1 charge:1 those:1 excluded:2 under:1 baranger:1 te:2 alternating:7 case:9 takes:3 very:6 implicitly:1 connects:1 wave:7 electron:3 every:1 chooses:1 chodos:1 difference:3 matrices:2 condition:2 entire:1 school:1 hamiltonian:5 did:1 ref:2 applicable:2 large:11 discrete:2 vector:1 ǫn:2 small:1 eigenvalues:2 bertsch:1 smaller:1 faculdade:1 consistent:1 coefficient:1 japanese:1 sign:3 nonessential:1 go:1 second:9 further:1 odd:4 even:5 trick:2 what:4 appear:6 brackets:3 sum:10 alternate:1 agrees:2 version:2 suspect:1 above:8 obvious:1 ground:1 ever:1 method:37 paragraph:1 body:3 respectively:7 applies:2 here:3 abandon:1 mev:1 situation:2 represented:1 consideration:1 along:1 sine:1 εn:1 logarithmic:1 violate:4 obtained:2 instituto:2 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quant-ph9812074.txt |@word consider:3 caused:2 illustrated:1 contributions:1 excludes:1 violate:1 presents:1 finally:1 chapt:1 excluded:2 te:1 amplitudes:2 straightforward:1 very:2 wave:1 conserved:1 entire:1 hamiltonian:3 turns:1 solution:1 large:1 discrete:1 small:1 eigenvalues:1 equation:4 says:1 faculdade:1 sign:2 second:3 will:1 what:2 appear:2 lt:1 above:2 waals:5 new:1 journal:1 coefficient:1 edited:1 zeits:1 exchange:2 respectively:2 here:1 atoms:6 expansion:1 strong:2 appears:1 interpret:1 obtained:2 instituto:1 shift:7 elaborate:1 reports:1 usually:1 hospitality:1 plenum:1 replace:1 logarithmic:1 summation:3 total:1 takes:1 positive:10 contains:2 visit:1 charge:1 calculation:1 explicitly:1 theoretical:2 more:1 validity:1 particular:2 known:1 hole:1 high:1 include:3 der:6 work:1 three:1 following:1 meet:1 dec:1 example:1 process:1 relativistic:8 confused:1 states:9 council:1 sense:1 hydrogen:4 end:1 rather:1 acts:1 polarizabilities:1 answer:1 instead:1 may:1 earlier:1 consequence:1 wrong:1 amparo:1 physik:1 engineering:1 natural:1 sectors:1 explicit:1 coutinho:1 so:2 fundamental:1 paulista:1 definitions:6 order:3 restriction:1 developed:1 over:1 perturbed:1 interpreted:2 london:5 argued:1 its:2 how:4 energies:1 interesting:2 absence:2 mention:1 hamilton:1 effects:3 they:3 nor:1 february:1 dirac:5 always:1 university:2 orthonormal:1 nonessential:1 differential:1 energy:24 feinberg:3 principles:1 related:4 operator:1 antiparticle:1 used:2 static:1 quantum:9 our:1 eq:2 ep:19 out:3 canada:2 shown:2 matrix:1 rev:3 research:1 particles:2 method:2 ref:7 correct:1 theory:13 ısica:1 differ:2 possibility:1 perturbation:6 york:1 e2:1 definition:1 interaction:2 discussing:2 creates:1 turn:1 vac:4 hence:1 already:1 suffix:1 number:1 wqm:6 done:1 force:6 given:5 medicina:1 antiparticles:2 rewritten:1 eqs:1 system:24 their:1 intermediate:4 calculations:2 molecular:1 gives:1 part:4 theorie:1 than:1 polarized:1 unfortunately:1 zero:2 matter:1 amplitude:2 treated:1 distinguished:1 paulson:1 function:1 occupied:2 depending:4 essentially:1 note:3 sciences:1 potential:3 take:3 forces:5 techniques:1 unperturbed:5 electric:9 wht:7 most:1 ht:4 pair:1 considered:1 clear:1 feynman:2 electrons:1 principle:2 physics:1 notion:1 quantity:1 supported:1 tecnol:1 relation:1 solutions:1 ground:2 funda:1 quoted:1 should:1 only:1 going:1 polarizability:7 do:3 his:1 notation:2 de:6 during:1 target:2 continuum:1 arxiv:1 summary:1 qe:1 qm:1 thanks:1 ignored:1 set:1 reference:1 clarified:2 toyama:1 see:1 result:1 w1:3 discussions:1 terms:4 subject:1 brazil:2 said:1 binds:1 state:9 mcmaster:2 between:5 complications:1 recently:1 burkholder:1 confusion:1 weak:1 however:1 suggested:1 both:1 sucher:8 limits:1 qft:4 ıfico:1 compton:2 equal:1 connection:1 und:1 casimir:2 distinction:1 argue:1 relevant:1 point:1 appeared:2 corresponds:1 cancel:1 constant:1 leads:1 basis:2 addition:1 due:1 been:2 micha:1 cient:1 treat:2 ph:1 compositeness:1 refered:1 received:1 influence:1 photon:2 remark:1 external:3 c1:3 contexts:1 ǫi:6 examine:1 value:1 trick:1 orica:1 vi:5 refs:6 binding:2 positrons:1 examined:2 different:3 apparently:1 make:1 same:1 paulo:4 shifts:2 quant:1 emphasize:1 pauli:2 literature:1 estadual:1 hand:1 ion:1 purpose:1 estado:1 recent:2 framework:1 polder:1 model:2 dimension:2 distances:1 l8s:1 just:1 obtain:2 atomic:1 ogico:1 scattering:4 yet:1 4m1:1 application:1 regarded:2 nacional:1 other:2 know:1 background:10 vacuum:18 press:1 using:1 like:1 particle:18 unnecessary:1 arbitrary:1 rearrangement:1 inter:1 stationary:1 therein:1 because:3 honored:1 often:1 creation:1 understood:1 electromagnetic:1 fapesp:1 assuming:1 conselho:1 equivalent:1 illustration:1 relating:1 refers:2 zur:1 about:1 discussed:2 desenvolvimento:1 range:3 raised:2 h0:6 within:2 integral:1 bound:12 negative:16 nothing:1 references:2 elementary:1 proportional:1 ontario:1 van:4 assumed:1 there:2 question:4 long:3 dispersion:4 start:2 low:2 way:1 was:7 lowest:2 complete:1 form:2 but:7 neutral:1 atom:4 cnpq:1 removed:1 he:6 inhomogeneous:1 whether:2 levin:1 systematics:1 up:1 us:5 ur:1 below:1 limit:2 problem:1 mechanics:2 associated:1 defined:2 abstract:1 am:3 ao:5 general:2 single:5 αe2:2 au:1 universidade:2 again:1 no:4 when:3 field:4 setting:1 papers:2 department:1 elements:1 pesquisa:1 retardation:1 important:1 nucleus:1 included:2 astronomy:1 longer:1 assume:1 nogami:1 equivalently:1 time:1 far:1
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quant-ph9812075.txt |@word concept:1 consider:2 results:2 four:1 commute:1 computation:1 consists:2 denotes:1 issues:1 whose:1 maximally:1 depend:2 pˆk:1 tr:2 young:1 environment:1 analogous:1 applied:3 supported:3 expressing:1 straightforward:1 orthogonal:2 far:1 hewlett:1 condition:1 trm:3 turns:1 solution:1 large:3 solved:1 vector:8 small:1 smaller:1 deutsch:1 10b:1 10c:1 10a:2 sin2:1 10d:1 second:2 cost:1 further:1 ues:1 even:2 will:6 what:1 projectors:1 multiqubit:3 sum:3 subspaces:5 new:2 3a:1 degree:1 respectively:3 teleportation:1 focused:1 cos2:1 separation:1 along:1 obtained:1 sending:2 great:1 antisymmetric:3 study:4 vectors:2 allows:1 leaving:1 p2:2 resulting:3 permutation:1 usually:1 symmetrical:1 conveniently:1 involves:1 plotted:1 via:3 useful:2 addresses:1 uncorrupted:1 outcomes:1 austria:1 achievable:2 apply:6 unit:1 use:1 superpositions:3 would:1 prove:1 covariant:1 positive:3 therefore:3 means:1 more:2 bennett:2 successful:2 becomes:1 operators:8 depolarizing:1 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