text
stringlengths 0
190k
|
|---|
quant-ph9806002.txt |@word essay:1 limited:5 concept:4 consider:13 represent:1 groundwork:1 novelty:1 focus:1 leads:1 eds:1 abner:1 proposition:8 polarizers:6 overlap:2 grateful:1 edu:1 bergmann:3 cases:7 inferences:1 whose:2 nous:1 depend:1 calculate:4 prejudice:1 spin:13 subjected:4 illustrates:1 interactions:1 finally:1 does:15 those:11 under:7 passion:1 maryland:2 include:2 tb:3 ta:4 case:58 belonging:1 returning:1 far:1 implicitly:3 rise:4 exception:1 stipulate:1 results:12 weighting:1 untenable:1 every:3 should:8 anonymous:1 arrow:2 affect:2 difference:2 exact:1 condition:23 four:3 obvious:1 level:1 turns:2 notes:1 t2:41 t3:1 t1:22 large:3 pα:1 convenience:1 vector:11 science:1 eigenvalues:3 drop:1 noted:6 histories:6 application:1 employing:2 says:1 core:1 miller:3 consistent:8 sin2:4 prediction:1 past:4 consists:6 second:7 rigorous:1 further:6 copenhagen:1 correspond:5 requiring:1 substitute:1 bold:1 even:7 established:1 what:12 appear:2 incompatible:1 giving:1 section:6 selected:33 abl:75 taup:1 expressed:1 debate:1 henceforth:2 version:2 tenable:3 above:15 conduct:2 new:4 fall:1 consisting:4 θcb:12 edited:1 1997a:8 s10:4 degree:1 respectively:2 quantifications:1 modify:1 here:2 s16:3 met:1 asymmetry:7 operating:1 cos2:10 lev:1 others:1 represented:1 causality:1 along:12 auxiliary:1 directions:3 appears:2 change:2 clarification:1 obtained:6 rely:1 exemplified:1 suitably:2 my:1 vectors:5 allows:1 qualify:3 commonly:1 ignoring:2 spheres:3 calculations:1 resulting:4 permit:1 action:14 antecedents:1 suitable:2 makes:1 criticism:1 appropriately:2 showing:2 formulated:1 shorthand:1 griffiths:7 family:1 exhibit:1 problematic:2 belongs:1 advisor:1 concurrently:1 logical:1 replace:1 county:1 put:1 addressed:1 analogous:1 logically:1 apply:4 total:7 establish:1 causal:2 truly:1 readily:1 use:15 lecture:1 usa:1 distinct:1 contains:3 predictions:2 next:1 discrepancies:2 comparing:1 live:1 doubt:1 call:8 therefore:14 typical:1 themselves:2 type:4 entails:1 reflects:3 more:10 possession:1 pβ:1 flaw:1 comparison:1 successful:1 becomes:3 apparent:1 occurred:5 validity:2 s9:2 s3:4 fixed:15 virtue:1 particular:5 known:1 foundations:2 objections:3 hold:8 ontological:3 must:19 me:1 md:1 account:12 uncontroversial:1 augment:1 indicates:1 postselection:3 originally:1 getting:1 discussions:2 modified:1 theories:7 labeled:1 anywhere:1 values:7 following:5 fulfill:1 root:1 example:15 proof:10 claim:11 compare:5 weaker:1 employs:1 figure:14 give:4 calculation:8 accepts:1 cited:1 arise:1 purposes:2 studies:1 states:14 effectively:1 mixture:14 performed:27 degenerate:1 phrase:2 interpreted:1 sharp:6 confuses:1 hereinafter:4 occur:1 calculated:1 axis:2 information:4 ones:2 s8:1 end:2 sphere:9 caption:1 rather:4 s2:23 discussion:6 holds:13 s7:4 s6:1 s5:3 s4:1 very:1 criterion:1 consist:1 pure:1 reject:1 instead:6 ordinary:4 constraints:1 parameter:2 ensemble:13 e2k:2 inputs:2 product:2 intended:1 microworld:1 may:6 overall:1 philosophy:4 derived:8 pqm:2 collection:1 1997b:1 reflect:1 hence:1 membership:1 plane:1 lay:1 demonstrating:1 cambridge:2 fi:3 fj:3 choice:2 data:2 referring:1 ambiguous:1 changes:1 discusses:2 natural:1 e21:1 e22:1 onto:1 description:3 explicit:5 yielding:3 introducing:1 element:3 fortunately:1 advocates:3 so:10 specifying:1 asserts:3 enter:1 definitions:6 subsequently:2 began:1 superscript:1 restriction:1 circularity:1 least:2 interpretation:17 numbers:1 indeed:4 over:2 move:1 vary:2 outset:1 argues:6 course:2 paper:4 including:2 statistical:4 committed:1 argued:5 statements:1 satisfies:2 still:4 its:4 putting:1 before:2 derive:3 symmetry:5 how:3 rejects:2 interesting:2 temporal:4 subensemble:5 exhibits:2 actually:25 aviv:2 systems:34 disagrees:1 mistakenly:1 covered:1 hidden:1 might:4 image:1 s1:20 maximal:1 non:14 factor:1 qualifies:1 views:1 obtaining:6 material:5 runs:3 number:2 process:3 effects:3 they:15 oxford:2 formulating:1 now:19 griffith:1 discuss:2 nor:4 suppose:1 worlds:11 term:2 indentity:1 stated:2 s11:2 always:2 university:6 hamiltonian:1 identified:4 inequivalence:1 iff:3 academic:1 truth:7 eigenvalue:7 found:8 bona:1 side:10 characterized:1 referred:7 individually:1 just:4 directly:2 weight:9 simplicity:1 experiment:8 there:15 1996a:9 1996b:3 applicable:1 fraction:2 obtains:2 measurement:97 quantum:46 our:5 happen:1 beyond:1 special:10 out:7 shown:7 precisely:2 closest:10 ejk:5 restricted:1 furthermore:1 since:22 crucial:1 denote:1 denotes:1 particles:4 re:2 asymmetries:1 ζi:8 denoted:1 formula:2 get:2 receiving:1 supports:1 correct:11 shows:1 earlier:4 theory:17 raises:1 written:1 differ:2 possibility:4 standard:1 difficulty:3 reason:1 amato:2 imagine:1 ask:1 intermediate:6 alert:1 e1:4 universally:1 e2:2 s15:3 definition:18 backwards:1 derivation:4 4a:3 via:8 could:2 omit:1 excluding:1 times:11 creates:1 appearing:1 disturbed:4 period:1 preselection:3 consequence:5 ture:1 facilitate:1 neglect:1 s14:2 first:14 xj:9 blackwell:1 intuition:2 xi:2 probability:47 succeeds:2 describes:1 variables:1 powerful:1 disregarded:1 nested:1 instances:1 philosophical:2 omission:1 simplified:1 specifically:2 proposing:1 impossible:1 dissertation:1 clarity:1 aharonov:8 passes:2 given:28 necessarily:3 rewritten:2 indicate:1 introduction:1 meaningful:1 observes:1 system:33 analog:3 their:7 assumption:7 brevity:1 too:2 statement:17 justified:2 final:10 gives:9 eigenvectors:1 assign:1 hypothetical:5 relationship:1 centered:1 reversed:4 exactly:2 park:1 immediate:2 direct:1 employ:1 coplanar:1 part:1 authors:4 july:1 than:8 lebowitz:4 aad:3 kind:3 determines:1 was:20 yet:3 zero:1 matter:1 future:8 contrary:2 polarizer:6 were:9 outcome:23 projections:1 pre:36 false:9 footnote:4 lines:2 cohen:13 argument:7 kastner:1 already:1 say:3 defending:1 need:2 seen:3 seem:1 counterfactuals:15 any:15 viewed:2 accounted:1 symmetrized:21 angle:2 mermin:2 depending:1 able:1 overcoming:1 note:10 mix:1 ideal:4 concerns:1 take:5 analogy:1 finding:2 subject:1 mit:1 residue:1 begin:1 fundamental:4 shall:4 arguing:1 albert:2 price:14 object:1 realism:1 falls:1 asymmetric:7 most:3 involving:2 25i:2 position:1 pair:1 decision:1 measured:24 why:1 inconsistency:1 sub:2 workshop:1 considered:7 clear:5 later:2 order:8 traditional:1 σb:1 symmetrically:7 error:1 mechanical:8 usual:7 physics:6 responded:1 fact:13 conditionals:4 incorporate:1 selection:26 invited:1 show:9 lewis:15 supported:1 defended:1 archimedes:1 relation:2 inconsistent:3 conditional:11 substituting:1 consequent:5 find:5 based:5 ensembles:22 e11:1 situations:1 e12:1 assertion:1 start:1 peculiar:1 only:25 explicitly:5 want:1 specify:1 ambiguity:4 postulated:3 employed:1 dispute:1 do:7 his:10 sense:4 goes:1 notation:2 exceptional:1 dependent:1 closeness:1 referees:1 quantified:1 retrodictive:1 satisfied:4 incompatibility:1 cannot:6 legitimate:1 words:2 despite:2 during:1 quantifier:1 conjunction:10 subscript:4 evolution:1 intuitive:2 held:2 approach:2 arxiv:1 comprising:1 yield:2 acknowledgments:1 imposed:1 e1k:2 redefined:2 common:1 though:5 ascertain:1 through:3 θab:10 θac:11 ψjk:1 view:4 intervening:35 requirement:5 set:7 reference:4 sep:1 physically:1 relative:1 differs:2 namely:2 individual:2 college:1 result:12 existence:3 fail:4 terms:16 unacceptable:1 best:2 definitely:1 fails:6 dropping:1 setting:1 incorrectly:2 inappropriate:1 ways:2 subsequent:5 review:7 eigenstates:1 symmetric:5 state:59 smallest:1 various:1 correctly:4 between:26 conceptual:1 probably:1 neither:5 reading:19 conditions:23 choose:2 publishers:1 recently:3 statistically:2 nature:1 legitimacy:1 component:3 notion:8 points:1 however:16 succeed:1 premise:1 distinguish:3 distribution:3 both:15 interpretations:4 brown:2 desired:1 σc:8 many:1 taking:1 trades:1 according:10 against:2 fulfilled:2 etc:1 connection:2 harvard:1 figures:1 context:1 faces:2 passing:2 argue:6 shanks:6 asked:1 experimental:1 permitted:1 cj:21 ci:7 uniformity:1 space:1 point:6 reasons:1 seems:1 corresponds:2 insist:1 analyzed:1 ab:1 simply:4 assertions:1 respect:4 throughout:6 factors:1 considers:1 baltimore:1 considering:3 pp:1 light:1 described:6 asks:1 basis:2 addition:3 arbitrary:1 three:3 been:28 strategy:1 much:1 z2:4 basic:2 timereversed:1 ph:2 pi:1 correction:1 define:3 refuted:2 box:12 direction:10 arises:1 corresponding:5 observable:41 quantities:5 sufficient:2 photon:14 essentially:2 readings:5 convention:1 angles:1 c2:13 c1:42 maximally:1 irrelevant:1 spirit:1 present:1 applied:6 noncommuting:1 novel:2 defining:1 means:1 value:6 will:20 while:3 preselected:8 replaced:1 applies:4 situation:8 property:2 region:3 procedure:2 correspondence:1 detailed:2 would:33 sorts:1 robert:2 thus:20 additional:3 equal:7 ii:12 24a:2 contradiction:1 orthogonal:3 alone:1 comments:1 full:1 different:10 verified:1 putative:1 justification:1 σz:2 perform:3 make:7 problems:1 satisfying:3 same:15 clearly:4 member:3 quant:3 arguments:3 mixtures:3 going:1 several:1 events:5 fide:1 independent:1 jeffrey:1 used:3 imply:1 see:10 trivially:2 upon:1 hand:10 viewing:2 assessing:1 uses:3 symmetrical:1 entanglement:1 invariance:1 judgment:1 identity:3 recent:1 relies:1 stipulated:1 recourse:1 center:1 expression:5 possessed:2 tel:2 well:5 orientation:3 analysis:1 vaidman:38 bohm:1 objection:2 solve:1 comes:1 components:1 easily:3 claims:4 consistency:1 stating:1 left:7 composed:1 permissible:1 proposed:8 less:1 being:17 generally:2 lorentz:1 obtain:5 mistaken:1 ideas:1 proposes:4 relevant:1 identify:1 potentiality:1 world:39 facts:1 brackets:1 projection:1 preprint:2 kluwer:1 instance:1 stalnaker:5 characterization:1 had:7 except:2 postselected:3 benefited:1 valid:5 propositions:1 usage:10 input:1 merely:2 generalized:2 identical:1 evaluation:1 references:1 depends:5 represents:2 read:1 z1:11 subensembles:5 advocate:1 posed:1 possible:22 cf:1 objective:1 boxes:3 hiley:6 know:4 background:23 resolves:1 press:3 using:8 outcomes:11 moreover:1 advanced:14 occurring:6 necessary:3 like:3 particle:19 identifying:1 follows:3 reduces:1 performing:1 admitted:1 mirror:1 history:2 yields:2 either:13 fully:4 happened:1 aug:1 prior:3 terminology:1 satisfactory:1 because:18 butterfield:1 successfully:1 some:10 back:1 experiments:3 understood:1 permitting:5 nothing:1 examples:1 sight:1 specified:2 critique:1 curious:3 proofs:1 provided:4 asserted:4 jeremy:1 pinpoint:1 confirm:3 broad:1 objected:1 measurements:20 recorded:1 counterfactual:112 umd:1 asking:1 decomposition:1 disappears:1 provides:1 assuming:2 steps:1 semantically:1 refer:2 destroys:1 vacuously:4 who:1 run:2 contingent:1 s13:2 s12:3 equivalent:6 each:10 bi:2 illustration:2 bk:25 likewise:1 shimony:1 although:1 substitution:1 similarity:3 post:51 includes:2 properties:4 after:3 chapter:1 deriving:3 about:3 asserting:1 actual:15 carried:2 face:1 entailed:1 pλ:1 certainty:1 discussed:10 dependence:5 o:22 pν:4 rejection:1 probabilities:6 range:3 ensure:1 stand:1 introduced:1 slightly:1 book:1 considerations:1 raised:1 rev:2 letters:4 flawed:2 previously:2 into:7 within:2 ηk:10 due:1 down:1 included:2 appropriate:4 inapplicability:1 accounts:1 conjoined:1 operator:5 ei:13 valuable:1 fixing:2 physical:11 wam:1 formulate:1 assumed:2 support:2 initial:5 question:4 equation:7 class:2 strict:4 noting:1 inner:1 way:12 crucially:1 sections:1 propagator:1 assumes:4 goodman:5 function:1 considerably:1 himself:2 complete:2 form:4 quantity:2 restrictions:1 removes:1 reasoning:1 but:21 idea:1 failure:5 related:1 bub:3 criticize:1 clarify:2 true:27 he:9 again:5 made:12 applying:5 evident:1 whether:7 inside:2 up:9 us:8 until:1 record:1 below:1 demonstrate:1 problem:7 similar:4 called:2 b1:54 mechanics:13 wants:1 ac:1 required:2 associated:6 b2:24 classic:1 defined:5 certain:2 abstract:1 describe:2 am:1 accessibility:1 general:17 single:5 diverse:1 right:4 together:4 formulation:1 journal:3 exist:4 formalism:1 commuting:1 defines:1 incorrect:5 entailment:1 compared:1 weakened:1 no:27 amounts:2 allow:2 commutes:1 when:18 detail:2 invalid:1 reality:7 started:1 other:9 holding:3 brings:1 department:1 electrons:2 really:1 satisfiable:1 concerning:4 weak:1 conclusion:1 picture:1 briefly:1 elements:5 variably:1 topic:1 calculating:1 separate:1 searched:3 distance:1 contested:1 prepared:1 a1:86 concurrent:1 meaning:2 allowing:2 studied:1 variable:3 scrutiny:1 antecedent:7 implies:2 longer:1 calls:1 assume:2 starting:2 interval:2 changed:1 rule:71 having:7 equivalently:2 weights:8 experimenters:1 time:103 observables:6 laws:3 requires:1 original:1 augmented:1
|
quant-ph9806003.txt |@word limited:1 monte:1 similarity:2 depends:1 caused:1 thouless:2 bandgap:1 results:4 φ1s:4 cases:1 localized:9 particles:1 concerned:1 undetermined:1 must:1 does:2 rokhsar:2 under:2 lh:2 applied:1 supported:1 orthogonal:2 modes:1 geometrical:1 electron:3 stays:1 condition:1 treating:1 believed:1 hamiltonian:1 ref:2 applicable:1 large:3 solved:1 convenience:1 small:5 barbara:1 degeneracy:1 possibility:1 upper:1 l2c:6 smaller:1 disordered:2 miller:1 sin2:1 direct:1 approximation:3 zero:6 enhancement:4 carlo:1 linear:1 even:1 nonlinear:3 appear:1 imamo:1 λcr:1 expressed:2 uniform:2 above:5 lifshitz:1 occupation:1 consisting:1 thin:1 coefficient:2 edited:1 chose:1 exchange:1 trivedi:2 here:3 l20:1 cylindrical:1 them:1 healing:2 separation:3 directions:1 path:1 along:1 strong:2 observing:1 appears:2 superconductor:1 obtained:1 solid:1 noticeable:1 studied:1 allows:1 controversy:1 advantages:1 glu:1 ork:1 halperin:1 via:4 spatially:1 semiconductors:2 private:1 screens:1 decrease:1 aimed:1 condensates:4 apply:2 total:3 unit:1 gaas:4 plot:1 would:2 sake:1 positive:2 negative:1 comparing:1 sample:1 therefore:4 associated:1 until:4 more:2 becomes:2 odinger:2 glass:4 correspondingly:1 varying:1 known:1 hole:2 presumed:1 me:3 topic:1 ma:3 quantized:2 φdφ:1 science:1 equation:9 dmitri:1 oscillator:4 mh:3 temperatures:4 mr:2 following:4 making:1 example:1 nikonov:1 transition:4 renormalization:1 figure:5 give:1 predict:1 neglected:1 purposes:1 high:1 his:1 sharp:2 rescaling:1 normalize:1 cooperativity:1 rather:1 divided:1 chemical:6 how:1 criterion:1 lh2:1 parameter:10 sin:3 simplicity:1 de:1 description:1 fi:1 minimizes:1 wave:2 grow:1 stress:1 short:1 liquid:1 recombination:1 ziman:1 so:3 allow:2 correlation:2 representation:1 order:9 lθ:1 stoof:1 bijlsma:1 over:1 mainly:1 radiators:1 course:1 experiments:1 statistical:1 argued:1 linewidth:1 its:4 before:1 group:1 lc:7 decay:11 decreases:4 systems:1 insulator:1 pergamon:1 might:1 bogolyubov:1 macroscopic:1 non:6 good:2 motivated:1 thereby:1 numerically:2 material:1 fig:5 introduce:1 disregarded:1 scaling:1 effects:1 oxford:1 now:1 february:1 several:1 profound:1 always:2 university:2 presented:1 gerrit:1 sufficiently:1 l2:2 trap:1 l0:4 each:3 disregard:1 2m:5 mean:2 primarily:1 krauth:1 ed:1 energy:1 sov:1 gaussian:1 related:2 solution:4 used:1 obtains:1 measurement:1 quantum:9 our:3 approximated:1 ketterle:1 shown:4 3rd:1 space:4 06m:1 since:1 rev:21 research:1 increase:5 collisions:1 europhys:1 cause:1 foundation:1 theory:1 localization:17 divergence:1 1s:3 free:3 approaches:3 vinokur:1 california:2 term:1 besides:1 estimate:3 e0:2 publication:1 interaction:10 ata:1 widths:1 impose:1 times:1 length:21 view:1 neglect:1 substrates:1 first:1 features:1 variables:2 number:6 reaches:4 relations:1 rink:1 bjork:2 electronic:2 angular:1 size:8 given:6 temperature:23 zimanyi:1 condensate:43 occupancy:1 their:1 assumption:2 structures:2 murayama:1 gives:1 fraction:7 trapped:1 optical:1 authors:1 than:5 traps:1 peaked:1 determines:3 third:1 rate:8 limiting:1 inversely:1 determined:3 were:1 bauer:1 treated:2 function:2 mind:1 need:1 concentration:1 seek:1 any:3 strength:14 angle:2 depending:1 self:2 butov:2 jacobson:1 polarization:1 ideal:1 potential:15 take:1 singh:2 accuracy:1 kac:4 gunn:1 scalettar:1 broglie:1 though:1 wells:4 impurities:1 depths:1 most:1 boltzmann:1 phase:3 inserted:1 trapping:3 kb:2 especially:2 kk:1 average:6 adopt:1 physica:1 dimension:1 part:1 boson:4 physics:3 superfluidity:1 incorporate:1 gold:1 random:4 radii:1 relation:2 solutions:7 thickness:1 decade:1 ground:1 indicator:1 based:1 parameters:1 aψ:1 state:3 only:5 screening:1 factor:5 employed:1 do:2 narrows:1 means:1 express:1 cannot:1 dr:4 reveal:1 singapore:1 densities:5 encounters:1 druten:1 arxiv:1 paper:1 contain:1 pitaevskii:8 set:4 exists:1 see:5 computer:1 radius:8 result:2 discussions:1 uncorrelated:1 best:1 lee:3 still:1 interacting:3 enlightening:1 pattern:1 dipole:3 superradiant:6 µm:4 outside:2 smallest:1 weichman:1 between:2 approach:2 µc:2 available:2 notice:1 terms:5 nature:1 overestimates:1 weak:1 however:2 vanishing:1 uψ:1 extent:1 bose:19 thank:1 suggested:1 limits:1 feldmann:1 region:1 termed:1 according:3 connection:1 unc:3 share:1 whole:1 experimental:1 cos2:3 presumably:1 cm:3 corresponds:1 dimensional:6 cx:1 coordinates:1 cr:1 ceperley:1 described:1 equations:4 radiative:7 much:1 change:2 interest:1 superradiance:1 ph:1 universal:1 choose:1 dots:1 interparticle:3 direction:2 corresponding:2 coherence:7 gas:1 bulk:1 determination:1 external:1 former:1 case:5 laser:3 pacs:1 indefinitely:1 reliable:1 value:5 excited:1 will:5 while:1 ongoing:1 taking:1 characterizing:1 a20:1 larger:2 girvin:1 n2c:2 refs:1 thus:1 site:1 equal:1 middle:1 eberly:1 technology:1 different:2 hubbard:1 pau:1 lengths:1 media:1 make:1 lett:11 same:4 quant:1 rashba:1 pai:1 dimensionless:5 finite:3 grows:4 higher:2 reasoning:1 pandit:2 extended:3 infinity:1 batrouni:1 leonid:1 appreciably:2 numerical:3 hand:1 a2c:3 infinite:4 landau:1 totally:1 lower:1 schr:2 center:3 disappears:1 modeled:2 well:15 bohr:1 solve:2 model:4 latter:1 usual:1 restore:1 nc:9 less:2 superconductors:1 obtain:6 identify:1 atomic:1 immediately:1 yamamoto:1 scattering:3 grinstein:2 note:1 density:23 ramakrishnan:1 lake:2 wavevector:1 lattice:2 add:1 treatment:1 extensive:1 transformation:1 momentum:2 rescaled:1 saturation:1 increased:1 2j1:1 advances:1 possible:3 increases:1 quest:2 press:2 integer:1 modifications:1 collective:3 schmitt:1 porous:1 specific:1 ramasesha:1 integrals:1 arbitrary:1 become:2 disorder:10 exceed:1 often:1 some:2 indirect:2 gross:7 vol:1 scale:2 describing:1 dimensions:5 opposite:1 per:2 critical:12 tends:7 chemla:1 scientific:1 power:2 lakes:3 bj:1 santa:1 found:1 zimmermann:1 exciting:1 properties:1 world:1 stationary:1 discussed:1 dependence:7 excitons:15 range:3 ensure:1 consequently:1 onogi:1 cambridge:2 h2:5 communication:1 into:1 integral:2 nsf:2 down:1 references:1 determine:3 ullah:1 proportional:5 binding:1 methods:2 statistics:1 van:1 log:1 area:5 long:1 width:3 bosons:15 way:1 8k2:1 was:5 m0:1 questionable:1 medium:4 differences:1 jun:1 but:2 properly:1 illustrative:1 he:1 made:2 packard:1 intuitive:1 characteristic:1 us:5 theoretical:1 below:7 limit:2 fluctuations:2 distribution:2 similar:1 called:1 strongly:3 bearing:1 ac:1 later:1 constant:5 defined:3 certain:1 abstract:1 describe:1 influence:1 general:1 engineering:1 exist:3 wavelength:5 lifetime:2 work:1 physical:1 again:1 functions:1 compared:1 no:1 exciton:11 wavefunction:2 when:1 ne:3 ng:5 field:1 other:4 electrical:1 spatial:1 department:1 conclusion:1 separate:1 models:1 photon:1 variation:1 emission:6 a0:2 important:1 fisher:5 ago:1 condensation:17 implies:2 coulomb:3 assume:1 curve:3 together:1 equivalently:1 depth:1 4m:1 mass:2 nelson:1 krishnamurthy:2 understand:1 starting:1 having:1
|
quant-ph9806004.txt |@word replacing:1 secondly:1 partial:1 consider:1 chinese:1 magnetic:1 generalize:1 go:1 causes:1 2r0:12 ihep:1 particles:2 depend:1 concerned:2 nonlocal:1 tail:5 critical:13 those:2 inwards:2 nodes:1 include:2 supported:1 very:2 wave:21 electron:1 rm:58 affect:1 difference:3 condition:14 vidensk:1 presented:1 did:2 solution:17 large:5 discrete:1 small:10 degeneracy:2 smaller:2 sturm:10 sign:13 jump:3 zero:51 further:2 mπ:1 even:1 established:3 what:1 appear:1 section:4 iκr:2 expressed:2 version:1 goes:3 3b:1 3a:1 method:5 satisfy:2 devoted:1 κn:1 simultaneously:7 ibid:1 respectively:1 modify:1 here:1 ranges:4 china:5 free:3 address:1 equations:1 appears:13 logarithmic:18 box:4 numerator:8 institute:3 shift:37 study:2 changed:3 reason:2 drm:1 usually:2 changes:22 useful:1 br:1 rosenberg:2 imπ:1 requiring:1 prefer:1 total:3 establish:2 derivatives:3 use:1 eψ:1 prove:3 positive:16 contains:1 negative:17 next:7 definiteness:1 nucl:1 going:2 therefore:6 recommend:1 outwards:1 becomes:7 odinger:17 knm:1 known:1 cases:6 iii:2 must:1 high:3 springer:2 monopoles:1 ma:5 integrating:1 science:2 equation:22 work:1 modified:5 theories:1 following:1 example:3 proof:6 beijing:4 relativistic:1 organized:1 near:2 states:14 trieste:1 imϕ:1 numbers:1 tan:10 galbraith:1 conversely:4 verlag:2 needs:1 discussion:4 means:3 regions:1 far:1 hou:1 plus:1 parameter:2 sin:2 oscillatory:1 simplicity:2 mat:1 may:4 variant:5 waves:2 natural:1 third:1 counter:1 so:7 fundamental:1 keeps:7 divided:1 holds:5 jν:3 essence:1 pointed:1 satisfied:4 paper:3 through:2 signs:1 satisfies:3 its:3 decay:3 d32:1 decreases:22 d31:1 πkr:3 according:1 choose:1 derivative:14 main:1 into:1 non:4 good:1 combination:1 introduce:2 half:16 singularity:2 now:5 discuss:6 term:6 2r:4 always:5 university:1 sufficiently:10 theory:4 2a:2 2b:4 radial:12 2m:3 repeating:1 square:4 ei:1 another:2 independent:2 ed:3 energy:32 related:1 owing:1 quantum:4 laboratory:1 beyond:1 eq:31 out:1 leave:1 shown:2 overcame:1 nuovo:1 since:5 rev:8 denotes:2 increase:2 re:3 surprise:1 get:1 cause:1 occurs:7 math:2 foundation:1 linear:1 interactions:1 gesztesy:2 effect:1 hankel:2 completely:2 york:2 conflicts:1 log:4 definition:2 r0:65 r2:8 r3:1 similarly:2 times:7 turn:2 generalizations:1 first:6 origin:4 a56:1 xi:1 symmetry:2 relate:1 powerful:1 number:15 reaches:5 will:10 multiplying:1 dong:1 electronic:1 angular:4 given:9 necessarily:1 their:3 introduction:1 leading:9 eqs:1 needed:1 too:1 statement:1 convention:4 8r0:2 speaking:1 a31:1 way:1 academy:1 tool:1 exactly:1 nahm:1 part:1 centrifugal:1 than:6 wide:1 kind:1 determines:1 effective:1 sections:2 cimento:1 second:2 goddard:1 determined:4 were:1 sec:6 spectrum:4 already:1 need:1 seen:1 any:2 angle:3 lin:3 note:2 k2:2 potential:27 take:1 green:3 formulas:1 continuous:3 multiple:2 who:2 phase:41 why:2 especially:1 calculated:3 later:1 coincides:1 order:1 kr:14 proceedings:1 yang:1 levinson:35 physics:4 fact:1 show:1 nπ:2 hm:3 notations:1 helv:2 relation:1 solutions:5 carefully:1 substituting:1 d2:2 find:1 based:1 title:1 enough:3 should:4 analytic:1 only:9 explicitly:2 factor:8 integrable:4 constant:4 fort:1 monotonically:8 his:1 above:1 viewpoint:1 distance:1 uncountable:1 24b:1 words:2 new:9 dr:6 prime:1 singapore:1 evident:1 arxiv:1 acknowledgments:1 nν:6 qi:1 shi:1 declared:1 set:2 hν:1 violated:4 depends:2 radius:3 result:1 recently:2 analog:1 liouville:10 tend:1 symmetric:3 state:39 between:6 invariant:3 boundary:2 conditions:1 across:14 multiplied:1 terms:9 attention:1 however:2 jm:7 vanishing:4 analyzed:2 come:1 both:4 cos:4 last:1 cot:1 jauch:1 region:8 equal:8 kjm:1 sensitive:1 hψ:1 tangent:2 disappears:2 experimental:1 cos2:2 arbitrarily:1 cn:1 point:1 simple:2 period:1 except:3 dimensional:3 cancel:1 respect:7 forms:1 equivalent:1 due:4 been:2 change:4 interest:1 ph:1 meeting:1 define:1 corresponding:1 versa:1 argument:1 c2:7 careful:1 present:2 case:25 unlike:1 solid:1 value:23 trick:1 while:1 match:2 behavior:2 wilk:2 property:3 taking:1 discretize:1 larger:4 thus:1 iv:3 ii:2 24a:2 technology:1 different:3 italy:1 grant:1 pay:1 noncentral:1 same:2 shifts:2 quant:1 finite:6 difficult:1 conflicting:1 used:3 infinity:16 see:4 ni:2 monotonic:5 hand:1 purpose:1 potentials:2 infinite:4 changing:1 lower:1 literatures:1 schr:17 center:1 well:2 roughly:1 analysis:3 without:1 solve:1 comes:3 firstly:4 model:1 latter:2 spherical:1 λv:1 just:1 newton:6 obtain:4 spherically:1 scattering:10 previous:3 hai:1 integer:2 sciences:1 seems:1 wen:1 jost:2 appeared:1 interested:2 lett:3 easy:4 theorem:42 remaining:4 momentum:16 real:1 acta:2 spruch:2 early:1 fys:1 increases:29 world:2 2nd:2 advanced:1 acute:1 energ:1 necessary:2 like:1 particle:3 follows:1 martin:1 conclusion:1 because:6 methods:1 namely:8 people:3 some:4 back:1 examples:1 proofs:1 matching:6 dimensions:15 medd:1 kr0:26 overlap:6 does:10 provides:1 tends:4 bessel:2 demonstrated:1 denominator:12 scientific:1 jumps:13 each:9 boll:2 expansion:1 2µe:6 meets:1 although:1 worthy:1 nℓ:2 asymptotic:3 comparison:2 about:1 discussed:4 o:4 nonvanishing:1 addition:1 range:1 nothing:2 introduced:1 cutoff:1 convergent:2 h2:6 ηm:68 bound:43 three:5 κr:2 cylindrically:2 determine:1 proportional:1 neumann:2 additional:3 removing:1 there:12 fast:3 lot:1 was:4 a54:1 function:29 complete:1 form:1 m2:7 jun:1 but:11 atom:1 line:1 subtracted:2 intuitive:1 versions:1 whether:2 up:2 us:1 mth:1 limit:5 continuously:2 problem:3 monopole:1 similar:1 called:2 mechanics:1 ac:1 proved:7 worthwhile:1 defined:3 am:53 general:3 dξ:2 our:1 check:1 physical:2 again:2 functions:1 selsk:1 nm:14 national:1 no:7 zhong:1 when:47 detail:1 field:2 other:4 republic:3 papers:1 department:1 nice:1 node:4 denote:1 calculating:1 a0:2 important:2 ξn:2 variable:1 danske:1 sides:2 vice:1 assume:1 discontinuously:1 mass:1 time:7 requires:1
|
quant-ph9806005.txt |@word secondly:1 consider:1 chinese:1 forbidden:1 go:1 2r0:9 ihep:1 inverse:1 depend:1 concerned:2 nonlocal:1 tail:1 monotonically:6 under:1 include:2 orthogonal:1 far:2 wave:3 difference:2 condition:12 vidensk:1 solution:10 large:2 discrete:1 small:6 smaller:2 sturm:6 dealing:1 sign:8 jump:4 zero:34 18d:1 theory:5 even:1 established:1 what:1 appear:2 section:1 near:1 expressed:1 experiment:1 goes:1 new:7 method:5 satisfy:1 simultaneously:3 ibid:2 respectively:3 never:2 modify:1 ranges:4 china:5 cos2:1 address:1 represented:1 equations:1 appears:10 change:8 box:4 great:1 numerator:5 institute:3 shift:33 elaborate:1 studied:3 reason:2 published:1 therein:1 changes:11 useful:1 rosenberg:3 imπ:1 prefer:1 decrease:1 total:2 establish:1 derivatives:4 use:1 eψ:2 would:1 prove:1 positive:21 negative:12 next:4 definiteness:1 linear:1 noting:1 therefore:8 m2:4 means:3 more:2 composite:1 becomes:4 niemi:1 odinger:8 normalized:1 integrable:1 known:1 cases:5 must:2 high:3 springer:1 monopoles:1 ma:7 integrating:1 science:2 equation:15 work:1 ρm:16 theories:1 obvious:1 following:3 example:1 proof:1 beijing:4 imφ:1 process:1 relativistic:2 organized:1 saito:5 states:14 numbers:2 tan:5 galbraith:1 conversely:2 occur:2 verlag:1 end:1 s2:1 divided:1 holds:4 orthogonality:2 regions:1 trieste:1 hou:3 plus:1 establishment:1 sin:1 oscillatory:1 simplicity:1 mat:1 singular:2 may:5 variant:4 waves:1 italy:1 derives:1 natural:1 succeeded:1 light:1 parameter:2 redundant:8 used:2 keeps:1 representation:1 discussion:1 origin:5 helv:2 essence:1 over:1 satisfied:3 paper:4 through:3 signs:1 satisfies:5 its:2 write:1 semenoff:1 rapidly:1 decay:1 solving:1 d32:2 decreases:18 d31:1 πkr:2 systems:1 derivative:9 main:1 into:1 non:17 good:1 combination:1 introduce:2 22b:1 half:7 front:1 singularity:1 now:1 discuss:4 2v:1 finite:2 always:4 university:1 sufficiently:4 radial:10 2m:2 em:2 square:1 ei:1 another:1 meets:1 ed:2 energy:34 related:2 decays:1 changed:1 quantum:1 laboratory:1 beyond:1 out:2 nuovo:2 since:4 rev:13 denotes:2 particles:1 rem:53 denoted:1 ro:1 occurs:5 math:4 foundation:1 mπ:1 interactions:5 little:1 free:3 effect:1 hankel:2 completely:1 included:2 york:1 e0:2 additional:3 definition:1 interaction:4 r0:40 r2:3 ds2:1 times:4 turn:2 first:5 separable:2 xi:3 symmetry:1 number:7 reaches:5 multiplying:1 dong:3 electronic:1 angular:2 given:4 necessarily:1 similarly:2 introduction:1 leading:6 system:1 their:4 assumption:1 too:2 convention:4 8r0:1 speaking:1 academy:1 continuous:2 nahm:1 authors:1 kiers:1 than:5 wide:1 kind:1 l47:1 third:2 showed:1 jumps:9 cimento:2 second:2 submitted:1 matter:2 determined:6 yang:1 radius:1 perturbative:1 modern:1 argument:1 need:2 seen:2 any:2 angle:1 convenient:1 latter:2 sciences:1 potential:18 generalized:2 forces:1 so:4 added:1 multiple:2 denominator:11 simplify:1 phase:34 why:2 subtracted:2 dijk:1 later:1 physica:1 2nd:1 kr:7 proceedings:1 points:1 principle:1 levinson:25 physics:5 fact:2 ambiguities:1 tamagaki:2 show:1 nπ:2 supported:1 relation:1 solutions:2 d2:3 find:1 finally:1 based:2 just:2 enough:1 should:2 only:9 going:2 ambiguity:1 factor:4 employed:1 local:26 pointed:1 do:1 newton:2 above:1 viewpoint:2 distance:1 words:1 dr:11 ds:2 prime:1 singapore:1 evident:1 fields:1 arxiv:1 acknowledgments:1 europhys:1 qi:3 shi:3 body:2 set:1 exists:1 physically:5 national:1 namely:1 sec:4 close:1 goddard:1 nuclear:1 symmetric:6 state:38 between:7 boundary:2 conditions:2 across:12 multiplied:1 terms:4 august:1 attention:1 however:4 jm:8 vanishing:3 group:1 come:1 both:8 cos:2 jauch:1 taking:1 according:2 kjm:2 hψ:1 tangent:2 expression:2 comes:1 cn:1 nonrelativistic:1 reasons:1 effective:1 period:1 except:4 dimensional:3 respect:4 throughout:1 appeared:1 addition:2 three:4 been:2 blankenbecler:1 logarithmic:11 interest:1 ph:1 meeting:1 gesztesy:1 corresponding:1 versa:2 spectrum:2 c2:5 denote:2 those:1 case:16 explicitly:1 pacs:1 solid:1 value:20 spontaneously:1 will:11 iκr:2 match:2 behavior:2 wilk:1 property:1 region:6 larger:2 almost:1 thus:2 equal:7 canceled:1 vanish:1 technology:1 disappear:1 different:3 verified:1 grant:1 pay:1 same:1 shifts:1 quant:1 pauli:1 modification:2 proved:5 several:1 independent:3 literature:1 infinity:9 see:4 ni:2 monotonic:1 hand:3 potentials:9 infinite:3 lower:1 knm:1 schr:8 center:1 disappears:1 obstacles:1 well:2 analysis:1 without:2 solve:1 does:5 firstly:2 model:1 lin:1 usual:1 distances:1 λv:1 λu:1 generally:1 compound:1 obtain:4 integer:1 scattering:7 letting:1 hai:3 accepted:1 preprint:1 point:2 wen:3 jost:1 simple:2 interested:1 lett:4 easy:4 theorem:29 guarantees:1 remaining:1 momentum:11 real:3 acta:2 spruch:3 term:5 fys:1 increases:25 vidal:1 world:2 unique:1 r0m:2 advanced:1 acute:1 energ:1 necessary:1 particle:3 follows:1 martin:6 nucleons:2 mathematical:1 satisfactory:1 because:2 methods:3 people:3 some:7 back:1 examples:1 matching:8 dimensions:11 medd:1 kr0:17 extra:1 overlap:5 critical:5 tends:4 prog:4 bessel:1 mesonic:1 scientific:1 equivalent:1 each:6 boll:1 bk:1 although:1 found:1 asymptotic:2 constraint:1 commun:1 discussed:3 o:4 range:1 nothing:1 cutoff:2 22m:1 ηm:43 integral:1 bound:36 22a:2 due:1 κr:1 cylindrically:4 references:2 neumann:2 van:1 log:3 removing:1 there:13 nucl:1 fast:1 thirdly:1 way:2 was:4 function:17 form:2 a56:1 jun:1 singlevalued:1 but:9 hm:2 fort:1 intuitive:1 whether:2 up:2 liouville:6 owing:1 limit:3 continuously:1 monopole:1 similar:2 called:3 ac:1 kh:1 constant:1 defined:3 abstract:1 describe:1 am:37 doesn:1 convergent:2 proves:1 our:1 check:1 physical:2 resonating:1 again:3 nk:1 selsk:1 nm:9 no:10 zhong:3 wavefunction:4 when:31 green:1 field:2 other:7 republic:3 department:1 theor:4 nice:2 suppl:1 calculating:1 problems:3 a0:2 important:2 a9:1 variable:1 boyanovsky:1 danske:1 sides:3 faster:1 vice:2 assume:2 proposed:1 required:2 discontinuously:1 mass:1 time:4 nuclei:1 dϕ:1 requires:1
|
quant-ph9806006.txt |@word secondly:3 consider:2 chinese:1 results:1 four:1 ihep:1 inverse:1 depend:1 calculate:2 concerned:2 tail:6 does:8 under:1 include:1 case:29 g1:6 far:1 wave:5 additional:3 affect:1 condition:12 vidensk:1 solution:12 large:3 admissible:1 convenience:1 math:4 small:15 smaller:3 sturm:5 sign:19 jump:3 zero:36 iσ2:1 iσ1:1 even:1 established:1 plays:1 appear:1 sum:4 while:2 expressed:1 goes:2 new:7 acknowledgments:1 κn:3 simultaneously:7 ibid:1 respectively:2 component:1 here:1 ranges:9 china:5 gesztesy:1 address:1 based:1 equations:4 appears:10 logarithmic:1 box:4 numerator:5 institute:3 shift:28 study:5 studied:2 changes:26 useful:1 br:1 rosenberg:3 beijing:4 iet:1 total:2 use:1 asymptotic:4 prove:1 positive:34 contains:1 negative:36 next:5 definiteness:2 nucl:1 monotonically:6 therefore:7 a56:1 e2:2 theoretical:1 becomes:19 niemi:1 odinger:3 integrable:4 cases:10 iii:2 must:1 logarithm:1 high:3 springer:1 monopoles:1 ma:6 integrating:1 science:2 equation:9 work:1 modified:4 theories:1 obvious:1 following:3 proof:3 f1:6 indicated:1 relativistic:5 near:5 states:14 numbers:1 tan:13 keep:1 conversely:7 evidently:1 verlag:1 galbraith:1 κr0:2 holds:8 regions:1 trieste:1 hou:2 instead:3 establishment:1 sin:9 ieaµ:1 simplicity:1 mat:1 may:4 variant:10 waves:1 natural:2 effective:1 light:1 so:16 keeps:8 helv:2 jα:3 satisfied:1 course:1 paper:2 through:1 signs:1 satisfies:1 its:6 semenoff:1 decay:2 energies:4 solving:2 d32:2 decreases:32 d31:1 πkr:6 derivative:1 main:2 non:7 introduce:1 ηj:76 subtraction:1 half:19 front:2 singularity:1 now:4 discuss:8 term:4 vidal:1 dirac:7 parameter:2 university:1 sufficiently:13 radial:7 2m:45 side:1 2j:28 square:4 ei:8 dong:2 ed:2 energy:36 related:1 changed:3 quantum:2 laboratory:1 eq:32 special:1 shown:2 dominates:1 driving:1 furthermore:1 since:2 rev:12 denotes:2 particles:2 formula:1 ref:1 occurs:6 interchanging:1 foundation:1 theory:3 8m:1 free:1 hankel:1 completely:1 york:1 nα:3 e1:6 care:1 r0:93 r2:1 times:7 turn:4 hence:3 first:5 origin:3 xi:2 number:10 reaches:10 another:1 electronic:1 angular:4 given:6 tangent:1 similarly:3 introduction:1 leading:8 eqs:6 their:1 too:3 convention:2 national:1 academy:1 continuous:1 nahm:1 part:1 kiers:1 than:8 wide:1 kind:1 determines:1 18d:1 sections:2 cimento:1 namely:6 submitted:1 matter:1 determined:2 sec:6 minus:2 modern:1 increment:1 further:1 need:1 seen:1 any:1 strength:1 angle:1 lim:1 lin:1 able:1 note:2 sciences:1 potential:19 generalized:6 formulas:1 multiple:3 denominator:14 cylindrically:1 fjm:2 coincides:1 physica:1 2nd:1 kr:33 proceedings:1 yang:1 levinson:22 physics:5 section:3 fact:1 dijk:1 nπ:3 text:1 supported:1 merit:1 relation:2 solutions:11 substituting:2 find:1 finally:8 ratio:20 state:65 should:2 only:10 factor:9 integrate:1 employed:1 constant:2 nj:23 means:2 words:1 dr:10 fields:1 arxiv:1 summary:1 europhys:1 qi:2 shi:2 nβ:3 physically:1 violated:1 hα:2 see:4 radius:1 discussions:1 terms:7 goddard:1 satisfying:2 tend:1 symmetric:1 enough:2 between:12 invariant:2 boundary:3 across:22 recently:1 jauch:1 combining:1 however:1 jm:1 vanishing:4 key:1 analyzed:1 c22:3 both:4 cos:11 c21:6 limits:1 jπ:2 taking:1 equal:6 variance:3 disappears:5 experimental:1 arbitrarily:1 cn:1 point:3 period:1 except:1 dimensional:1 respect:1 throughout:1 forms:2 second:1 addition:1 due:2 been:3 blankenbecler:1 change:3 interest:1 ph:1 meeting:1 obtained:1 aj:75 corresponding:1 versa:1 c2:1 general:2 those:4 applied:1 solid:1 value:23 will:14 iκr:10 suppose:1 match:9 behavior:1 wilk:1 region:9 larger:3 thus:4 them:1 iv:3 ii:2 canceled:1 vanish:1 technology:1 different:1 italy:1 grant:1 shifts:9 quant:1 units:1 finite:6 used:1 infinity:13 singapore:1 ni:2 monotonic:2 hand:3 potentials:1 infinite:1 changing:1 hβ:2 normalization:1 lower:1 schr:3 center:1 well:1 solve:2 sets:1 firstly:5 λv:1 less:2 newton:2 obtain:14 rest:7 world:2 scattering:23 previous:4 letting:1 hai:2 preprint:1 integer:2 wen:2 interested:1 lett:4 easy:3 theorem:27 role:1 momentum:14 take:2 acta:2 aspects:1 spruch:3 replaced:1 iγ:1 fys:1 increases:43 using:1 replace:1 advanced:1 acute:1 energ:1 necessary:2 particle:1 follows:2 gjm:2 always:2 conclusion:1 therein:1 because:2 neumann:1 people:3 some:2 matching:1 dimensions:7 medd:1 kr0:29 overlap:10 critical:22 tends:5 bessel:1 scientific:1 jumps:19 each:16 boll:1 step:1 ratios:3 properties:1 comparison:3 commun:1 discussed:3 o:4 range:1 important:1 plus:2 cutoff:2 into:4 bound:57 jβ:3 three:1 κr:5 phase:37 right:1 references:1 determine:1 ea0:1 van:1 log:7 there:5 fast:2 was:2 function:9 form:3 differences:1 jun:1 but:16 hj:4 aµ:1 hm:1 fort:1 evident:2 whether:3 up:2 liouville:5 limit:2 problem:3 monopole:1 similar:1 called:5 jj:12 ac:1 proved:1 defined:3 describe:2 am:1 denote:1 dξ:2 relates:1 check:3 selsk:1 again:2 functions:3 nm:1 no:5 zhong:2 when:54 detail:3 field:2 other:4 republic:3 department:1 nice:1 a1:1 a2:1 variable:1 boyanovsky:1 danske:1 sides:7 vice:1 assume:2 martin:2 discontinuously:1 4m:1 mass:1 time:15 nuovo:1
|
quant-ph9806007.txt |@word partial:3 gr:4 chinese:2 similarity:1 issued:1 nition:2 gg:1 eds:1 scalar:1 proposition:2 entropy:1 computation:2 edu:1 crete:4 sci:2 primes:1 gi:4 consider:3 paris:1 illustrates:1 tr:3 λn1:3 finally:1 under:5 tr1:2 analogous:1 include:2 norm:6 activities:1 gini:1 straightforward:2 rise:2 harmonics:1 choice:1 coprime:6 difference:1 matrices:17 encounter:1 dim:1 trk:1 presented:1 tra:1 proposals:1 solution:4 standards:1 discrete:3 vector:1 math:2 indices:3 seminumerical:1 equation:2 upper:1 zn:6 lewenstein:1 deutsch:2 direct:1 imply:1 zz:3 dynamics:1 implemented:3 theory:2 index:11 abe:1 cast:1 diag:1 sum:3 expressed:3 version:3 above:4 paraskevi:1 new:4 congruences:3 satisfy:2 ibid:1 respectively:2 applies:1 component:3 teleportation:1 here:2 reported:1 groups:6 address:1 grouplike:2 along:1 respect:1 appears:1 interpret:1 engage:1 division:2 wesley:1 technical:1 involved:1 study:5 larger:1 example:1 p2:1 periodic:1 products:2 fourier:1 involves:2 york:2 uniquely:1 orthonormality:1 captions:1 transformations:1 classification:2 λn2:1 jm1:5 floratos:3 b228:1 viz:3 counts:1 additive:1 proceed:3 usa:1 remains:1 positive:3 contains:1 toffoli:1 qni:1 nucl:1 m1:27 therefore:1 m2:31 πn1:4 λmn:1 bu:1 sentation:1 theoretical:1 diagrams:1 more:3 bennett:2 coassociative:3 composite:5 becomes:1 operators:2 ellinas:3 constructs:1 correspondingly:1 virtue:1 projective:3 cases:2 hold:1 entangle:1 isomorphism:7 frobenius:1 ρi:2 ndimensional:1 challenge:1 mn:4 ρm:2 itly:1 following:7 closing:2 πnt:4 proof:2 figure:1 give:1 permutations:1 m21:10 states:5 numbers:2 sense:1 respective:3 gcd:2 provide:1 verify:1 holds:1 write:1 maps:2 zn1:1 ρn1:1 pure:2 explains:1 sin:1 obeys:1 map:12 product:4 frobenious:1 algebra:5 earlier:1 mapping:1 lab:1 diagram:3 fkl:3 parallel:1 types:2 computations:1 zni:2 explicit:2 su:6 greek:1 so:2 correlation:10 representation:2 order:1 horne:1 interpreted:1 cambridge:1 existence:1 still:1 its:9 before:1 group:14 zn2:1 chosen:1 interesting:1 inclusion:1 forms:1 wrt:1 systems:10 main:1 yi:6 them:2 good:1 motivated:1 propose:1 fig:7 introduce:3 framework:1 now:3 developments:1 term:1 name:2 university:2 trn:2 huelga:1 appropriate:1 possibilities:1 applied:1 l2:1 each:3 comultiplication:3 2i:1 subsystem:1 square:3 england:1 barnett:1 ρi1:1 ρi2:1 elementary:1 frequency:1 hli:2 sion:1 quantum:20 beyond:1 eq:1 special:2 shown:1 matrix:18 factors:7 m2t:10 quantify:1 since:1 induces:3 research:1 m2l:2 re:1 acting:2 m2i:17 print:2 induced:1 induction:2 independence:1 benjamin:1 commutation:1 linear:2 possibility:1 enveloping:1 residues:4 elsewhere:2 emblematic:1 holt:1 remainder:2 e3:1 e2:1 definition:3 via:1 computers:1 days:1 m22:1 mahler:1 turn:3 first:2 symmetry:1 pn1:1 omitted:1 pn2:1 number:4 infinite:1 open:2 given:7 e1:1 similarly:1 unitarity:1 appear:1 πn:10 system:9 relations:4 their:5 realization:1 1i:4 1l:1 gives:1 commutativity:1 secretariat:1 cup:1 pnt:1 pni:1 b233:1 than:1 coefficients:4 distance:2 cyclic:4 namely:1 inversely:1 determined:9 pairwise:2 tion:1 radix:1 symmetries:1 entail:1 conjugate:2 recover:1 any:2 relatively:1 lie:2 subsystems:2 isolated:1 note:3 take:1 algorithms:2 heisenberg:8 trace:3 investigations:1 measures:2 but:1 letter:1 2tr:1 pair:1 class:2 inequalities:1 δn1:4 consequences:1 δn2:1 considered:1 possesses:1 proceedings:1 hi:1 mechanical:1 physics:5 notion:1 fact:5 dover:1 dualizing:1 2m1:1 violation:1 factorize:1 spaces:1 relation:3 decompositions:1 based:4 implementation:1 commutators:1 should:2 only:1 generators:4 factor:1 local:3 hopf:2 abelian:1 cryptography:1 means:4 express:1 joint:1 tranformations:1 dv:1 gen:2 prime:12 µn1:4 µn2:1 densities:1 crt:9 podolsky:1 arxiv:1 expansions:1 factorization:2 hereafter:1 nν:1 counted:1 view:2 moduli:1 set:3 modulo:1 ser:1 achieved:2 correlations:8 see:2 sec:1 greece:3 terms:5 uncorrelated:1 nonlocality:1 project:1 tensor:2 kl:3 ways:2 nuclear:1 diverge:1 state:5 various:2 between:5 invariant:5 reading:1 conditions:4 email:2 available:1 recently:1 jm:32 jn:11 tuc:1 observable:1 essentially:1 last:2 acknowledge:1 equal:1 contract:1 admit:1 became:1 iv:1 embedding:1 expression:1 otherwise:1 unitarily:2 co:1 characterization:1 hm2:3 m11:6 m12:1 moreover:1 second:1 considering:1 nni:1 pt:1 basis:6 associativity:1 due:3 been:4 balian:1 ml2:1 describes:1 z2:2 pd:15 ph:3 pi:3 b425:1 pm:3 compositeness:1 congruence:1 partly:1 m1i:12 itzykson:1 concerning:1 natl:1 m1l:1 coherent:1 determination:1 m1t:8 those:1 case:4 schmidt:1 variances:1 evaluated:1 will:3 institute:2 aij:2 property:4 unitary:10 coupled:3 vol:1 von:1 according:4 ii:1 reads:3 ij:1 properties:1 coassociativity:2 dual:2 technology:1 id:10 different:3 verified:1 suggests:2 make:1 connection:1 same:1 archive:2 complex:1 quant:3 morphic:1 knuth:1 finite:6 hermiticity:1 used:3 http:1 dimh:2 hand:1 entanglement:2 nl:1 invariance:2 recent:2 lower:1 shortly:1 mention:1 analysis:2 components:1 dimension:3 λu:1 rosen:1 obtain:3 tasks:1 questions:1 using:2 λi:1 schwinger:1 λn:3 λm:7 previous:1 generator:2 density:24 bell:2 lattice:1 other:4 combine:1 lett:11 theorem:2 transformation:1 euler:1 real:1 explained:1 σn2:1 aml:1 evaluate:1 possible:3 e123:1 early:1 vδ:9 sanpera:2 integer:1 unique:2 decomposes:1 mod:17 dimensional:3 necessary:1 alternatively:1 bn1:1 1n1:1 werner:1 arbitrary:3 reduced:2 acad:2 neumann:1 classical:2 some:2 zz2:1 examples:1 convex:3 images:1 b224:1 2l:1 dimensions:2 behave:2 decomposition:16 provides:7 three:4 proc:2 bf:1 power:3 journal:1 analysed:1 expansion:1 zzn:4 although:1 b218:1 notation:2 hilbert:4 bz:1 takes:1 integers:2 concretely:1 tracing:2 fairlie:2 distinct:2 extensions:2 stand:1 act:1 mixed:4 ti:10 introduced:3 soc:1 rev:12 an2:1 follows:1 jδ:2 communication:1 into:10 integral:1 isomorphic:1 copies:1 πni:1 hermitian:1 weyl:1 references:1 determine:1 einstein:1 operator:7 next:1 refinements:1 support:1 there:1 vedral:1 lond:1 start:2 workshop:1 labelling:1 kinematics:1 gik:2 function:3 complete:3 form:7 hs:1 regard:1 jul:1 hj:2 hh:1 construction:2 hn:19 hg:1 raising:1 algebras:2 embedded:2 horodecki:1 type:2 bounds:1 us:3 ωi:4 hni:3 below:1 mk1:2 problem:1 define:1 similar:1 called:1 mechanics:2 associated:2 ag:1 addison:1 defined:1 abstract:1 measure:3 condition:1 general:5 peres:1 quantification:3 single:1 ing:1 commuting:2 check:1 inc:1 ni:30 nj:6 completeness:1 demokritos:1 ekert:1 when:3 vanishes:1 reality:2 tr2:1 valid:3 department:1 mathematics:1 nt:6 sufficient:1 arithmetic:1 polar:1 briefly:1 elements:7 phoenix:1 covariance:1 generated:1 important:3 bounded:1 massachusetts:1 observables:1 ariadne:1 implies:2 factorized:1 l63:1 assume:1 established:1 clauser:1 space:5 l69:1 together:2 periodicities:1 factorizes:2 n1:27 n2:36 n3:10 original:1
|
quant-ph9806008.txt |@word limited:1 four:6 entropy:15 consists:4 whose:1 const:2 calculate:2 under:4 rise:2 lecture:1 affect:1 skills:2 solution:4 vector:2 enhance:1 ups:4 consistent:1 estimates:7 direct:1 approximation:1 likely:3 estimated:4 even:13 established:3 errors:67 new:15 net:1 deemed:1 simultaneously:2 error:71 here:17 met:1 fairly:1 active:5 path:1 interpret:1 obtained:5 luther:1 property:5 leaves:1 changed:1 approaches:3 suitable:5 changes:3 projection:3 plenum:1 replace:4 brought:1 achievable:1 total:9 unit:7 would:7 chooses:2 distributing:1 leaks:1 call:1 therefore:17 until:4 tolerated:5 successful:5 brings:1 berlin:1 hold:2 me:2 kraus:1 springer:1 err:2 work:3 my:3 example:18 indicated:1 give:20 bennett:6 india:1 involve:1 indicates:1 overheard:2 guarantee:1 end:1 provide:2 verify:1 enk:1 damage:1 how:6 brassard:10 description:3 replacing:1 reconciled:26 after:9 italy:1 summarize:2 law:2 attempt:3 helsinki:1 neglect:1 davies:1 ultimate:1 enter:3 triggering:1 operations:1 restriction:4 feedback:1 over:12 undetected:2 guidance:1 london:1 thesis:3 japan:1 satisfies:1 before:8 directional:6 fix:3 better:2 differently:1 potentially:1 fin:1 overcome:1 maximal:3 them:6 affected:5 combination:2 safe:4 effects:1 they:16 represents:2 tampering:1 each:29 side:8 mean:1 schemes:1 evolve:1 extract:1 restricted:2 crucial:1 re:8 laid:1 maurer:3 linear:8 associate:2 free:2 standard:2 assures:1 corrects:3 c01:4 estimate:31 muller:1 starts:1 correctness:1 nondemolition:1 unknown:1 onto:9 already:2 coding:1 duˇsek:2 restrict:1 another:3 clarity:1 illustrate:2 similarly:2 needed:2 zeros:1 too:2 tol:16 eqn:6 leaking:2 rejected:1 target:3 roles:1 rate:35 classes:1 extracting:1 rewrite:1 rao:2 mind:1 manner:1 seen:3 seem:1 tells:2 contents:1 secure:11 analyzers:3 responsible:1 oriented:1 causing:3 transmit:2 explanation:1 optimizes:1 simplify:3 optimized:2 involving:1 phase:1 observation:4 partition:2 detectors:17 points:1 principle:1 sum:2 channels:3 probe:2 wegman:2 tempted:1 d2:2 d3:1 d1:2 proposed:3 implementation:5 delays:1 rich:1 axiom:1 do:9 cryptography:9 dd:5 de:1 report:2 bar:2 method:2 multitude:1 clean:1 detection:21 depends:2 projections:2 fail:5 optimum:1 best:2 techniques:2 away:1 symmetric:2 drawn:1 caves:1 approach:5 glasgow:1 wd:24 terms:3 extend:1 nature:1 handful:1 however:15 received:13 protect:4 reported:2 against:9 receiver:5 exceeds:1 uni:4 contribution:11 expense:2 represented:5 conference:1 puts:1 basis:16 three:3 been:5 much:2 basic:3 expected:31 quantities:12 concerning:3 coherent:10 worked:1 applied:3 transformation:1 employ:2 balance:1 procedure:11 iv:6 ii:2 im:7 faked:1 interacts:1 grown:1 containing:5 perform:2 make:13 quant:3 split:2 incorrectly:4 several:4 grows:1 independent:3 hand:2 normalization:1 niu:1 prescribed:1 postponed:1 kept:3 maximizing:3 scenario:9 failing:1 academic:1 contact:1 left:3 unified:1 protocol:37 just:2 rotated:1 previous:8 monitored:1 ideal:6 passive:7 technological:1 tolerable:1 opt:6 possible:14 possibly:2 poses:1 occurring:1 performing:1 alice:53 specific:12 steps:6 arbitrary:3 security:34 right:1 deal:5 sends:6 successfully:2 unnecessary:1 subclass:2 contributing:2 linearly:1 unavoidably:1 bangalore:1 proceed:1 eavesdropper:34 o:1 essential:3 distinct:1 statements:1 presence:1 refines:1 remarks:1 hermitian:1 unambiguous:3 support:2 initial:1 approximate:2 fraction:13 was:10 form:7 becoming:1 encodes:1 failure:14 encoded:1 versions:1 hoeffding:3 maximum:3 anew:1 faking:1 b1:1 originating:1 computing:1 peres:1 guessed:1 exist:2 distributions:1 check:3 physical:2 faithful:1 dotted:4 no:21 ekert:1 nd:14 b9:2 nx:2 unambiguously:2 role:2 papers:1 ns:17 picture:1 a11:27 a10:20 models:1 hashing:1 longer:2 assume:5 modules:1 together:3 nmin:1 reception:1 time:15 quantity:2 logarithms:1 concept:1 leads:11 comments:1 grateful:1 certainly:1 amplification:17 technique:6 finally:2 analogous:2 string:14 advantage:3 orthogonal:7 choice:11 dim:4 presented:11 did:1 solved:1 upper:6 occurrence:1 maximization:2 appear:1 shares:1 shared:9 falling:2 satisfy:1 realizations:1 ρak:4 bi:7 cos2:3 groups:1 along:3 change:18 wait:1 sending:1 incoming:1 institute:2 vectors:12 accomplished:1 usually:1 bob:81 adjustable:1 useful:2 griffiths:1 extra:2 problematic:1 marked:1 fake:1 eψ:3 prove:2 positive:7 prec:22 hilbert:10 scenarios:2 perr:8 going:1 encode:3 scope:1 today:3 introducing:2 acceptable:2 validity:1 appendix:13 cases:1 franson:1 attacks:15 fock:1 values:11 growing:17 making:3 trans:1 claim:1 figure:4 sample:2 abort:1 posing:1 performed:7 occur:1 monitoring:3 yk2:1 discussion:2 write:1 optimal:12 absolute:2 parameter:20 map:2 product:3 may:4 sacrifice:1 designed:1 revealed:1 grow:2 sz:1 succeeded:1 joint:1 switch:1 so:18 definitions:2 nout:2 typical:3 subsections:1 indeed:3 pointed:3 a01:54 flips:1 course:1 experiments:7 statistical:2 differs:2 peterson:1 still:5 ieee:3 group:1 monitor:2 decreases:2 inflicted:1 decreased:1 main:4 norway:1 non:6 thereby:3 introduce:6 bound:20 arriving:4 now:17 discuss:2 nor:2 equality:1 individually:3 weighted:1 manifests:1 entering:2 sifted:49 shown:8 accomplish:1 space:11 furthermore:2 increase:2 contained:1 formula:1 correct:14 shows:5 earlier:1 theory:4 possibility:2 complicated:1 care:4 derivation:2 transition:1 thing:1 place:1 slutsky:3 βi:2 first:12 xk:3 symmetry:4 omitted:1 variables:1 huttner:3 directly:2 message:9 open:2 tomorrow:2 size:2 interchange:1 given:41 necessarily:5 iak:1 iae:4 iab:6 realization:10 bits:58 gives:14 way:15 cope:2 eliminated:1 copy:1 than:22 wide:1 distill:1 were:4 outcome:10 san:1 generality:1 remained:1 correction:28 argument:2 dash:2 say:1 recover:1 any:15 efficient:5 note:5 emphasis:1 potential:4 take:10 bailey:1 performance:1 coincide:3 switching:1 channel:33 formulas:2 begin:1 sure:5 correlation:1 satisfying:1 pair:2 especially:2 discarding:8 average:17 later:3 implications:1 refining:1 typically:3 laws:1 precise:1 show:6 notations:1 slot:1 aφ:1 aψ:5 only:20 explicitly:1 get:2 expectation:2 satisfied:2 aim:1 held:2 eavesdropping:18 bounds:2 relative:1 actively:1 collects:1 detect:3 inequalities:1 subsequent:3 definite:1 enough:2 between:24 αi:2 vertical:2 comp:1 analyzer:2 signaled:1 ǫmax:11 article:4 x2k:2 many:2 according:3 flipped:1 concentrate:2 expression:8 comes:1 sampling:2 pom:15 spans:1 moreover:1 tuning:1 encryption:1 absence:1 shortening:4 attaching:1 workshop:2 combined:2 fig:4 nrec:22 direction:1 unsafe:1 formed:6 photon:55 observe:2 coherently:1 those:5 case:25 hughes:2 proves:1 situation:10 theo:1 orientation:1 discrepancy:1 binary:2 different:13 multiphoton:1 same:11 authentication:30 verifies:1 pad:1 distilled:1 extended:3 trivially:1 nm:4 estimation:3 modes:6 polarisation:1 roughly:1 without:10 solve:2 components:2 very:2 model:2 ia:1 being:9 when:6 guided:1 rest:1 compromising:1 announcement:2 photons:11 seems:2 improvement:1 b15:1 treatment:3 samples:1 eigenstate:1 real:10 mor:2 sums:1 simmons:1 listening:2 vacuum:4 disadvantageous:1 accepted:4 correcting:6 mod:4 identifying:1 collective:3 discarded:16 either:1 output:1 reduced:1 satisfactory:1 conditional:2 cr:2 provided:2 authenticate:5 dimensions:1 legal:1 critical:2 refer:2 scientific:1 power:4 seconds:1 equivalent:1 mayers:3 qnd:1 graaf:1 comparison:5 central:1 meaning:1 practical:8 notifies:1 unbounded:1 determine:2 operator:6 accumulated:2 formulate:1 her:20 assumed:4 there:9 decode:1 start:4 intends:1 complete:6 regard:2 delayed:7 survived:1 elimination:1 improved:3 define:2 subclasses:1 expect:1 detailed:1 ohm:1 leaked:7 certain:1 ak:55 describe:2 am:1 general:3 kimble:2 governed:1 formulation:1 corresponding:6 fvac:4 again:2 acknowledgments:1 valid:1 you:1 forcing:1 separate:6 a1:2 a3:1 important:6 bounded:6 a4:1 a6:1 included:1 curve:4 hirota:1 starting:2 represent:3 epeau:2 sci:1 consider:1 caused:1 splitting:2 scalar:3 commute:1 invariably:1 research:1 subjected:1 tr:35 participants:1 kα:4 protocols:2 amplitudes:1 far:4 worst:1 difference:7 condition:8 splitter:8 large:2 small:1 employing:1 discriminates:1 zero:3 design:1 further:3 richard:1 sun:2 section:17 version:9 subspaces:3 utkenhaus:4 public:14 contrast:1 revealing:1 full:2 hash:10 tags:4 component:1 operating:1 concluding:1 strong:1 equations:7 mult:1 search:1 sender:3 losses:1 allows:6 experience:1 prior:1 amount:5 pick:1 action:3 via:5 establish:6 readily:1 eye:1 takes:4 probabilities:10 contains:1 comparing:2 taken:3 achieving:1 more:12 knows:9 operators:12 corrected:12 particular:3 known:5 foundations:1 presumed:1 none:1 tr2:2 equation:12 sent:7 morgan:1 learn:5 strategies:2 f0:2 f1:2 compare:1 omit:1 synchronized:1 messages:2 share:9 states:19 collision:25 minimum:3 numbers:6 sense:4 sharp:6 information:68 needs:3 goal:2 rather:2 maps:2 signature:1 mapping:2 tries:1 fd:9 coming:1 fi:2 horizontal:2 fk:3 short:6 supervision:1 negligible:5 help:3 september:1 mixing:1 paper:8 existence:1 computers:1 susceptible:1 polarizing:3 lateral:5 actually:5 late:1 detected:3 systems:2 might:12 yk:4 good:2 return:1 bigger:2 easily:1 finite:2 always:3 level:2 capability:2 2e:1 2f:1 inequality:8 fψ:2 found:5 characterized:2 weight:4 generation:4 reduce:1 idea:5 numeric:1 obtains:2 measurement:26 quantum:44 operation:1 beyond:2 biham:2 divide:3 since:26 denotes:3 acting:1 safety:2 denoted:4 occurs:1 ass:1 belief:1 difficulty:1 reason:2 put:4 generate:1 definition:6 pairs:3 finland:2 exponentially:1 threat:1 consequence:1 assign:1 major:1 probability:87 number:41 done:4 least:8 introduction:1 leading:9 construct:1 assumption:1 calculations:4 compromise:1 scheme:8 store:1 statement:9 part:12 shifter:3 polarized:2 fuchs:2 strathclyde:1 contrary:1 treated:1 interactive:5 beforehand:4 randomly:2 conjugate:1 option:1 depending:3 scotland:1 generalized:14 2d:1 towards:5 index:2 serve:1 measures:1 reach:2 most:4 position:7 nothing:2 measured:10 salvail:3 clear:2 coincides:1 traditional:1 optical:2 exp:4 physics:3 think:4 session:1 relation:3 fine:1 find:40 parameters:9 failed:1 subsection:1 pretty:1 factor:3 his:4 notation:2 resent:2 closely:1 international:2 during:24 resend:1 showed:2 arxiv:1 common:4 activity:1 doubles:1 locating:1 set:22 achieved:3 achieves:3 see:7 individual:10 close:2 learns:5 damping:1 currently:1 various:3 transfered:1 knowing:1 recently:1 statistically:1 complement:1 attention:1 disallow:1 distinguish:4 both:2 prescription:1 desired:1 whole:4 finds:1 experimental:8 arbitrarily:2 point:7 corresponds:1 pp:1 described:8 stamp:3 create:2 acceptance:1 due:5 strategy:14 pb:3 pc:17 secret:26 describes:3 pd:11 ph:4 pl:1 lett:1 generating:1 partly:1 c2:1 p2:4 bφ:1 look:1 exponential:1 solid:3 bψ:4 b01:6 b00:7 while:17 optimization:1 replaced:2 behavior:1 intercepts:1 shortened:4 unitary:1 itself:1 authenticated:3 fibers:2 shorten:2 shorter:4 imoto:1 reachable:1 products:3 higher:1 calculation:3 used:24 keys:8 uses:10 user:2 recent:1 lower:6 task:3 analysis:5 picks:1 c5:1 secrecy:2 abbreviation:1 tasks:1 using:14 guaranteed:2 signals:80 location:1 theorem:2 input:3 guarantees:1 remaining:9 amended:1 insert:1 evaluate:2 logical:1 appendices:1 bit:24 translucent:1 helpful:1 follows:1 signal:49 separately:1 continue:1 reduces:1 methods:8 creation:2 some:15 back:1 b4:1 b5:1 b6:1 b7:2 examples:1 b2:2 b3:1 b8:2 ourselves:1 describing:2 affects:1 measurements:9 exceeding:1 per:6 efficiencies:2 run:11 processing:1 confidence:4 bk:17 step:24 bs:3 optimize:3 bz:1 projector:3 kwiat:1 range:1 block:3 seeing:1 computational:1 into:25 within:7 appropriate:1 steven:1 statistics:1 question:3 long:5 forward:1 translate:1 sections:1 link:2 line:3 consist:2 transmits:1 up:9 us:6 un:1 fluctuations:2 similar:4 called:2 gisin:3 associated:2 reconcile:3 defined:10 flow:4 specified:2 influence:2 single:14 defines:1 codes:5 crypt:1 application:4 b14:1 priori:4 b12:1 b13:1 b10:7 b11:9 draw:1 elements:11 conventionally:1 problems:1 generated:2 allowing:1 structure:2 cryptographic:1 zbinden:1 required:1 correlates:2 incomplete:1 requires:1 having:2 once:1 discards:1 code:6 results:13 steve:1 eds:2 go:3 contributions:9 issues:2 concerned:1 deterministic:2 send:1 include:4 resources:1 ρa:5 random:7 implicitly:3 bounding:1 matrices:5 transmission:5 positions:10 notes:1 eve:81 deals:1 deleting:1 noted:4 smaller:2 carter:2 click:5 reconciliation:38 giving:1 expressed:1 experiment:4 exchange:5 respectively:5 gathered:1 following:8 explore:1 intercept:1 separation:1 others:1 involved:2 leaving:1 resulting:7 implement:1 makes:2 explain:1 examinations:1 danger:2 outcomes:1 decrease:3 pxc:14 apply:1 tools:1 manipulate:2 use:41 remains:4 next:6 few:1 themselves:2 noisy:3 possession:1 becomes:3 benchmark:1 occurred:2 detects:1 iii:3 hints:1 entangle:1 account:6 extension:1 challenge:1 averaged:2 tag:4 fulfill:1 proof:3 control:4 process:3 shizuoka:1 purposes:3 high:2 effectively:4 assumptions:1 holds:6 sif:1 instead:3 blocks:1 hashed:4 hazard:2 hashes:1 ambiguous:18 realized:1 lines:1 redundant:3 element:7 allow:7 divided:1 interpreted:1 including:2 mentioned:3 perfect:2 chosen:12 estimating:1 degrees:1 spoiling:4 communication:6 polarizations:1 practice:1 day:2 february:1 university:1 transmitted:2 mode:8 subset:4 barnett:2 related:3 measure:11 our:7 shannon:33 out:4 respects:1 announces:1 rev:6 holevo:1 reformulate:2 posteriori:3 performs:1 rec:9 cause:2 achievements:1 completely:1 york:3 dmax:1 log:16 interaction:6 could:12 keep:4 length:27 vac:1 manuscript:1 succeeds:1 reached:1 precisely:1 privacy:17 data:2 system:9 relations:5 their:7 attack:5 perfectly:1 final:31 townsend:3 psucc:2 academy:1 completed:1 exactly:1 manipulation:1 yurke:1 observed:4 limiting:2 distinguished:1 result:12 unchanged:3 discussions:1 need:14 viewed:1 angle:2 able:5 polarization:25 instance:2 concerns:1 detector:11 subject:2 who:1 but:13 device:3 class:4 stronger:2 proceedings:3 lowered:1 fact:4 encrypted:4 supported:1 anyway:3 bring:1 rough:2 trivial:1 based:4 knowledge:25 should:9 jan:1 bases:6 postulated:1 a00:77 achieve:3 exchanged:2 means:8 syst:1 overall:1 lucky:1 beam:10 ones:1 timing:1 procedures:1 evolution:1 naut:8 she:15 pulses:1 fixed:9 view:5 available:2 omission:1 exists:1 acquired:1 operates:1 computes:1 computer:2 state:3 correctly:7 progress:1 neither:2 interfere:1 efficiency:6 key:197 amer:1 problem:6 thank:2 restrictions:3 limits:3 norbert:1 taking:4 equal:5 attributed:1 ln:4 heart:1 safely:1 boyer:1 otherwise:1 splitters:2 relevant:6 conclude:4 respect:4 second:7 cauchy:6 treat:1 rates:1 choose:9 arises:1 controlled:1 commutes:1 sufficient:4 subspace:1 cos:51 c8:1 angles:2 c3:1 last:4 c1:1 repetition:1 c7:1 c6:1 present:12 c4:3 multi:10 subsets:8 bb84:3 value:19 will:40 vi:1 delaying:3 thus:2 cross:1 unity:1 parts:1 party:1 gets:1 phd:1 eurocrypt:1 infinite:1 identity:2 modeled:1 well:10 factorises:2 thought:5 sets:1 comparisons:1 arising:1 stores:1 less:11 obtain:5 ak11:13 sources:1 clocks:1 paul:1 disturbance:39 density:3 combine:2 developments:1 c10:4 match:1 identical:2 increases:1 know:5 press:2 immediately:2 loss:7 necessary:4 like:5 success:5 sizes:2 wooters:1 become:3 accessible:1 parity:15 because:1 classical:21 sequence:4 choosing:3 proofs:1 happens:3 lead:6 leak:1 avoid:3 overlap:1 does:10 intersections:1 noise:2 selecting:1 expansion:1 although:3 yuen:1 stage:4 gained:3 about:23 actual:3 world:2 certainty:2 eqns:1 dependence:3 a2:1 discard:4 introduced:1 px:1 faithfulness:1 functional:2 en:4 promise:1 van:2 additional:3 transfer:2 faithfully:2 intention:1 trigger:1 naturally:1 function:20 triggered:6 preparations:1 repeated:2 construction:1 gain:12 a5:1 he:5 count:1 made:2 whether:3 below:7 limit:16 distribution:9 mechanics:4 denote:8 interchanged:3 inf:1 identities:1 functions:2 d4:1 percent:1 detail:2 other:12 compares:2 special:1 stat:1 francisco:1 variation:1 chance:1 auxiliary:5 4t:1 indirectly:1
|
quant-ph9806009.txt |@word concept:1 partial:1 chinese:3 crucial:2 comparatively:1 results:1 unchanged:2 four:5 scalar:1 manages:1 go:2 contributions:1 seemed:1 calculate:4 shanghai:2 disability:1 corrections:1 environment:1 glaser:1 1930s:1 th:5 under:1 teaching:1 enjoying:1 divergent:8 case:1 proved:1 sinica:2 very:3 reader:1 induce:1 choice:2 puzzles:1 electron:5 putting:2 formula:1 telling:1 inherited:1 ticket:1 difference:1 continued:1 encounter:1 leads:1 annihilated:1 level:4 did:1 ref:1 solution:1 correct:1 large:6 epstein:1 avoiding:1 gauge:1 equation:1 triumph:1 enjoy:1 upper:1 talked:1 renormalized:4 warns:1 prediction:1 sign:1 approximation:1 imply:2 subtle:2 chen:5 further:3 estimated:1 substitute:2 theory:13 even:4 trick:4 what:5 appear:1 giving:1 deeply:1 section:1 selected:1 expressed:1 version:1 goes:2 new:9 method:13 contrast:1 evolving:1 calculations:1 degree:1 eternal:1 never:1 equals:2 here:3 lu:2 china:2 separation:2 irrespective:1 concluding:1 ratio:1 quite:2 appears:2 logarithmic:2 knowledge:4 obtained:1 great:1 technical:1 shift:3 inspired:1 larger:3 approaches:4 contradiction:1 airport:1 ineffective:1 loop:6 professor:2 published:1 opinion:2 chain:1 spacetime:1 sticking:1 emerge:1 via:4 useful:1 scales:2 suddenly:3 search:1 merely:1 explained:1 nanjing:2 replace:2 limn:1 univ:1 imaginary:1 unit:3 unilateral:1 use:3 metaphor:1 would:7 commun:1 covariant:1 positive:1 century:1 charge:4 next:2 calculation:11 nucl:1 going:2 call:1 m0:4 m2:5 type:1 achieving:1 possible:1 more:5 formally:1 continue:1 relax:1 becomes:3 naive:1 stable:1 limitation:1 phone:1 berlin:1 carrying:1 varying:1 rendered:1 hole:1 departure:1 must:4 me:5 keeping:1 claims:1 quantized:3 henri:1 reducing:1 science:4 originally:2 work:1 modified:1 remain:1 renders:2 evolved:1 mr:5 following:5 making:1 arrive:1 my:4 example:4 control:2 claim:2 internet:1 renormalization:13 give:1 process:5 discussed:2 share:1 high:2 sphere:1 beautiful:1 lorentz:1 something:3 want:1 sense:3 keep:1 hydrogen:1 occur:2 quark:1 gev:1 lamb:2 needs:2 rather:4 means:3 river:1 write:1 how:6 nontrivial:2 stemming:1 low:2 answer:1 place:3 parameter:14 description:1 may:6 suppose:1 after:9 regularization:9 bothered:2 diagram:3 applications:1 wrong:3 plane:2 inst:1 deviates:1 mh:6 concentrating:1 constants:4 ambiguous:1 realized:1 natural:3 third:1 higgs:5 maybe:1 explicit:3 correspond:1 su:1 predicted:3 provide:2 so:14 sect:2 seems:2 order:3 breaking:1 words:1 essence:1 over:2 satisfied:1 years:8 paper:1 through:2 thesis:1 mentioned:3 existence:1 still:1 its:8 before:5 derive:1 group:1 located:2 ln:5 interesting:2 relativity:2 actually:3 according:2 condition:2 quant:2 main:1 might:2 eventually:2 them:2 evening:1 return:1 combination:1 introduce:2 break:1 they:2 instead:1 conformity:2 singularity:12 now:11 2s1:1 nor:2 mystery:1 term:3 several:1 lies:3 cognition:4 university:5 accompanying:1 reasonable:3 each:1 found:4 difficult:1 chapt:1 upward:1 square:2 just:4 weight:1 doing:1 series:3 energy:17 hard:1 taught:2 poincare:1 forgot:1 quantum:3 our:11 beyond:3 eq:5 er:1 try:1 shown:1 flower:1 space:3 furthermore:1 since:3 lagrangian:4 research:1 particles:1 redefined:1 emerged:1 dutch:1 lecture:1 forth:1 integrated:1 shows:1 attended:1 linear:1 mσ:4 divergence:22 free:1 standard:5 difficulty:7 reason:1 surely:1 encountering:1 hep:6 enlightened:1 hand:5 beginning:2 e0:1 e2:4 interaction:2 your:1 created:1 discussing:2 could:5 transition:2 times:3 motion:2 thing:3 expecting:1 hence:4 view:4 think:2 first:4 unsatisfied:1 note:2 symmetry:3 subtlety:1 number:6 clear:1 reflects:1 nonperturbative:2 another:5 comprises:1 reached:1 xp:1 xu:1 given:2 introduction:2 data:2 top:1 system:2 approximately:2 needed:4 intermediate:1 too:3 statement:1 scheme:2 really:1 final:1 speaking:1 gives:1 shifted:1 shell:3 way:2 wang:1 explanation:1 authors:1 x2:1 absorbs:1 believe:2 than:4 achieves:1 kind:3 johnson:1 sections:1 second:2 matter:1 7th:1 historical:1 light:1 radius:1 treated:1 perturbative:3 lowest:1 rewrite:1 electrodynamics:2 ann:1 mind:1 argument:1 yielding:1 already:1 say:5 seed:1 seem:1 constrained:1 saw:1 any:8 viewed:1 collapse:1 zero:4 studying:2 latter:7 able:1 polarization:1 instance:1 internal:1 take:1 k4:1 sn:2 calculus:1 lectures:1 begin:1 added:1 shall:2 denominator:2 clearer:1 paid:1 most:5 preliminary:1 nothing:10 analytically:2 measured:1 why:3 don:1 grams:3 considered:1 year:2 calculated:2 sometimes:1 vertices:1 physica:2 dimension:8 feynman:3 yang:7 principle:1 levinson:1 physics:13 fact:4 quantity:1 precise:1 saying:1 emerging:1 violation:2 text:1 relation:1 calculable:1 substituting:1 d4:2 trivial:3 find:2 ground:1 feng:2 based:3 quoted:2 explain:1 hopeful:1 enough:1 should:6 analytic:1 only:10 experiment:8 black:1 screening:1 factor:1 integrate:1 he:1 local:1 density:1 do:1 his:1 dk:2 get:1 luke:1 between:4 methods:1 famous:3 cannot:1 dx:1 collins:1 during:1 boundary:3 ssb:5 reveal:1 qu:1 fields:1 seldom:1 arxiv:1 yield:3 morning:1 scientist:1 she:2 tunes:1 fixed:11 qm:2 approaching:5 2p1:1 available:1 set:2 questions:3 fair:1 publishers:1 undergoes:1 violated:1 observed:4 edition:1 see:3 bare:11 result:4 accelerators:1 progress:1 skill:1 acquires:1 reconfirm:4 leaves:1 said:2 definite:4 consequence:1 symmetric:1 state:7 closed:2 simplest:1 invariant:2 neither:2 previous:5 αm:1 email:1 µc:2 discovery:2 cancelling:1 basis:1 august:1 extend:1 nature:2 attention:1 weak:1 ascribed:1 however:4 wu:4 concentrate:2 ji:2 extent:1 visited:1 article:1 intelligent:1 abruptly:1 both:1 essentially:2 last:1 qft:11 freely:2 taking:2 gram:1 equal:1 quantization:5 etc:1 contribution:1 whole:1 experimental:4 comment:1 among:2 ci:2 relevant:1 cn:1 point:9 simple:3 effective:3 corresponds:2 coincidence:1 dimensional:4 pole:2 learning:1 cancel:1 moreover:1 rep:1 indefinite:1 conference:3 epistemology:1 raise:2 triviality:6 challenging:1 create:1 exceeded:1 radiative:2 due:2 been:6 teacher:2 much:4 treat:1 basic:1 poet:1 ph:3 anomaly:1 fudan:3 rge:2 life:1 arises:1 corresponding:3 observable:2 photon:2 covariance:1 understand:2 deep:1 derivative:3 improved:2 c1:3 general:1 former:1 present:4 p2:4 myself:1 handling:1 look:1 appearance:1 value:5 spontaneously:1 will:6 dept:1 while:6 proves:2 replaced:1 careers:1 behavior:1 many:6 situation:3 property:1 mhz:2 procedure:2 geometric:1 vol:2 thus:3 surprisingly:1 encountered:1 reads:2 itself:1 claimed:1 rid:1 disappear:1 different:2 italy:1 perform:4 things:1 same:2 clearly:1 complex:2 inquiry:1 evaluate:1 modification:5 dimensionless:4 finite:11 higher:2 development:1 incorrect:1 infinity:23 ni:12 pick:1 effect:1 phd:2 running:6 moving:2 purpose:1 unpublished:1 infinite:3 changing:1 yuan:2 totally:2 recent:1 lower:3 literatures:2 off:2 pµ:1 makes:1 well:1 roughly:1 analysis:1 thought:2 without:2 english:1 position:1 model:22 self:7 λr:4 guang:1 proposed:1 less:1 being:11 generally:1 accurate:1 half:1 obtain:1 aspect:1 facts:2 yes:2 yet:1 afterwards:1 adding:1 preprint:1 candidate:1 readers:1 thinking:1 had:6 except:1 add:1 setting:2 combine:1 lett:3 easy:1 theorem:2 role:1 iσ:1 excited:3 momentum:6 resolved:1 acta:2 rev:1 acute:1 read:1 devised:1 e20:1 know:1 vacuum:8 press:2 world:3 emergence:2 unique:1 counterterm:10 theor:1 like:5 particle:17 follows:4 collective:1 performing:2 extremely:1 δm:7 yields:1 either:1 arbitrary:13 popular:1 become:1 accuracy:1 qualitative:1 accessible:1 parity:1 because:2 theorists:1 often:3 deal:2 people:1 some:19 back:3 experiments:4 understood:2 sher:1 election:2 choosing:1 respect:5 diving:1 delivered:1 scale:8 proceeding:2 mood:1 bottom:1 electromagnetic:1 though:1 integration:5 philosopher:1 does:5 provides:2 prof:1 truth:1 bc:4 glimm:1 journal:1 unfixed:1 broken:2 step:5 although:1 therefore:2 emits:1 simpler:1 about:3 getting:1 capable:2 introduces:1 generated:3 remains:5 range:2 restoration:1 greatly:1 act:3 introduced:5 book:1 gamma:2 cutoff:7 raised:2 cambridge:1 into:10 within:1 integral:11 bound:4 down:2 phase:2 references:1 tiny:1 elementary:1 old:1 binding:1 quickly:1 mere:1 qed:4 span:1 classical:3 intrinsic:1 there:6 question:2 long:4 generation:3 quadratic:1 physicists:2 lot:2 lou:4 scientific:1 was:11 combined:1 function:5 survives:2 form:1 memory:2 jun:1 but:16 searching:1 change:1 reminds:1 gain:1 atom:1 padova:1 jaffe:1 fdi:9 up:5 us:6 until:2 liouville:1 limit:2 critical:1 fdis:2 continuously:1 problem:5 similar:1 called:7 mechanics:1 ac:1 diverges:1 constant:10 defined:2 abstract:1 describe:1 am:2 meaningless:1 correction:1 convergent:2 meanwhile:1 conserved:1 warning:2 phenomenological:1 floating:1 physical:4 tedious:1 again:8 mutual:1 no:20 whereas:5 attacked:1 when:13 virtual:3 field:4 other:6 remarks:2 normal:2 papers:2 department:1 mathematics:2 you:2 out:2 explaining:1 emerges:2 students:1 symbol:1 poem:2 precision:1 meaning:6 important:2 variable:2 ago:3 scharf:2 implies:2 coupling:5 values:1 tricks:1 together:1 4m:1 mass:45 doubted:1 time:6 far:2 international:1 overseas:1 original:4 once:3
|
quant-ph9806010.txt |@word represent:1 logarithms:1 partial:4 consider:3 springer:1 forbidden:1 reversibility:3 monti:2 four:1 roy:2 commute:4 per:2 computation:26 checkable:1 go:2 reasoning:3 gh:2 whose:4 supposedly:1 simon:1 violate:3 assumptions:1 show:2 presents:1 citing:1 turin:1 under:10 nodes:3 must:9 worth:2 apparatus:1 case:3 belonging:2 labels:2 amplitudes:3 advantage:1 orthogonal:8 far:1 ρr:2 h123:1 plausibility:2 polarization:1 unaltered:1 putting:1 interpreting:2 ρk:1 affect:1 1s:6 matrices:1 condition:28 entire:2 discretely:2 hamiltonian:11 diverging:1 t2:2 solution:7 t1:2 deals:1 solved:2 convenience:2 vector:23 science:2 small:2 1r:6 trr:1 barbara:1 noted:2 solutions:1 correct:1 excite:1 deutsch:1 dealing:1 grover:1 sin2:12 consists:1 likely:2 further:6 implemented:5 theory:5 even:1 established:3 what:2 abc:2 xor:4 appear:1 invertible:1 forgetting:1 diag:6 section:23 remain:4 current:4 version:1 1t:1 above:13 obvious:1 row:4 ever:1 method:1 stabilizer:1 satisfy:4 αij:5 respectively:1 loose:1 component:2 here:3 behaviour:2 desired:5 operating:5 cos2:13 others:1 alone:4 bk:2 equations:5 appears:2 obtained:4 search:1 antisymmetric:2 suitably:2 study:3 vectors:12 ignoring:1 exploitation:1 simultaneous:4 resulting:1 permutation:4 usually:1 symmetrical:3 implement:1 suitable:3 makes:2 foundations:1 uniquely:1 showing:1 tu:1 useful:2 projection:12 lloyd:1 vii:1 logical:10 highly:1 brought:1 boolean:9 decrease:1 logically:2 apply:1 total:1 establish:1 readily:7 undergone:2 projector:9 would:11 sake:1 toffoli:1 finally:1 next:2 anticommutation:1 going:1 therefore:7 taken:1 associated:2 25th:1 type:1 until:4 springs:2 more:5 introducing:2 eiδ2:1 eiδ1:1 becomes:3 operators:1 site:9 freezing:1 berlin:1 reversible:5 normalized:8 particular:3 known:2 rare:1 conditioned:1 iii:21 eγ:1 fermionic:4 hj:1 states:4 account:1 bernstein:2 ibm:1 ρi:1 ρh:2 equation:1 work:6 fast:1 dev:1 ρs:1 infinitesimal:2 drags:4 three:4 universe:8 following:7 ρz:1 root:1 example:6 performed:4 abcd:1 devise:1 renormalization:1 give:3 process:5 discussed:1 bennett:2 share:1 involve:1 minimum:1 o:4 degenerate:4 sense:2 keep:1 distinguishable:2 npcomplete:1 native:1 information:1 straightforward:1 rather:2 discussion:1 means:5 utilize:1 occur:1 how:4 pure:1 gate:30 sin:14 brassard:1 inputs:2 product:3 explores:1 whereas:2 algebra:1 may:1 max:6 after:4 diagram:2 applications:1 explored:1 lay:3 coming:1 destructive:1 heidelberg:1 short:1 purely:1 outline:1 effective:2 register:3 explicit:1 correspond:1 redundant:4 element:1 annealing:1 so:6 allow:1 keeps:4 looking:1 order:9 operations:1 exclusive:1 six:1 interpretation:11 developed:1 over:6 fredkin:1 satisfied:4 interpreted:2 course:11 during:1 own:1 through:5 filters:1 lattices:1 existence:1 satisfies:8 still:3 its:5 exchange:1 before:2 probability:6 energies:1 polarizing:1 solving:5 decreases:2 meantime:1 degrees:1 fig:9 hidden:1 might:8 happened:1 correspondence:1 symmetrization:1 them:3 good:6 affected:2 combination:5 a0r:3 a0s:2 outlined:1 a0v:2 introduce:5 disregarded:1 p12:6 p13:2 effects:2 they:4 symposium:4 oxford:1 rotation:5 now:15 nor:1 shadows:1 represents:2 february:1 fully:1 university:1 classified:1 labeling:1 establishing:1 factorizable:1 did:2 iff:1 qrs:7 truth:4 each:17 found:1 universit:1 polynomially:1 macchiavello:2 side:1 constraints:18 int:4 disregarding:3 eh:3 map:1 doing:2 series:1 energy:10 hard:2 ea:4 ec:3 eb:4 interferometer:1 abelian:1 used:4 factorization:1 entering:1 measurement:2 quantum:32 our:2 happen:1 beyond:1 eq:2 special:3 out:8 try:1 shown:2 network:66 driving:5 space:8 a1h:1 res:1 furthermore:2 since:10 interference:6 projected:2 cancels:1 research:1 particles:12 foundation:1 induced:1 ref:3 tautologically:1 attentions:1 occurs:1 weaknesses:1 turning:1 linear:5 hosted:5 diagonal:2 possibility:3 drives:1 vazirani:2 difficulty:1 completely:1 statistics:31 unwanted:1 term:4 besides:1 put:3 1u:1 anyhow:1 jozsa:4 generate:2 temperature:2 interaction:8 r1:1 r2:1 r3:2 could:2 excluding:1 times:2 motion:6 turn:1 isi:1 place:1 exponentially:3 consequence:2 approaching:1 think:1 βj:5 first:5 blind:1 initial:9 features:2 symmetry:12 variables:6 castagnoli:6 number:6 thereof:1 transform:1 channels:1 infinite:1 ars:17 done:2 relations:1 another:1 comprises:1 reached:1 genova:3 size:6 given:7 necessarily:3 checked:2 rewritten:1 needed:1 introduction:1 πi:3 system:8 least:1 their:4 assumption:2 identity:3 statement:1 1h:1 siam:1 perfectly:1 ranging:1 gives:7 free:13 exploring:1 continuous:9 interesting:1 part:10 off:1 operates:1 than:3 specify:1 wide:1 level:2 penrose:2 sections:1 anticipate:1 yet:1 see:8 submitted:4 onal:1 determined:3 pairwise:3 amplitude:5 published:3 hz:2 symmetries:2 generality:1 rewrite:1 conventional:2 turned:7 kitaev:1 peculiar:3 already:3 say:4 violating:3 close:4 need:3 seen:7 seem:1 constrained:13 counterfactuals:1 any:19 sat:4 angle:2 zero:8 convenient:2 latter:5 complexity:1 note:5 hr:4 high:1 internal:6 generalized:4 analogy:2 bailey:3 algorithms:6 unconstrained:3 renormalizes:1 blunt:3 channel:1 annihilation:1 exactly:5 multiple:1 trace:1 shall:2 reach:4 clearer:1 zender:1 most:1 exploited:2 eight:2 significant:2 phase:2 future:1 extremely:1 ekert:3 mach:1 idealized:2 operate:3 richard:1 considered:2 adopt:1 heat:5 physica:1 typeset:1 proceedings:7 lowered:1 principle:2 mechanical:1 link:23 usual:2 notion:2 incomplete:1 nov:2 heuristics:1 shor:1 particularly:1 restriction:3 random:1 anyway:1 bring:2 hh:4 fermions:1 substituting:1 find:1 ground:18 santa:3 based:6 spite:1 irreversible:2 distributed:1 hrs:22 should:21 values:1 only:9 sequential:5 hamiltonians:7 hope:1 do:1 temporarily:1 occupied:3 notation:3 di:1 de:3 overall:11 antisymmetrization:2 generalizable:1 cannot:4 legitimate:1 words:1 combinations:2 wise:1 dt:7 shaping:3 prime:1 acm:2 evolution:32 conditions:21 hinges:1 arxiv:1 yield:2 bad:2 roger:1 common:1 mapped:1 london:1 creates:1 strengths:1 require:1 view:1 set:2 reference:1 habit:1 physically:1 undergoes:2 fe:2 0s:6 notice:1 maximum:1 namely:8 triplet:2 result:7 p23:2 operated:1 recently:1 subject:6 preparation:4 phases:2 wire:5 computer:3 tensor:4 missing:1 sites:4 label:4 symmetric:3 initially:1 state:71 unable:1 use:1 between:5 αi:4 contrary:1 boundary:1 approach:5 ends:1 never:2 terms:1 visualization:1 qubits:15 however:5 operator:1 formalization:1 spare:1 come:1 problem:15 0r:7 both:2 essentially:1 0v:2 2n:1 0t:2 always:2 taking:1 annual:4 according:1 quantization:2 etc:5 a123:2 context:1 logic:5 qubit:44 mean:6 whole:4 h12:18 experimental:1 otherwise:4 unitarily:1 among:3 relativity:1 simple:2 relaxation:4 corresponds:2 dimensional:2 represented:3 polynomial:8 respect:8 throughout:3 speak:3 considering:1 resorting:1 described:3 transformations:1 second:3 basis:16 union:1 z0:1 computing:5 due:4 been:7 strategy:1 defined:2 reduction:7 workshop:1 symmetrizing:1 porting:2 ph:4 ak:2 aj:3 corresponding:3 commutes:2 mind:2 sufficient:2 coherence:3 subspace:16 cos:14 external:1 suspected:1 denote:2 spin:7 former:5 those:1 applied:2 exponential:1 ez:3 frozen:2 transformation:12 will:21 dept:1 while:2 error:1 situation:3 revisited:1 35th:2 leaves:1 unitary:8 satisfying:6 vi:3 thus:14 non:2 repeating:3 iv:22 ii:30 disjoint:1 reads:1 itself:1 increase:1 technology:1 fermion:4 binary:1 different:3 italy:2 propagation:5 generic:6 things:2 make:5 coexisting:1 indistinguishable:2 same:4 clearly:1 highlighted:3 antisymmetry:1 complex:1 quant:4 split:3 products:1 grows:1 higher:1 independent:5 wires:1 imply:1 closest:1 assignment:4 everett:7 retarded:2 effect:10 driven:2 running:1 a0t:2 entanglement:3 changing:1 conveniently:1 normalization:1 cycle:1 implements:1 fourier:1 kept:1 database:1 finds:1 without:5 solve:1 components:2 sets:2 very:1 model:7 arising:1 dimension:1 left:1 gates:2 just:2 being:6 when:8 rotated:3 obtain:1 rest:3 identify:1 thanks:1 immediately:3 alternative:4 yielding:1 speed:5 eigenstates:6 previous:2 tables:1 rs:3 generator:1 density:4 ingredient:1 drive:1 character:2 antisymmetrical:2 mathematically:3 passive:1 lattice:4 add:1 belongs:5 transformed:1 advanced:2 relevance:1 input:20 excited:6 match:1 take:3 identical:10 satisfiability:2 depends:1 eigenvalue:1 checking:3 couple:1 repetitions:1 possible:2 spanned:3 elapsed:1 finding:4 predetermined:1 know:1 vacuum:1 press:1 using:2 intersection:1 moreover:1 projects:1 mod:1 loss:1 promising:1 appearing:1 like:3 particle:48 shaped:3 follows:3 interestingly:2 specific:2 communications:2 yields:6 either:5 δi:1 translated:1 output:23 giuseppe:1 works:2 essential:1 mathematical:3 right:2 classical:1 discrete:1 conditional:2 some:7 back:2 palm:2 28th:1 table:10 curious:1 generates:1 provided:2 eiδ:1 operation:5 ported:1 affects:1 avoid:1 measurements:1 novelty:1 counterfactual:11 finkelstein:2 does:7 compute:1 proc:2 active:1 refer:1 measuring:2 conference:3 run:1 s12:5 equivalent:3 confidence:1 constructive:1 revtex:1 although:3 become:2 standpoint:2 hilbert:7 proceed:1 about:1 actual:1 working:1 extension:1 constraint:17 freedom:1 introduces:1 recognized:1 compatible:1 remains:1 cancelation:1 nothing:1 stand:2 connected:2 suggestions:1 introduced:3 consequently:4 projectors:2 soc:2 orthog:1 formerly:2 into:5 rotations:1 bath:5 down:3 pair:1 because:6 references:1 inverting:3 determine:1 computational:1 watchdog:9 reducing:1 bosonic:2 rows:2 span:5 prepare:1 removing:1 strictly:1 there:9 vedral:1 lond:1 submit:1 occupy:1 noting:1 way:19 ed:3 az0:1 was:1 propagator:1 function:5 project:1 a1u:1 creation:1 complete:8 form:10 kb:2 duly:1 reduce:1 differences:1 jun:1 independently:3 but:10 sophisticated:1 philosophers:1 expected:4 repeated:2 hi:15 hn:16 justify:2 line:1 removed:2 true:2 deployed:2 made:1 applying:9 evident:1 whether:6 wish:1 inside:2 uv:1 up:13 us:5 achieving:1 below:1 exploration:1 submitting:1 sum:2 continuously:2 0h:1 distribution:1 deadlock:1 similar:2 called:1 mechanics:3 a1t:1 constant:7 zeno:1 a1r:2 ai:10 abstract:2 describe:2 quantph:3 general:1 conserved:3 interchanged:1 formulation:4 journal:1 partly:1 commuting:3 check:3 physical:5 mosca:1 nm:2 want:1 no:7 amounts:2 index:1 individual:1 relax:1 generally:1 detail:2 application:3 build:1 other:10 branch:1 spatial:1 np:10 mathematics:1 er:3 satisfiable:7 shows:1 conclusion:2 node:1 picture:3 ξz:3 elements:3 superposition:2 a12:7 photon:1 ξr:4 problems:1 inherently:3 prepared:2 meaning:1 ξn:5 dissipation:1 ranges:2 matrix:3 eν:1 tailored:1 implies:3 algorithm:1 assume:9 starting:1 required:7 theor:3 together:4 ascertained:2 nasa:2 fact:8 a1s:2 time:34 cleve:1 decoherence:1 requires:5
|
quant-ph9806011.txt |@word pto:3 consider:1 rev:6 results:1 existing:1 scalar:2 proposition:5 computation:1 compact:1 depend:1 tr:20 th:1 norm:2 orthogonal:3 very:1 bratislava:1 putting:1 umk:3 eigenvalues:4 optics:1 mn:3 deutsch:1 theory:2 spectral:3 plays:1 sum:3 analogously:1 sup:1 ek2:1 ek1:1 respectively:1 component:2 equals:1 leo:1 separation:1 represented:1 obtained:3 institute:1 vectors:4 products:1 hospitality:1 explained:2 limn:1 use:2 would:1 fl1:1 positive:1 negative:1 next:1 therefore:4 composite:7 operators:4 cardinality:1 states:8 mo:5 work:2 following:2 proof:3 give:1 bennett:1 involve:2 inseparability:1 ijkl:1 information:2 write:1 pure:1 acta:1 product:3 after:1 centrum:1 fj:19 geometrical:1 fl:7 fn:5 natural:3 so:3 correlation:1 order:1 typical:1 separable:8 over:2 paper:2 its:2 before:1 eui:2 thank:1 majewski:3 interesting:1 degrees:1 systems:6 matematyki:1 schmidt:3 maximal:1 combination:2 βkl:2 vidal:1 equality:2 fizyki:1 iff:2 l2:5 l1:7 referred:1 em:5 ei:19 ek:7 hard:1 related:2 quantum:11 our:3 special:1 out:1 divincenzo:1 shown:3 matrix:5 space:1 since:4 crucial:1 print:2 squares:2 issue:1 linear:2 diagonal:4 estimate:1 jozsa:1 definition:2 language:2 kuna:5 vjl:5 think:1 first:1 origin:1 indebted:1 done:1 another:2 takesaki:2 given:3 necessarily:1 similarly:1 adjoint:4 system:5 relations:1 needed:1 continuous:1 part:2 than:1 coefficients:5 kind:1 characterizations:1 transferred:1 preparation:1 need:1 bhs:3 any:12 decomposing:1 subsystems:3 self:4 note:1 k2:5 k1:8 take:1 fj1:4 fj0:4 even:1 trace:2 vnl:3 most:3 αt:1 ko:1 physica:1 kl:3 physics:1 notion:2 fact:1 show:3 supported:1 spaces:4 decompositions:1 find:1 only:5 mixture:2 handle:1 cryptography:1 means:2 simplest:2 cannot:1 procedures:1 arxiv:1 maciej:1 e1i:4 e1k:1 view:1 set:3 exists:3 correlations:2 namely:1 recently:1 tensor:6 state:6 smallest:1 between:1 limit:1 barenco:1 terms:1 nature:1 inseparable:1 eˆk:6 tensors:1 last:1 equal:3 jo:5 otherwise:1 characterization:3 simple:7 character:1 dimensional:1 werner:1 ps:3 described:8 transformations:3 pt:28 aˆ:3 ah:3 ph:3 choose:3 case:1 nska:1 value:1 will:3 procedure:4 unitary:3 vol:1 sas:1 ij:13 properties:2 cone:2 io:1 supremum:1 binary:3 different:1 grant:1 lett:5 quant:3 modification:1 finite:1 hermiticity:1 purpose:1 entanglement:4 brussels:1 recent:1 off:1 poland:1 components:2 dimension:2 less:2 obtain:4 gda:2 facts:1 polish:1 density:4 point:1 seems:1 e0k:1 e0i:4 real:1 possible:1 know:1 sanpera:3 press:1 using:3 unique:1 like:1 tomita:2 follows:1 specific:1 collect:1 wooters:1 continue:1 steps:1 because:1 classical:1 some:1 choosing:1 convex:2 nonzero:1 dimensions:3 comments:1 does:3 decomposition:13 minimal:1 step:1 βij:6 hilbert:8 about:2 pα:5 column:1 basis:7 discussed:1 o:1 important:1 fl0:1 os:8 projectors:4 nsk:1 flemish:1 h2:5 communication:1 into:1 h1:5 references:1 determine:2 operator:7 there:2 u1:2 u2:2 ijmn:3 fˆl:6 slovakia:1 way:1 infinitedimensional:1 was:5 function:2 elsewhere:1 form:3 hs:2 smolin:1 jun:1 hi:1 horodecki:4 maximum:3 us:1 ul:1 ui:1 problem:1 called:1 associated:3 czachor:1 uik:5 describe:1 am:1 general:1 peres:2 separating:1 archive:2 physical:2 again:1 no:7 slovaca:1 ekert:2 ρsep:4 other:2 role:1 aˆ2:2 elements:1 models:1 june:1 a2:3 qω:1 realising:1 assume:1
|
quant-ph9806012.txt |@word gt:4 sci:1 consider:3 maximum:1 rev:24 magnetic:1 results:2 four:4 computation:5 implement:1 define:1 depend:1 graph:2 deterministic:7 young:1 γt:2 environment:1 under:1 maitre:1 division:1 g2:2 frequencies:8 rise:1 differently:1 engineered:1 wave:1 p1:1 every:1 trough:1 resonant:1 experimentally:3 difference:3 cool:1 leads:1 copropagating:1 vibrational:2 level:2 issue:1 standards:1 large:3 small:1 smaller:1 occurrence:1 pulse:6 approximation:3 rate:2 implemented:1 linear:1 even:1 what:1 trapping:1 apparatus:1 sum:1 selected:1 while:2 access:1 experiment:3 above:4 shared:1 3a:1 ground:2 equivalent:1 contrast:4 agreement:1 spacing:3 here:3 atoms:1 focused:1 separation:2 address:2 directions:1 based:2 along:5 quite:1 observing:2 dashed:1 naval:1 institute:1 studied:1 allows:3 resulting:3 conveniently:1 sinusoidal:1 plotted:1 tasks:1 gov:1 scales:1 inducing:1 modulated:1 apply:1 counts:2 total:1 establish:1 manipulate:1 use:3 would:2 army:1 probabilities:1 laflamme:1 pedagogical:1 tightly:1 a51:1 few:1 a54:1 ψb:11 today:1 more:3 bennett:3 populations:3 operators:1 envelope:1 normalized:1 known:2 cases:1 aligned:1 producing:1 must:1 entangle:1 states:27 account:1 mf:6 quantized:2 pursue:1 when:3 ρm:2 labeled:1 grover:1 example:3 performed:1 control:1 ions:16 indicated:1 process:2 cited:1 preserving:1 purposes:1 high:1 indicates:1 numbers:1 david:1 axis:1 lamb:1 information:2 requirements:2 quantph:2 carriers:1 provide:1 s1:5 xˆ:3 δk:6 write:1 varies:1 pure:1 elliptical:1 optimal:1 parameter:1 sin:1 massive:2 may:1 after:1 explored:2 matt:1 fits:1 end:1 grangier:1 data:5 types:1 efficiently:1 diagonal:3 computations:1 lines:1 ghz:2 so:2 fundamental:1 order:4 bins:1 figs:1 operations:2 gershenfeld:1 office:2 developed:1 over:4 move:1 thermal:1 experiments:3 through:1 fidelity:3 its:2 controllable:3 thank:1 fit:4 decay:2 τd:2 imperfection:1 wineland:2 detected:3 production:1 itano:1 fig:20 rabi:14 travelling:1 arrange:1 count:1 non:2 good:3 squares:1 groundstate:1 evolution:2 scaling:1 steane:1 effects:1 rotation:3 now:3 february:1 2p:4 2s:3 university:1 sideband:5 micro:6 trap:5 2b:3 each:7 inherent:2 mean:2 differential:4 england:1 significantly:1 evolve:1 generation:2 colder:1 energy:2 displacement:2 related:1 accumulators:1 frequency:9 static:2 proportional:1 quantum:20 our:7 transitions:5 eq:5 array:1 out:2 leave:2 shown:10 matrix:2 driving:5 factors:2 rep:1 since:5 crucial:3 research:3 particles:3 rf:5 print:6 induced:2 ref:1 red:2 shows:2 doppler:2 theory:2 pumping:3 drives:2 ask:1 jozsa:1 generate:2 driven:6 pairs:2 interaction:1 r1:3 r2:3 r3:1 transition:3 times:2 motion:12 exponentially:1 incorporated:1 unknown:1 first:7 major:1 there:1 probability:5 corey:2 number:4 approximate:1 approximately:1 directly:1 representations:1 ring:1 clarity:1 electronic:1 given:2 law:1 iω2:1 leading:1 histograms:2 least:1 1a:2 cooling:2 1b:4 rates:1 realization:1 siam:1 scheme:3 bits:1 final:1 store:1 gives:2 imperfect:2 trapped:7 tom:1 contribute:1 rsb:6 speakable:1 technique:3 optical:3 differentiate:1 manipulation:1 x2:1 x1:1 than:2 center:3 king:2 polarized:1 determines:1 taken:2 isolation:1 measured:3 zero:2 submitted:1 2ωc:1 preparation:6 future:1 amplitude:1 were:1 toward:1 seminal:1 function:3 addressing:5 fashion:1 sees:1 unchanged:1 measure:2 curves:3 operated:1 manuscript:1 seen:1 null:3 any:1 relatively:1 subsystems:1 strength:1 angle:2 agency:1 able:1 peculiarities:1 note:4 extracted:1 ideal:1 potential:1 build:1 analogy:1 hyperfine:1 multiple:1 electric:2 opposite:1 price:1 sets:1 singlet:6 involving:1 connected:1 letter:2 pair:3 probabilistic:1 appear:1 approximates:1 cause:1 tittel:1 average:1 drive:3 kl:2 principle:1 effect:2 maxima:1 typically:1 shor:1 selection:2 intensity:2 show:1 random:2 scattered:1 purely:1 chuang:2 degraded:1 diagonals:1 d2:6 d3:2 pkl:1 d1:3 ratio:1 copyright:1 entangling:1 only:2 wood:1 generators:1 factor:2 thompson:1 havel:1 local:1 oct:2 coherences:3 boulder:2 do:1 cryptography:1 means:2 beams:7 secular:1 de:1 overall:1 scalable:1 2a:1 beam:4 3b:1 freedman:1 processes:3 increasing:1 podolsky:2 conditions:2 arxiv:1 qc:5 europhys:1 roger:1 double:1 pulses:1 fixed:1 nist:2 atomic:1 inferred:1 set:1 reference:3 achieved:2 national:2 j0:4 j1:2 flip:2 detection:8 depends:1 individual:5 quantitatively:1 discussions:1 alternative:1 subject:1 detect:1 resonantly:1 hagley:1 away:1 motional:6 µs:4 µm:1 case:5 state:31 between:6 approach:1 arrival:1 triplet:5 recently:1 ability:1 nature:2 qubits:5 comp:1 efficiency:4 contamination:1 distinguish:1 suppressed:1 ωc:11 both:4 cos:5 limits:1 acknowledge:1 equal:1 sensitive:3 involve:1 logic:4 qubit:4 fry:1 com:4 experimental:1 relevant:5 co:5 bell:7 simple:2 poissonian:1 harmonic:1 proton:1 simply:2 moreover:1 throughout:1 second:3 strong:1 cycling:2 transformations:2 geometries:1 basis:5 stretch:6 due:6 been:3 underlying:1 describes:1 interest:1 collected:1 jefferts:1 ph:5 systems:2 arises:2 corresponding:1 sufficient:1 coherence:1 photon:3 readings:1 bulk:1 coherent:2 observe:1 alley:1 demand:1 general:1 spin:5 present:1 applied:1 p3:2 novel:1 laser:6 solid:2 polarization:1 kimble:1 will:1 technical:1 near:2 du0:1 procedure:2 turchette:2 coupled:4 averaging:1 characterize:1 vs:1 technology:1 monroe:2 different:3 unaffected:1 assure:1 perform:1 stimulated:1 quant:5 several:1 prerequisite:1 independent:1 used:3 barenco:1 conversion:1 v0:2 ion:40 levels:4 moving:1 unpublished:5 entanglement:11 contribution:1 recent:1 off:4 modes:2 nevertheless:1 modeled:1 severe:1 without:1 trials:2 position:4 ekert:3 usual:2 responsible:1 exploits:1 proposed:1 isolate:2 accurate:1 rest:1 via:1 transforms:1 aspect:2 paul:1 scattering:1 previous:1 adding:1 zoller:3 density:3 cornell:1 photons:8 point:1 had:1 dicke:1 wavevector:1 source:1 internal:5 lett:19 samples:1 heavier:1 transformation:1 opt:2 increased:1 magnify:1 government:1 innsbruck:1 decomposed:1 caps:1 interrogation:1 entangled:9 background:1 press:1 using:2 mod:3 rotate:1 like:1 particle:2 signal:4 austria:1 δl:1 mhz:5 either:3 security:1 differentially:1 reduced:1 spins:4 because:2 qed:1 sequence:1 shelving:1 huelga:1 conditional:1 some:1 elements:2 specified:1 oscillations:3 myatt:1 scale:4 confirm:1 cavity:2 univ:1 per:2 manipulations:1 critical:1 connecting:3 unit:1 provides:1 prog:1 propagating:4 bessel:1 demonstrated:2 refer:1 noise:2 nmr:1 arrow:1 2µm:2 journal:1 undergone:2 step:2 eiφ:2 described:6 selectable:1 actual:1 cavities:1 completing:1 o:1 practical:1 kwiat:1 range:3 carrier:13 mixed:1 ou:2 cambridge:2 previously:1 into:1 splitting:1 three:1 down:1 phase:3 weighted:1 references:1 determine:2 einstein:2 cascades:1 bollinger:1 infidelity:2 rely:1 institut:1 additional:1 prepare:2 classically:1 transfer:1 support:1 initial:4 u0:5 ordinate:1 start:1 mandel:1 way:1 raman:7 creation:1 kielpinski:1 jun:1 but:7 histogram:2 expected:1 illuminates:1 larger:2 removed:1 true:1 utilizing:1 ωy:1 ωx:4 ωz:1 applying:2 deterministically:1 prevents:1 ωt:3 us:4 ur:1 ωi:14 record:1 limit:1 spectroscopy:1 fluctuations:1 distribution:2 ψe:10 shih:1 distance:1 mechanics:2 khz:3 cirac:4 associated:2 computing:1 defined:1 certain:1 universal:1 describe:3 am:1 mode:8 clauser:1 single:5 controlled:1 work:1 distributions:2 eric:1 physical:1 bouwmeester:1 nm:2 no:5 dressed:1 whereas:1 rosen:2 meekhof:1 field:4 other:1 spatial:1 experimentalphysik:1 heats:1 confine:1 conclusion:1 area:1 repeat:1 superposition:1 ultimately:1 prepared:1 ξi:2 generated:3 peak:1 structure:2 coupling:1 fluorescence:2 dφ:1 4b:1 pseudo:1 leibfried:1 mass:2 parallelism:1 time:13 push:1 starting:2 unspeakable:1 4a:1
|
quant-ph9806013.txt |@word breadth:1 consider:6 limited:1 brownian:1 results:3 existing:1 gg:1 entropy:15 certainly:1 depend:1 violate:1 γq:2 finally:2 lanford:1 th:1 under:5 γc:2 analogous:2 include:2 p2:1 orthogonal:1 very:1 desirable:1 springer:1 choice:1 exact:2 generalised:1 leads:1 randomness:1 transmission:3 ref:1 michael:1 large:7 discrete:2 small:1 referred:1 upper:1 occurrence:1 probabilities:1 consistent:1 ornstein:2 zero:5 further:4 dynamics:1 estimated:1 requiring:1 canonical:3 employ:1 appear:1 sum:1 axes:5 thickness:1 above:7 replaced:1 increasing:1 method:1 exercise:1 edited:1 respectively:5 concepts:1 component:1 equals:1 here:3 compressed:1 ρx:3 represented:2 strong:1 appears:3 obtained:1 solid:1 technical:1 prior:2 amount:2 schumacher:1 suitable:2 uniquely:1 via:1 useful:3 projection:7 marginal:2 sloane:1 achievable:1 total:3 planck:1 additive:1 indicated:3 uniformity:2 commun:1 remains:1 hilbert:4 memoryless:1 depicted:1 bialynicki:1 associated:1 more:2 preserving:1 composite:2 operators:1 maximise:1 berlin:1 warm:1 particular:3 cases:2 iii:5 logarithm:3 involve:1 ρc:6 characterised:1 ρi:7 work:1 ρl:4 ρq:5 ρp:3 westmoreland:1 ulm:2 following:3 making:1 trans:1 root:2 example:4 proof:2 wang:1 figure:1 sense:3 states:9 minimum:4 numbers:2 allowed:1 counting:1 robinson:1 simple:4 absolute:1 information:7 respective:1 rather:2 discussion:1 holds:1 regions:2 pure:4 renyi:3 axis:3 ensemble:37 isotropic:1 product:6 blocks:3 description:1 may:13 thermodynamic:4 oscillators:1 different:1 collection:1 applications:2 date:1 law:3 data:4 constants:2 natural:3 dynamical:3 third:2 joint:2 lines:1 correspond:1 perhaps:1 secs:1 fundamental:1 order:1 recognised:3 interpretation:8 indeed:3 over:2 vary:1 satisfied:2 paper:1 statistical:4 existence:1 satisfies:2 still:1 ieee:1 its:4 before:1 derive:1 ln:6 microstates:2 fruitful:1 systems:4 pergamon:1 non:6 greater:4 finitedimensional:1 now:2 hall:2 eigenvalue:1 2v:2 equality:1 always:1 sufficiently:2 davydov:1 inequality:3 transmitted:3 each:1 found:1 universit:1 constraints:1 subsystem:1 square:2 due:1 energy:2 gaussian:2 related:1 elementary:1 toda:1 frequency:1 measure:13 quantum:31 eq:16 shannon:6 shown:3 space:13 restricted:1 since:2 rev:8 holevo:6 denotes:2 contained:1 denoted:1 suffices:1 math:1 unifying:1 foundation:1 log2:4 theory:6 free:2 approaches:1 york:1 darkened:2 temperature:4 derivation:4 microstate:1 could:1 times:2 length:2 derivations:2 wehrl:1 hence:4 onto:3 first:3 xj:1 xn:1 humboldt:1 probability:3 coding:1 number:8 channels:2 choose:2 approximately:4 directly:2 size:1 equating:1 given:5 cartesian:4 rewritten:1 eqs:8 amsterdam:1 relations:3 indicate:1 relationship:1 tool:1 continuous:1 somewhat:1 x1:1 than:7 diffusion:5 detection:1 holland:1 fuchs:1 sth:3 second:2 sec:4 providing:1 projections:2 fig:4 yielding:1 close:1 seen:1 tightness:1 seek:1 any:3 convenient:1 latter:2 able:1 maximum:2 note:6 high:2 take:2 trγ:4 channel:4 heisenberg:1 play:1 exactly:3 trace:1 most:1 boltzmann:3 germany:1 overlapping:5 phase:7 measured:1 es:1 clear:1 ks:1 tech:1 exp:4 north:1 typical:4 physics:1 notion:1 fact:2 quantity:2 precise:2 probl:1 particularly:1 supported:1 maassen:1 purely:1 spaces:4 relation:6 uniform:1 mycielski:1 principal:2 based:2 ensembles:38 ellipsoid:4 claude:1 should:1 only:3 employed:1 equilibrium:4 mixture:3 viewpoint:1 syst:1 account:1 next:1 closely:2 new:1 2πe:1 alexander:1 evolution:1 arxiv:1 yield:2 common:1 discussing:1 approaching:1 ignored:1 requirement:1 set:2 bounds:2 relative:2 see:3 individual:3 geometrically:3 usefulness:1 wyner:1 captions:1 recently:1 uncorrelated:3 subject:1 satisfying:2 tensor:1 state:7 various:3 closed:1 between:2 invariant:5 geometric:19 caves:2 approach:1 ire:1 available:1 terms:1 nature:1 restricting:1 however:1 distinguish:1 improve:1 essentially:1 2n:1 limits:2 many:2 region:1 uncertainty:6 equal:3 context:5 receiver:3 expression:1 arbitrarily:5 generalisation:2 ch:1 co:1 bell:1 reasons:1 corresponds:4 2nd:1 dimensional:4 alone:1 normalisation:1 projected:3 writing:1 considering:1 ensures:1 transformations:5 basis:1 copies:1 been:2 describes:2 pj:1 ph:4 pi:9 pn:1 abstract:1 define:2 digits:1 arises:1 corresponding:11 quantities:1 formed:1 general:5 those:1 case:6 p1:2 processes:3 pacs:1 contexts:4 variances:3 rectangular:2 will:8 while:3 suppose:1 error:2 property:20 ix:1 unitary:2 chaotic:1 von:2 thus:5 them:1 surface:1 iv:6 ii:4 itself:1 result:4 binary:1 containing:1 lengths:2 make:1 concavity:1 quant:4 gibbs:1 mixtures:1 proved:1 four:1 independent:5 used:1 trivially:1 i1:2 appearances:1 possible:1 v0:4 kubo:1 invariance:4 relies:1 position:2 spherical:1 unified:3 just:1 less:1 being:2 obtain:1 valuable:2 ozawa:1 λj:2 heuristic:1 density:2 except:1 mathematically:1 signals:11 thermodynamics:1 spread:1 lett:3 theorem:4 guarantees:1 remaining:1 momentum:2 spinless:1 march:1 increased:1 term:1 usefully:2 vα:3 press:1 immediately:3 unique:2 vague:1 mod:3 semi:4 particle:1 sizes:1 follows:5 signal:15 yields:2 either:4 arbitrary:2 edn:1 reduced:2 because:1 often:2 classical:28 some:4 calculated:1 examples:1 choosing:1 moreover:2 entropic:2 represent:1 illustrated:2 2e:1 measurements:2 integration:1 per:3 quantenphysik:1 provides:6 proc:1 noise:3 equivalent:1 pp:2 abteilung:1 ratios:1 yuen:1 properties:11 bz:1 raise:1 gained:2 uffink:1 central:1 would:1 constraint:1 discussed:1 o:1 distinct:1 uhlenbeck:3 mean:2 block:13 considerations:2 equally:1 communication:4 into:2 within:1 bound:8 three:1 down:1 contrasts:1 appropriate:1 weighted:1 references:1 primarily:1 operator:1 proportional:3 conceptually:1 neumann:1 area:1 transfer:2 strictly:1 there:3 question:1 approximate:1 quadratic:1 was:1 function:3 tight:1 medium:1 gibb:1 elsewhere:1 form:2 jun:3 but:2 volume:37 collected:1 hn:2 transmitter:1 irreversible:1 applying:1 whether:2 drummond:1 up:4 ur:1 below:2 limit:7 uk:1 distribution:5 similar:1 average:1 entropies:2 mechanics:5 constant:5 defined:1 universal:2 measurement:3 denote:5 single:2 inf:1 distributions:2 physical:1 no:3 dashed:1 generally:1 vanishes:1 rewriting:1 application:1 role:1 special:2 holding:1 papers:1 conclusion:1 picture:2 problems:1 deriving:1 bounded:3 birula:1 independently:1 implies:2 required:1 curve:1 together:1 reprinted:2 volumes:13 time:1 applied:1 original:1
|
quant-ph9806014.txt |@word limited:1 rev:10 focus:1 illustrated:1 quadrature:3 commute:2 entropy:6 issues:1 depend:1 concerned:1 technique:1 versity:1 finally:1 matlab:1 under:2 analogous:2 applied:3 conjecture:1 supported:1 amplitudes:3 orthogonal:6 far:1 frequencies:3 implicitly:1 results:1 print:1 experimentally:1 difference:1 condition:2 randomness:1 smithey:2 level:1 scalar:2 noiseless:1 discrete:1 dealt:1 small:1 shows:1 unsharp:2 equation:2 solutions:1 upper:2 illustrating:1 zi:5 renormalized:2 guaranteed:1 consistent:1 prediction:5 cosh:1 likely:1 estimated:3 linear:2 what:2 nonlinear:5 plays:1 appear:5 apparatus:1 incompatible:4 sum:2 expressed:1 ˆb:1 reconstruction:18 new:3 method:1 satisfy:1 supporting:1 full:7 ibid:1 aten:1 unobserved:1 helstrom:1 equals:1 here:5 met:1 sinh:1 peˇrina:1 represented:3 strong:1 equations:2 listopadu:1 larger:1 accomplished:2 products:1 characterizing:1 usually:1 fourier:1 missing:1 king:1 formulated:2 followed:1 family:3 weigert:2 austria:1 stern:1 linearly:1 flaws:1 projector:4 would:1 positive:2 definiteness:2 handles:2 ψn:1 taken:1 iteratively:1 type:1 theoretical:1 invertible:1 formally:2 successful:1 hradil:3 normalized:3 known:3 cases:1 given:6 iii:1 states:14 account:1 der:1 work:1 modified:1 reproduce:1 itself:1 values:2 era:1 erb:1 cal:1 following:1 fulfill:1 example:6 history:1 leonhardt:1 renormalization:2 give:1 neglected:1 reconstructed:3 minimum:1 numbers:1 degenerate:1 sharp:4 counting:2 guarantee:1 information:3 rays:3 provide:4 divided:1 photoelectrons:1 till:1 nontrivial:1 pure:3 instead:1 absolute:1 product:1 description:2 may:15 wallentowitz:1 designed:1 fits:1 fi:12 wave:1 data:16 branches:1 effective:2 light:2 explicit:1 yielding:1 rather:2 negligible:1 fundamental:3 correlation:1 representation:1 counted:3 bins:3 typical:1 interpretation:3 indeed:1 over:1 indistinguishable:2 already:1 statistical:3 cuts:1 existence:1 fidelity:1 its:2 perfect:1 rˆ:1 how:1 ln:3 actually:1 better:1 detected:1 permanent:1 degrees:2 fig:7 tors:1 hidden:1 might:1 outside:1 yi:27 yj:4 than:1 nonorthogonal:5 duˇsek:1 records:1 they:1 identically:1 possess:1 represents:4 february:1 finite:1 always:5 traced:1 nfi:1 sufficiently:1 each:3 found:1 universit:1 characterized:2 schemes:2 significantly:2 independent:2 ed:1 related:1 solution:2 measurement:13 quantum:41 beyond:1 eq:1 event:1 special:1 maximizes:1 matrix:16 space:4 since:6 crucial:1 denotes:1 particles:1 contained:1 maximized:1 medicine:2 ref:1 rk:4 theory:9 diagonal:8 free:2 standard:7 approaches:1 ρii:8 york:1 ρij:2 likelihood:5 derivation:1 language:2 ministry:1 optics:5 could:1 iterative:1 days:1 times:2 transfer:1 hence:2 xk:8 simplifies:2 probability:2 scanning:1 number:3 improvements:1 done:7 approximately:1 differ:1 similarly:1 unknown:2 histograms:1 system:4 relations:1 yij:1 confirming:1 observations:7 realization:1 normalization:7 postulate:3 recovered:1 exactly:1 direct:1 part:4 representing:1 peculiar:1 olomouc:1 relative:4 unfortunately:1 iteration:2 zero:1 recording:2 minimize:1 future:1 contrary:1 spoiled:1 outcome:1 distinguished:2 generality:1 palack:1 correspond:2 ible:1 need:1 seen:1 seem:1 recover:1 any:1 elsewhere:2 depending:1 ideal:3 simplified:1 xi:5 detector:1 accuracy:1 play:1 unless:1 though:2 mlynek:1 panel:3 most:2 overlapping:3 letter:1 phase:8 measured:5 φk:6 observation:2 considered:1 average:1 later:2 order:1 optical:1 physics:1 incomplete:3 particularly:1 show:5 random:7 contemporary:1 relation:8 gerlach:1 decompositions:1 rough:1 find:1 slov:2 based:1 just:1 parameters:1 ment:1 homodyning:3 should:4 only:2 envelope:1 various:2 extremum:3 do:1 subspaces:2 notation:1 di:2 cannot:3 closely:2 ˆi:1 opatrn:2 interpreted:1 5h:1 settings:1 conditions:3 arxiv:1 yield:1 cik:2 intervals:1 common:3 enhances:1 bars:4 questions:1 achieved:1 physically:1 frame:1 correlations:1 up:1 detection:8 depends:1 result:3 uller:1 discussions:1 optimum:1 techniques:3 subsequent:1 positivity:1 currently:1 state:28 determined:1 enumerated:1 between:1 tens:1 progress:1 approach:3 available:3 notice:1 never:1 complementary:1 however:1 deterministic:2 key:1 multiplier:1 suggested:1 observable:1 beck:1 many:3 region:1 uncertainty:1 parts:1 fulfilled:2 chosen:1 became:1 coh:1 estimation:4 whole:1 experimental:2 otherwise:2 necessary:2 point:2 reasons:1 overview:1 address:1 corresponds:2 hollow:4 dimensional:5 iterations:1 lagrange:1 respect:2 schleich:1 trˆ:1 late:1 described:1 basis:9 union:1 wien:1 been:6 itano:1 ph:1 λtr:1 systems:1 θj:3 corresponding:5 both:2 sufficient:2 subspace:14 zeilinger:1 coherent:1 general:5 spin:2 former:1 case:6 novel:1 uncertain:1 estimations:1 ǫn:1 value:3 will:8 while:1 suppose:1 behavior:1 error:1 squeezed:2 procedure:3 vogel:4 coupled:1 averaging:1 simulations:1 summhammer:1 ii:1 characterize:1 reads:2 vs:1 monroe:1 different:2 cji:1 grant:1 eigenvalue:1 amount:1 unity:1 complex:1 quant:1 pauli:1 several:2 events:2 neutron:2 european:1 exhaust:1 used:3 schiller:2 numerical:1 purpose:1 uni:1 infinite:1 identity:10 lower:1 center:1 matters:1 nevertheless:1 well:1 analysis:3 obviously:1 academic:1 approached:1 without:1 very:2 position:1 left:2 proposed:2 being:3 rotated:3 via:1 predicts:1 using:6 λk:2 regardless:1 eigenstates:2 network:1 cut:1 density:13 irradiated:1 seems:1 fitting:1 lett:5 republic:1 yv:1 eigenstate:1 real:1 acta:2 aspects:1 analogy:2 appreciated:1 easily:1 read:1 replaced:1 decomposed:1 inversion:7 spanned:4 homodyne:5 early:1 ρkj:1 ρki:1 vacuum:3 press:2 world:1 unique:1 coincide:2 loss:1 appearing:1 obvious:1 addressed:1 separately:1 characterizes:3 multiplicative:1 pereira:1 right:2 methods:1 classical:1 czech:2 successfully:1 phenomena:1 back:1 experiments:1 moreover:1 proper:1 guess:2 diagonalizing:1 provided:11 tmr:1 realistic:5 measurements:3 overlap:1 does:1 decomposition:4 provides:5 welsch:1 demonstrated:1 measuring:1 noise:3 eiϕ:1 performed:1 predicting:3 oscillating:1 illustration:1 although:1 banaszek:2 concreteness:1 imaginary:1 hilbert:3 raymer:2 noisy:2 comparison:2 about:4 freedom:2 faridani:1 o:6 wolf:1 insufficient:2 consequently:1 projectors:17 considerations:1 cambridge:1 wineland:1 into:4 numerically:1 functional:1 hermitian:1 inverting:1 operator:17 body:1 statistics:3 log:1 assumed:5 there:1 question:1 depicted:1 anderson:1 pared:1 low:2 was:2 synthesis:1 function:3 considerably:2 head:1 complete:4 enough:1 some:4 registered:3 jun:1 but:8 sophisticated:1 repeated:1 illuminating:1 rauch:1 solved:1 convergence:1 true:3 evident:1 fulfilling:1 cij:2 cii:1 attached:1 maximum:2 crystal:1 problem:4 panels:4 clear:1 nature:1 mechanics:1 coordinate:1 defined:2 geometrical:1 measure:1 denote:2 scanned:4 dθ:1 formulation:4 tomography:11 education:1 commuting:1 compared:1 completeness:2 when:3 meekhof:1 role:2 department:1 picture:1 elements:7 superposition:1 photon:1 searched:1 problems:1 prepared:1 generated:1 important:1 serious:1 variable:2 risken:2 opened:1 algorithm:4 assume:2 starting:1 factors:1 leibfried:1 time:1 observables:1 resolution:3
|
quant-ph9806015.txt |@word consider:1 rev:3 results:6 proposition:1 expressions:1 causes:2 scr:1 whose:1 const:2 calculate:1 subjected:1 γt:2 intensive:1 tj:11 tk:2 under:2 case:4 amplitudes:6 kτ:2 very:8 wave:1 every:3 cook:1 experimentally:1 gov:2 hamiltonian:2 turns:1 t2:1 large:3 discrete:1 small:1 upper:1 slower:1 cosn:6 repetitive:3 sin2:3 rate:2 further:2 dynamics:18 gm:1 theory:1 even:2 nonlinear:4 expressed:3 method:2 coefficient:1 full:1 archives:2 degree:2 respectively:1 equals:1 here:4 atoms:2 cos2:2 represented:2 consideration:2 equations:2 institute:1 approaches:1 periodic:1 products:3 published:1 usually:1 resonance:1 history:1 scales:1 decrease:1 linearly:1 environment:1 takes:1 remains:1 h0:3 properties:1 few:2 call:1 therefore:7 until:2 undecayed:1 zh:1 factor:1 odinger:2 known:1 must:1 khalfin:1 integrating:1 equation:5 mn:3 spontaneous:1 proof:1 randomizing:1 process:1 chiu:1 states:12 numbers:1 hydrogen:2 evidently:1 counterpart:1 decaying:2 ghirardi:1 ultracold:1 till:1 sin:4 map:3 may:7 after:10 space:1 mapping:1 law:4 revealed:1 short:8 natural:1 dynamical:1 element:1 so:3 imθ:1 essence:2 over:1 soon:3 through:1 existence:1 facilitates:1 yamaguchi:1 its:3 before:2 derive:1 decay:20 fiz:2 interesting:1 temporal:1 lithuania:1 exhibits:1 absence:2 itano:1 systems:15 rabi:1 main:1 easier:1 correspondence:1 non:5 delocalization:2 heinzen:1 effects:2 now:1 discuss:1 represents:1 2p:1 2s:1 university:1 presented:1 sufficiently:1 gt2:3 each:2 el:4 rink:1 energy:5 frequency:2 expect:1 measurement:19 quantum:47 transitions:7 eq:1 out:1 matrix:5 solved:1 furthermore:1 since:1 interference:1 chaos:4 investigation:1 print:2 electronics:1 induced:6 math:1 lithuanian:2 linear:3 localization:5 kaulakys:4 quite:1 reason:1 stochasticity:1 e0:4 interaction:3 pascazio:1 transition:6 times:3 motion:3 length:1 place:1 βm:1 teor:1 onto:2 frequent:6 features:1 probability:9 variables:1 number:3 another:1 knight:1 force:1 given:1 perturbation:1 introduction:1 leading:2 eqs:1 system:33 intermediate:4 wilkinson:1 chirikov:1 trapped:1 optical:1 manifestation:1 shortly:1 than:2 population:1 diffusion:3 depends:1 preparation:3 contrary:1 amplitude:1 outcome:2 exhibit:1 rimini:1 ann:1 confirms:1 any:1 relatively:2 acceleration:1 angle:1 zero:1 depending:1 convenient:1 isolated:1 k2:1 potential:2 opposite:2 jun:1 microsecond:1 phase:2 analytically:1 measured:2 deviations:1 observation:2 consequences:3 calculated:1 coincides:1 exp:3 physics:2 quantity:1 phenomenon:3 show:1 random:3 nτ:10 schenzle:1 nϕ:4 slow:1 only:4 postulated:1 quantph:1 get:1 de:1 ϕm:3 during:2 evolution:14 continuum:1 arxiv:1 predicted:1 reveals:1 undergoes:1 quasiclassical:1 observed:1 namely:1 result:5 misra:2 terms:1 uncorrelated:1 phases:3 state:21 simplest:2 t21:1 recently:1 nature:3 initially:1 however:4 jm:3 extent:1 modeling:1 understanding:1 suppressed:2 observable:4 cos:5 reverse:1 tractable:1 many:1 region:2 sodium:1 according:1 experimental:1 detailed:1 simple:5 asymptotically:1 period:1 anti:5 gn2:1 jetp:1 described:2 analyse:1 simplification:1 due:1 been:4 reduction:1 pd:5 ph:2 pm:1 both:1 suppress:1 coherence:1 observe:2 axiomatics:1 external:3 kicks:3 general:2 p2:6 inhibit:1 p1:6 exponential:17 excited:1 will:3 contemp:1 while:1 behavior:1 property:1 maximal:1 chaotic:4 fonda:1 casati:1 bollinger:1 verified:1 randomization:1 complex:1 quant:2 resulting:1 finite:2 independent:1 http:2 see:2 sudarshan:2 effect:20 hand:1 driven:4 action:2 moment:2 frequently:1 tunnelling:1 lower:2 schr:2 well:3 analysis:1 more:2 greatest:1 model:1 prevention:2 just:1 generally:2 obtain:1 intervals:4 eigenstates:1 density:1 gτ:2 diagonalization:2 eigenstate:2 kick:4 disappearance:1 survival:4 possible:2 early:1 inhibition:4 accepted:1 projects:3 facchi:1 like:2 accelerating:1 unstable:2 essential:1 replacement:1 therein:1 greenland:1 classical:8 some:2 duration:1 vilnius:2 scale:1 unpredictable:1 measurements:11 prog:2 yields:1 bessel:1 performed:1 journal:1 analysed:1 expansion:1 standpoint:1 between:6 simpler:1 about:1 freedom:1 discussed:1 dependence:1 probabilities:7 greatly:1 act:1 introduced:2 mechanics:2 wineland:1 into:1 bound:1 appropriate:1 references:2 sov:2 proportional:1 cho:1 additional:1 initial:5 long:4 quadratic:2 analyze:1 naturally:1 function:3 interest:1 form:1 nonexponential:1 but:1 repeated:2 multilevel:9 atom:2 eksp:1 level:2 theoretical:2 limit:1 jτ:2 stages:1 similar:1 called:4 strongly:1 lanl:2 zeno:18 certain:1 am:6 evidence:1 eu:4 functions:1 paradox:1 no:1 when:1 field:3 other:1 department:1 nr:2 theor:1 conclusion:1 deviation:6 xxx:2 superposition:2 guarneri:1 shepelyansky:1 a1:6 chance:1 a2:7 suppression:3 influence:2 astronomy:1 n2:1 izrailev:1 interval:1 time:26 nuclei:1 requires:1 rep:3
|
quant-ph9806016.txt |@word limited:1 partial:1 consider:1 both:1 results:5 existing:1 illustrated:1 postponing:1 grateful:1 dynamik:1 expressions:1 whose:1 inverse:1 depend:2 calculate:4 aτ1:1 containing:1 γn:1 th:1 under:1 aux:1 anharmonic:1 applied:1 iuk:1 jensen:2 far:1 frequencies:3 harmonics:1 choice:1 additional:1 difference:4 exact:2 condition:3 treating:1 x0j:4 x0i:4 ref:1 applicable:1 large:1 sine:1 eigenvalues:1 tognetti:3 lines:1 upper:1 work:3 prudnikov:1 det:1 arnimallee:1 direct:1 cosh:2 approximation:13 me4:3 second:19 value:7 equal:1 dynamics:1 chem:1 odd:2 even:3 optimize:1 section:6 brief:1 d3:4 reinhard:1 lt:1 axel:1 above:1 obvious:1 satifies:1 increasing:4 unintegrated:1 cuccoli:2 satisfy:1 systematic:1 respectively:1 component:1 here:2 desired:4 giachetti:2 smearing:19 sinh:5 path:8 strong:1 logarithmic:1 contraction:1 obtained:3 singapore:2 involved:1 trial:7 periodic:2 products:2 action:4 fourier:3 der:1 involves:1 plotted:1 via:1 useful:1 convolution:1 subtracts:1 polymer:1 summations:1 vii:1 coinciding:1 gordon:2 planck:1 plot:1 use:2 remains:2 contains:3 next:2 calculation:1 going:2 ψn:4 therefore:1 m3:2 eiωm:1 compactly:1 type:1 diagrams:1 more:2 becomes:4 corrected:1 odinger:5 berlin:4 correspondingly:1 sharply:1 breach:1 known:2 cases:1 iii:2 must:2 obeying:1 account:1 quartic:1 equation:2 averaged:3 oscillator:6 theories:2 values:7 temperatures:5 ms:2 following:4 field:1 example:1 stimulating:1 f1:25 f2:9 figure:1 dτ3:2 dτ2:6 dτ1:8 high:3 minimum:1 dxk:1 numbers:1 want:1 extremality:1 xmin:1 tions:1 needs:1 vanish:1 end:1 feature:1 optimal:2 ordinary:5 dσ2:1 sin:2 dσ1:1 product:2 fu:1 singular:3 may:3 thermodynamic:2 after:6 ω2t:3 dx2:1 dx1:2 dx0:1 cubic:1 ω2l:3 deviates:1 physik:1 improving:1 fk:1 fn:6 efficiently:1 forschungsgemeinschaft:1 natural:1 third:5 dσe:1 explicit:1 yielding:2 element:1 so:3 correlation:9 definitions:1 integrand:1 order:41 origin:2 help:2 cumulant:3 over:11 lαn:1 paper:1 statistical:1 mentioned:1 existence:2 its:2 τn:4 derive:1 longitudinal:4 τk:15 temporal:1 laguerre:1 exhibits:1 absence:1 systems:3 x1t:1 τp:2 yl:4 combination:1 numerically:1 fig:5 effects:1 now:4 2t:8 represents:2 term:11 w2:2 enlarged:1 inequality:3 mode:2 radial:1 2l:8 2a2:1 universit:1 side:2 en:10 successively:1 series:4 energy:20 hypergeometric:1 reduce:1 gaussian:4 solution:1 frequency:13 measure:1 quantum:14 our:2 beyond:1 eq:2 special:2 out:2 projections:1 shown:2 matrix:8 restricted:2 since:2 rev:3 denotes:4 mβ:2 formula:20 wick:4 squares:1 evaluation:2 correct:1 shows:2 benjamin:1 sinh2:1 vaia:2 theory:7 interactions:3 derived:1 mω:9 diagonal:1 free:4 standard:1 nth:2 convolutions:2 e4:2 e1:1 e0:5 e3:1 rewritten:1 15c:1 interaction:7 r0:53 excluding:1 times:4 length:3 isotropic:7 δij:1 consequence:1 generalizations:1 top:1 mvn:3 first:21 xj:2 xk:2 xi:2 xl:2 xm:3 wave:1 xf:1 number:1 theoretische:1 symmetry:1 done:2 directly:1 simplifying:1 brychkov:1 precisely:1 given:3 perturbation:22 temperature:8 introduction:1 2ωt:1 system:9 intermediate:1 constants:1 variational:27 gives:1 ryzhik:1 centered:2 transverse:2 part:1 authors:1 x2:5 x0:150 abandoning:1 distance:1 molecular:1 determines:1 effective:16 approximations:8 zero:8 matter:1 classes:1 iωm:1 denominators:2 powers:4 decompose:2 truncating:2 lowest:1 rewrite:1 hagen:1 fluctuation:1 unchanged:1 argument:1 generalization:1 deutsche:1 need:1 orders:5 paths:2 ax0:2 minimally:1 min:1 xre:1 lim:5 note:2 decomposing:1 potential:42 generalized:2 green:1 coincide:2 strengths:1 mit:1 eff:7 accuracy:2 formulas:2 pelster:1 shall:1 connected:3 gradshteyn:1 pair:3 assessed:1 inserted:1 kb:1 consequences:1 average:1 partition:9 coincides:1 possesses:1 feynman:5 exp:23 mechanical:3 physics:2 sum:7 fact:1 quantity:1 slope:1 particularly:1 rayleigh:6 german:2 janke:1 relation:1 solutions:1 trivial:1 find:7 ground:13 x1:9 based:2 knowledge:1 only:3 explicitly:1 factor:1 integrate:1 constant:1 local:15 extremum:1 δxl:1 δxk:2 goes:1 notation:2 dependent:1 express:1 expectation:12 yielded:1 ones:3 dx:9 invariant:1 δxt:1 dr:1 runs:1 transversal:2 arxiv:1 expansions:3 yield:1 summary:1 approaching:1 set:1 thesis:2 exists:1 hβ:27 correlations:1 lett:5 bounds:1 observed:1 edition:3 depends:1 result:8 w1:2 discussions:1 york:1 vint:22 best:1 eigenfunctions:1 review:2 definite:1 liouville:1 symmetric:1 state:13 various:1 between:2 crude:1 limit:13 boundary:1 reading:1 approach:6 law:1 terms:1 extend:1 initially:1 wn:8 ikx:1 however:1 reproduces:2 fluctuations:7 x1l:3 2πa2:1 undetermined:1 x2l:2 cos:2 last:2 many:2 taking:1 density:1 according:6 marichev:1 bachmann:2 context:1 x2t:2 peierls:2 expression:2 ll:1 detailed:1 abbreviate:1 cl:7 simple:1 harmonic:11 16c:1 dimensional:3 werner:1 decreases:2 polynomial:3 respect:5 specializing:2 extrema:1 described:1 three:6 been:2 quickly:1 describes:1 basic:1 anisotropic:4 ph:1 ann:1 attractive:1 dots:1 σk:1 corresponding:3 ωt:24 arcsin:1 quantities:3 new:3 observe:1 curves:1 func:1 demand:1 general:1 fokker:1 those:1 case:1 replaces:1 exponential:1 straight:1 resummation:1 evaluated:1 will:5 euclidean:2 while:2 viii:1 evaluating:2 procedure:2 eaux:2 vol:1 vi:2 von:1 thus:4 vn:3 iv:2 ii:2 reads:5 im:1 ready:1 pochhammer:1 generalizes:1 different:3 grant:1 make:1 expanded:3 same:3 any:3 freie:1 parts:1 quant:1 emphasize:1 largest:1 units:3 higher:6 development:1 independent:4 extended:3 a2t:13 see:2 lie:1 extremization:1 upon:2 effect:1 hand:3 v0:5 moment:1 moving:1 purpose:2 potentials:3 infinite:1 a2l:29 kleinert:8 schr:5 acknowledgement:1 depending:1 efficient:1 without:1 components:1 exponentials:1 position:3 dimension:3 spherical:1 distances:1 world:2 r02:10 just:1 being:2 obtain:10 abbreviation:3 orthonormality:1 atomic:2 using:2 previous:2 rapid:1 instance:1 point:3 weiss:1 reasons:1 treatment:4 guarantees:1 plasma:1 remaining:2 take:1 real:1 around:4 easily:1 rules:4 decomposed:3 sums:1 nonpolynomial:2 21c:1 press:1 immediately:3 insert:1 particle:1 δx:32 visible:1 reduces:3 performing:3 δl:2 δm:2 yields:5 gω:1 integrals:8 arbitrary:1 reduced:1 replacement:1 right:3 classical:16 truncated:2 some:2 springer:1 calculated:3 deduce:1 exemplarily:1 table:1 proper:2 happens:1 dimensions:2 bottom:1 highest:1 integration:1 does:1 decomposition:3 assuming:1 a2τ:3 minimal:1 ωij:1 inserting:4 considering:1 run:1 scientific:2 power:1 equivalent:2 expansion:17 imaginary:4 2n:8 meyer:1 extension:2 saddle:1 dependence:2 o:1 carries:1 a2:4 germany:1 slightly:1 considerations:1 outlook:1 contractions:1 presence:1 h2:4 h3:2 into:12 within:1 integral:13 square:1 accounts:2 determine:1 rossi:1 schrodinger:1 statistics:3 institut:1 log:13 support:1 there:2 approximate:1 fast:4 extremizing:1 accordingly:1 quadratic:1 low:2 way:1 forward:1 was:4 function:15 academic:1 form:2 vanishing:1 jun:1 hu:1 construction:1 convergence:3 line:1 removed:1 dissipative:2 faster:1 absent:1 2πm:1 up:4 us:4 ur:1 below:1 ωm:5 ωl:32 uk:3 ωn:3 demonstrate:2 matsubara:2 similar:1 called:1 mechanics:2 associated:1 verrucchi:1 defined:2 certain:1 convergent:1 dλ:5 simulations:1 kl:1 check:1 e2:8 functions:11 nk:1 rederive:1 no:3 fixing:1 whereas:2 when:1 arctan:1 application:3 other:1 elements:3 calculating:2 condens:1 symbol:1 primed:1 polynomials:2 γex:1 du:1 important:2 a4:4 variable:1 risken:1 dϕ:2 implies:1 coupling:2 coulomb:17 requires:1 dτ:8 packets:1 dσ:1 rule:4 4m:1 mass:1 time:8 2mω:2 starting:1 original:4 dϑ:2
|
quant-ph9806017.txt |@word represent:1 concept:1 partial:1 consider:8 scd:1 magnetic:2 results:2 alien:1 nates:1 scalar:10 gd:4 generalize:1 edu:1 go:4 perturbations:1 expressions:5 research:1 rot:4 localized:2 sch:1 whose:3 inverse:1 depend:3 calculate:3 pˆk:1 pˆj:1 sapiro:1 acting:1 passage:8 γj:2 charge:1 according:1 th:2 under:3 uchebn:2 tc:19 norm:3 division:1 straightforward:1 implicitly:2 conditions:9 dokl:4 wave:10 electron:3 matrices:13 rn:3 condition:7 leads:1 obvious:1 immediately:1 hamiltonian:14 eva:1 differentiating:1 solution:7 deals:1 item:1 english:8 vector:12 small:1 eigenvalues:1 div:3 ρk:1 possibility:3 upper:1 work:2 neighborhood:1 zj:4 foundation:2 direct:2 literature:2 approximation:3 second:2 zz:3 further:3 estimated:1 substitute:2 linear:1 ˆp:24 index:2 nonlinear:1 const:1 appear:1 section:4 analogously:2 uniform:1 current:1 ˆd:3 polinomials:1 new:2 ˆj:6 modo:1 method:5 contrast:2 satisfy:8 zeits:3 simultaneously:1 tnc:1 fiz:3 d1:7 respectively:7 component:10 here:10 odintsov:1 met:1 bj:7 σxi:1 represented:3 ratio:1 along:2 constructive:1 equations:25 change:1 z3:1 obtained:12 remark:3 antisymmetric:1 institute:3 study:1 vectors:1 allows:4 amount:1 buchbinder:1 action:2 opinion:1 auxillary:1 fourier:1 polytechnical:1 orthonormality:1 useful:1 f1:2 namely:1 pˆl:1 baier:1 replace:1 aˆt:2 malkin:1 linearly:1 derivatives:1 use:3 quasi:1 asymptotic:9 usa:3 found:1 positive:6 h0:8 contains:3 negative:5 hilbert:2 choosen:1 definiteness:2 derivation:1 msk:1 m0:46 expanding:1 taken:6 associated:1 type:3 more:3 nauka:2 heisenberg:3 gyromagnetic:1 sokolov:1 operators:19 odinger:18 berlin:1 appendix:7 everywhere:1 normalized:1 particular:4 known:3 cases:1 hold:3 iii:2 eγ:1 must:10 high:3 account:13 science:3 equation:57 averaged:3 det:1 reviews:1 values:7 dh:8 following:29 sci:1 averages:6 example:5 proof:26 f0:1 dn:4 transition:1 give:3 calculation:1 relativistic:15 magnitudes:1 organized:1 states:32 lorentz:1 allowed:1 sought:2 exclude:2 νk:4 νj:2 pseudovector:1 notation:1 verify:3 holds:20 xˆ:2 write:3 how:1 nontrivial:3 get:14 acta:1 r3x:1 verlag:1 parameter:1 product:3 express:1 description:2 singular:1 transforming:1 manuals:1 δik:3 derived:1 misunderstanding:1 applications:2 fundamental:1 inst:1 ζu:1 representations:2 fj:1 choice:2 fian:1 man:3 classics:1 physical:5 dynamical:5 succeeded:1 p98:2 explicit:4 su:1 green:5 allow:1 csd:5 representation:33 gitman:1 βk:8 order:14 michel:5 evolutionary:1 wigner:1 schwartz:1 essence:1 over:6 spectral:1 find:3 choose:1 symbols:1 paper:5 satisfies:2 γm0:1 its:8 thank:1 maps:2 chosen:1 exact:1 fix:1 solving:1 translation:1 coordinates:3 ds:1 lt:25 hxp:1 systems:3 mail:3 possessing:1 correspondence:1 them:1 good:2 return:1 material:1 introduce:1 landau:1 sssr:4 vyssh:2 hamilton:4 effects:2 they:4 half:1 own:1 now:3 yu:8 s0:8 wiley:1 fields:2 easily:2 term:5 φk:3 dirac:28 always:1 university:1 level:1 applied:1 l2:13 each:1 2m:1 side:1 characterized:1 referred:1 homogeneous:1 spinor:7 domain:1 differential:2 primarily:1 berestetskii:1 series:7 energy:2 ec:7 daµ:2 frequency:11 measure:3 quantum:40 our:5 eq:5 commuting:1 mat:4 ru:2 shown:1 rp:1 matrix:4 space:12 rep:1 since:10 rx:1 denotes:2 increase:1 orthonormalized:8 izv:2 formula:6 electronics:1 cause:1 integrated:1 math:7 shows:1 inevitably:1 i2:4 theory:15 associate:1 aˆb:2 standard:1 admits:2 indices:1 completely:1 york:1 put:3 estimate:3 publ:1 e0:10 e2:2 definition:4 r6:1 interaction:5 r1:3 r3:16 rule:1 omit:1 m20:3 nonnegative:1 motion:7 american:1 place:1 gordon:1 δij:6 unknown:1 corrections:6 teor:4 βi:6 βj:12 first:5 xj:7 xk:2 initial:7 symmetry:1 kernel:1 variables:5 xf:1 approximate:6 restrict:2 xx:1 multiplying:1 relations:10 another:1 zav:2 precisely:5 electronic:1 aharonov:1 given:10 perturbation:1 similarly:8 introduction:2 πk:1 adjoint:7 system:17 construct:9 1a:1 their:5 assumption:2 calculations:2 realization:1 eρ1:1 bagrov:12 scheme:2 ehrenfest:1 πt:14 academy:1 moscow:6 exactly:1 took:2 glauber:1 part:9 authors:1 natural:4 x0:2 than:3 atomizdat:1 variational:2 effective:1 sections:1 approximations:8 depends:2 normalizing:1 preparation:1 determined:2 fˆ:16 were:4 bargman:2 powers:6 russia:3 symmetries:2 generality:1 electrodynamics:1 ann:1 mind:1 generalization:2 already:1 manuscript:1 z0:39 need:1 r3p:1 any:13 zero:1 depending:2 lim:19 self:8 εp:1 polarization:4 erator:1 take:2 analogy:2 so:1 canonical:1 cl:16 formulas:2 electric:1 anandan:1 shall:4 δkj:1 correlation:2 simplify:1 aproximation:1 phase:5 ˆt:1 acknowledgements:1 class:11 tensor:2 fjk:1 hj:1 considered:6 calculated:4 coincides:2 physica:1 tpu:1 points:1 electrons:3 exp:8 mechanical:8 axj:1 axk:2 physics:2 notion:1 fact:2 2m0:13 spin2:1 lebedev:1 akhiezer:1 show:2 text:1 supported:1 fradkin:1 σpp:2 relation:26 solutions:24 substituting:2 d2:5 d3:8 d0:10 principal:10 q1:10 q2:1 based:4 outside:1 operational:1 λpp:8 lemma:10 only:6 explicitly:6 factor:1 λpx:3 hamiltonians:1 regularly:3 λx:3 sense:2 dk:23 klein:1 means:3 de:2 ko:3 obtain:12 aα:1 2mc:1 cannot:3 dz:1 dx:6 international:1 dt:32 aν:1 αk:1 dp:4 evolution:2 ˆk:1 ie0:5 arxiv:1 expansions:1 grav:2 imposed:2 investigate:1 nauk:1 lifshits:1 dodonov:2 qk:3 fixed:1 grad:2 view:1 magneton:1 set:12 constructing:3 hν:27 δjk:10 2i:1 quasiclassical:1 packet:1 rn3:1 see:14 result:2 discussions:1 limiting:1 analog:3 uν:3 radiates:1 phases:1 satisfying:1 commutation:2 trudy:1 review:1 consequence:1 tend:1 state:5 difficulties:1 closed:1 between:3 justified:2 approach:1 commute:1 λxx:2 terms:3 right:3 comp:1 wj:2 however:3 bose:1 dimensional:1 concentrated:9 observable:3 essentially:1 parentheses:1 instant:1 limits:2 eigenvalue:2 region:1 conclusions:2 equal:2 etc:1 bristol:1 passing:2 mean:2 expression:2 σu:2 unitarily:2 mechanics:7 relevant:1 nonadiabatic:1 nonrelativistic:7 simple:1 corresponds:1 semiclassical:45 pol:1 grants:2 σab:1 respect:17 writing:1 iρ1:1 iρ2:4 pp:11 described:3 aˆ:12 trajectory:31 px:1 kondrat:1 int:1 describes:3 asymptotics:2 pj:5 pk:3 ph:1 ak:2 define:6 aj:6 corresponding:12 σj:1 quantities:1 sufficient:1 coherence:3 subspace:1 precision:12 gen:2 coherent:25 external:8 c3:1 c2:39 denote:5 spin:15 iσ:2 c4:9 case:14 ǫb:1 p0:2 p1:3 σxx:2 propositions:1 value:1 spontaneously:1 will:4 near:2 replaced:2 momentum:1 behavior:1 situation:2 property:19 taking:7 2νk:1 unitary:7 averaging:2 wkb:2 thus:9 σf:1 ii:10 quantize:1 im:4 ave:2 c0:3 vanish:1 bargmann:7 orbital:2 verified:1 klauder:1 large:1 radiation:3 siberian:1 same:3 orders:1 beside:1 complex:9 quant:1 arguments:1 pauli:12 littlejohn:1 proved:14 constructed:7 higher:8 independent:4 used:2 trajectories:2 i4:3 hand:4 average:3 purpose:2 potentials:2 expand:2 eigenvectors:5 lower:1 schr:17 fˆ1:11 fadin:1 nevertheless:2 min:1 well:6 telegdi:5 bohr:1 concrete:2 directly:8 without:2 solve:4 sets:3 position:3 latter:4 left:1 λp:3 maslov:7 less:1 newton:1 tcs:6 rest:1 gravity:1 oxford:1 using:4 facts:1 momenta:5 frenkel:2 4m0:15 note:7 sπ:1 preprint:1 kluwer:1 density:2 point:3 seems:1 transparent:1 setting:1 combine:1 lett:1 easy:4 theorem:6 iπ:4 consideration:3 trifonov:8 iξ1:1 iξ2:1 generalized:2 real:1 rev:4 iξ:2 iγ:8 sums:1 iζ:1 know:2 appendices:1 integer:2 usually:1 mod:6 loss:1 mir:1 necessary:2 particle:18 follows:15 da:2 specific:1 4mc:1 yields:1 zitterbewegung:1 arbitrary:15 translated:1 ie:1 essential:4 acad:1 mathematical:1 lenin:1 interference:1 often:1 classical:24 absolutely:1 creation:1 some:2 springer:1 b0:3 b1:1 b2:1 b3:1 proper:1 neglecting:1 ourselves:1 ternov:3 cp:2 describing:1 lead:1 electromagnetic:7 does:1 unit:2 proc:2 preceding:1 power:3 uniformly:2 equivalent:1 2c:1 expansion:4 bk:2 substitution:1 cγ:5 cβ:3 properties:6 takes:5 about:2 tomsk:5 most:1 basis:3 anomalous:4 a3:1 o:69 reduced:1 osipov:1 ξk:4 introduced:1 hence:5 perelomov:1 eφ:10 ordinary:1 reidel:1 pergamon:1 into:25 h1:1 obtaining:2 ηj:1 equality:1 weyl:1 references:2 φxk:1 sov:5 operator:58 actually:5 germ:3 methods:2 novo:1 spinors:2 verbal:2 fˆx:2 there:4 transform:3 σxp:1 quadratic:1 way:3 was:18 eg:1 a2:1 function:22 σpi:2 complete:10 form:25 usp:1 jun:1 but:3 σpx:2 repeated:1 construction:5 aµ:3 related:1 russian:2 highest:2 themselves:1 hd:1 directed:1 applying:1 multiplicity:1 sˆµ:10 smooth:3 up:26 us:14 fˆ0:12 dordrecht:2 belov:14 limit:8 verification:1 fluctuations:3 problem:8 similar:2 called:4 assistance:1 detailed:1 gone:1 taylor:3 constant:2 uspekhi:1 defined:23 certain:3 abstract:1 pseudodifferential:1 influence:1 general:2 transl:8 tˆ:17 presented:1 dν:8 pˆ:2 sˆ0:13 formulation:1 ax:1 exist:3 viewpoint:2 dγ:7 fizika:2 defines:5 functions:23 completeness:1 no:5 hpp:2 when:3 detail:1 field:14 other:1 nat:1 department:2 mathematics:2 theor:1 dφ0:2 conclusion:1 briefly:1 elements:1 semiclassically:8 symbol:6 problems:2 a1:2 a0:2 ξj:1 important:1 ξl:2 dense:1 sides:2 ge:2 correlated:1 implies:4 faster:1 assume:3 cauchy:2 dτ:7 packets:1 usefull:1 together:1 portion:1 satisfied:1 time:4 n0:1 observables:1 requires:2 having:1 hilger:1
|
quant-ph9806018.txt |@word gw:18 concept:1 partial:2 leads:1 eds:1 scalar:1 commute:1 mnn:4 consists:1 sci:1 gl:2 isometric:1 trautmann:1 tw:4 tr:9 tp:1 finally:2 ti:1 td:1 conjecture:1 straightforward:1 orthogonal:2 very:2 rise:1 springer:1 induce:1 geometrical:1 every:1 matrices:8 turns:1 t2:4 solution:1 t1:7 vector:6 eigenvalues:1 inspection:1 fold:1 second:1 further:2 theories:1 linear:2 even:1 aim:1 invertible:2 sum:1 analogously:2 version:1 above:2 new:1 equals:3 tangent:2 governing:2 groups:1 address:1 directions:1 along:2 obtained:1 publisher:1 generalizing:1 vectors:5 action:2 suitable:2 quotient:1 projection:3 summation:1 univ:1 kobayashi:1 derivatives:1 use:2 takes:2 would:1 prove:2 covariant:2 positive:3 bundles:3 ekl:1 next:1 taken:1 more:1 flat:1 hermitean:1 becomes:2 operators:9 under:2 curvature:4 berlin:1 normalized:6 foundations:1 account:1 equation:8 radon:1 obvious:1 following:3 nonsingular:1 trans:1 proof:5 compare:1 cosmological:1 calculation:2 states:10 verlag:1 information:1 g1:5 s2:3 holds:2 feature:1 jochen:1 pure:1 hi:4 product:2 de:1 algebra:2 may:2 after:1 applications:1 inst:1 multiplication:3 horizontal:12 choice:2 parallel:2 λ2i:1 natural:1 remember:1 su:2 purification:3 so:1 order:1 indeed:2 years:1 symbols:1 course:2 paper:2 london:1 signs:1 satisfies:1 its:4 before:1 thank:1 summands:1 interesting:2 fix:1 affine:1 coordinates:2 actually:1 forms:2 fisher:1 lr:1 systems:2 derivative:2 schmidt:3 defining:1 good:1 ym:1 introduce:1 geodesic:1 they:1 half:1 now:1 represents:1 term:1 2w:7 january:1 orthonormal:4 universit:2 side:2 individually:1 differential:2 list:1 semifinite:1 related:4 parallelity:1 obtains:1 quantum:1 our:2 out:1 shown:2 eguchi:1 matrix:3 space:14 res:1 rep:2 since:1 denotes:1 re:1 geom:2 rel:1 formula:2 induced:1 math:4 theory:1 diagonal:2 free:3 standard:1 base:5 complicated:1 york:1 put:1 publ:1 beginning:1 tok:1 additional:1 derivation:1 language:1 geometry:2 length:2 hence:1 first:5 xg:1 augustusplatz:1 precisely:1 given:2 g2α:3 their:1 observations:1 structures:1 1l:4 gives:2 part:2 dittmann:5 uhlmann:5 distance:2 hanson:1 see:5 kakutani:1 declare:1 topics:1 argument:1 generalization:2 say:1 need:2 any:1 hessian:1 depending:1 rudolph:4 mills:9 note:3 lifts:1 gα:32 investigations:1 object:1 gλ:6 metrics:2 involving:1 formulae:3 reducible:1 class:1 especially:1 later:1 coincides:1 tα:9 yang:9 fact:1 nikodym:1 show:4 leibniz:1 notations:3 spaces:2 gauge:7 solutions:1 purifications:1 trivial:1 principal:5 fibre:1 just:1 assertion:3 only:1 explicitly:1 equipped:1 araki:1 local:1 hij:12 do:1 get:3 dg:1 express:2 words:1 hii:1 dt:1 gen:1 fields:6 λu:1 arxiv:1 grav:1 view:1 riemannian:9 kernel:1 set:3 namely:1 discussions:1 facilitates:1 analog:1 subject:1 gravitation:2 tensor:1 nondegenerate:1 state:3 µi:2 invariant:3 geometric:2 available:1 publishers:1 terms:2 vertical:5 wo:6 comp:1 vanishing:2 key:1 amer:1 ker:2 both:2 essentially:1 last:3 taking:1 thor:1 fulfilled:1 connection:12 became:1 berry:2 uni:1 cn:1 point:2 leipzig:4 dimensional:1 represented:2 sakai:1 conjugation:1 nomizu:1 moreover:5 described:1 submanifold:2 basis:4 due:1 gd:1 bures:13 algebras:1 define:5 corresponding:1 finishes:2 quantities:1 sufficient:1 subspace:1 spectrum:3 lift:1 mail:1 denote:3 manifolds:1 case:9 gilkey:1 classifications:1 value:1 heidelberg:1 will:5 equivariance:1 suppose:1 eii:1 eij:10 unitary:1 vol:1 metric:20 ir:1 thus:2 ii:1 properties:1 vanish:2 different:1 fibers:1 s2n:1 same:1 verifies:1 quant:1 emphasize:1 pauli:1 finite:3 used:1 dimh:1 interscience:1 hand:2 purpose:1 totally:1 well:1 academic:1 dimension:2 left:3 manifold:3 proposed:2 resp:4 obtain:2 underlying:1 identify:1 λj:4 λi:6 adw:1 kluwer:1 density:3 seems:1 parametrization:1 source:3 valid:1 lett:1 easy:1 theorem:7 complements:2 remaining:2 real:1 rules:1 sums:1 background:1 using:5 helpful:1 like:1 reduces:1 reduced:1 detw:2 because:1 classical:1 some:2 understood:1 respect:1 transport:2 dense:1 antihermitian:1 normal:2 hodge:2 does:1 decomposition:1 inserting:1 measures:1 kyoto:1 although:1 hilbert:4 extension:1 remains:1 terminology:1 mixed:6 soc:1 subbundle:2 into:2 preliminary:1 phase:3 hermitian:3 right:4 references:1 einstein:4 operator:2 statistics:1 institut:2 deal:1 was:2 function:1 complete:1 form:7 hs:3 regard:1 jun:1 but:3 construction:1 true:1 ph:1 observation:1 constitute:1 besse:1 similar:1 called:1 fulfills:2 constant:2 ad:1 defined:1 certain:2 abstract:1 contribute:1 general:3 aw:1 check:1 defines:1 completeness:1 faithful:3 no:1 mathematik:1 whereas:1 submersions:1 vanishes:1 field:6 other:1 mathematics:1 really:1 nw:1 mathematisches:2 polar:1 elements:1 star:1 bundle:14 generated:1 describing:1 eji:7 independently:1 implies:2 dω:1 rule:1 noncommutative:1 n2:1
|
quant-ph9806019.txt |@word supersymmetrical:2 concept:2 partial:1 consider:3 remarkable:1 represent:1 global:3 trigonometric:1 leads:10 roy:1 generalize:1 grateful:1 expressions:1 families:1 factorizing:1 ihep:1 whose:1 preserves:4 simon:1 depend:1 baye:3 paris:2 concerned:1 quasi:14 according:1 petersburg:3 th:5 under:7 include:1 worth:1 iui:4 division:1 g2:4 notations:1 without:1 very:3 b188:1 k02:1 wave:21 normalizability:9 witten:1 ζn2:1 ζn1:1 resonant:1 affect:1 iǫi:6 condition:10 illustrated:1 hamiltonian:14 irreducible:2 solution:5 damped:1 large:5 solved:2 phase:1 inversions:1 eigenvalues:2 mo:1 proof:4 milton:1 2k0:1 b202:1 sukhatme:2 dealing:1 consistent:1 benefitted:1 literature:1 cosh:8 second:6 displays:1 irreducibility:1 incidentally:1 dedonder:3 implemented:1 odd:3 renormalizes:1 spectral:4 what:2 sub:1 iterating:1 giving:1 several:1 section:4 sofianos:1 univer:1 above:7 new:6 increasing:1 preserved:1 exercise:1 paradoxical:1 satisfy:1 condensed:1 full:2 lee:1 ibid:1 excludes:1 respectively:1 here:3 behaviour:10 growing:1 possibility:2 sinh:1 nonsingular:2 represented:1 const:4 quite:1 equations:4 change:1 deduced:1 obtained:4 remark:2 suitably:2 technical:1 shift:6 study:3 studied:1 allows:4 commonly:1 p2:1 superpotential:6 resulting:2 khare:2 suitable:6 makes:2 cancellation:1 involves:1 york:4 appropriately:1 via:2 useful:2 4a3:1 namely:1 explained:2 ipn:1 treatment:1 rφ:1 decrease:3 support:2 neutrino:1 total:1 inc:1 use:3 asymptotic:3 would:3 found:2 positive:3 negative:3 france:1 comparing:1 nucl:3 pnpi:1 call:1 therefore:1 bender:3 isospectrality:10 type:3 theoretical:2 ψe:3 introducing:1 sons:1 l195:1 formally:2 hermitean:16 becomes:1 operators:2 falloff:1 interplay:1 borisov:1 berlin:1 correspondingly:4 everywhere:2 particular:4 known:4 cases:6 hold:2 states:12 account:1 c41:1 effectively:1 equation:11 work:1 oscillator:1 centrifugal:4 remain:1 ρr:1 obvious:2 publications:1 transparency:2 following:1 making:1 example:8 stimulating:1 performed:1 control:2 compare:1 finland:1 give:2 outline:1 allowed:2 neglected:1 involve:2 sphere:1 numbers:1 want:1 sense:3 unphysical:3 quark:1 axis:9 lamb:1 end:1 provide:5 verify:1 discussion:5 write:2 maps:2 nontrivial:1 reducible:1 pure:1 instead:2 ordinary:1 verlag:1 parameter:2 b15:1 oscillatory:1 map:3 fr:1 express:2 intended:1 singular:2 oscillators:1 after:1 derived:2 mapping:11 conjugations:2 applications:4 explored:1 studies:2 cannata:4 drastic:1 sankt:2 choice:1 2l0:3 constants:3 stress:3 natural:2 dynamical:1 sech:3 spectra:4 explicit:2 correspond:2 lahiri:1 rather:1 complexity:1 cannot:6 so:7 sect:12 allow:3 jussieu:2 heuristically:1 order:9 typical:1 least:2 interpretation:1 dx:2 zee:1 indeed:6 expects:1 interpreted:2 russian:1 course:1 paper:3 including:3 statistical:2 mentioned:3 existence:4 still:3 its:7 before:2 chemical:1 derive:4 how:3 energies:1 interesting:4 a21:1 conjugation:3 forms:1 absence:4 ǫ2i:2 systems:5 mail:3 andrianov:4 main:1 supersymmetry:1 ince:1 non:16 thereby:1 2κf:1 outlined:1 introduce:3 framework:3 repulsive:3 snoopy:2 half:5 1b:1 singularity:1 now:3 realize:1 wiley:2 easily:1 inversion:2 2w:1 beacom:1 university:4 presented:1 2x:4 normally:1 2f:2 2g:8 mode:1 l0:5 radial:9 2m:3 universit:1 chapt:1 2i:1 reactions:1 differential:1 successively:1 another:2 simplicity:1 hadronic:1 energy:14 try:1 feinberg:1 gaussian:2 related:2 each:1 operator:3 used:1 yield:1 quantum:13 our:6 approximated:1 differ:1 eq:12 special:2 er:1 ru:2 matrix:3 discrete:3 furthermore:2 since:6 rev:1 behaviours:1 financed:1 integrated:1 math:2 antiunitary:1 benjamin:1 foundation:1 numerical:1 theory:6 barrier:2 interactions:1 singularities:3 contain:1 fisica:1 free:2 standard:8 small:1 reason:1 complicated:1 term:1 hand:1 finite:3 possibly:2 definition:1 derivation:1 βr:2 determining:1 could:1 impose:1 int:4 produce:1 place:1 exponentially:2 leading:3 generalizations:1 dipartimento:1 first:8 origin:11 already:1 xn:1 aust:1 symmetry:1 researches:1 channels:1 2a2:1 relations:14 directly:1 dominating:1 angular:1 illustrate:3 given:9 necessarily:3 hyperbolic:1 introduction:1 bologna:1 eqs:2 they:1 construct:9 sech2:1 their:2 intermediate:4 zeros:1 realization:1 john:1 speaking:1 gives:1 a30:1 grant:2 relationship:1 tool:1 realized:2 optical:2 2ar:1 authors:1 attempt:1 translation:1 dissipativity:2 than:1 modes:2 develop:1 princeton:2 sections:1 require:1 zero:4 limiting:2 matter:2 determined:1 contrary:1 boettcher:1 treated:1 russia:1 ansatz:5 rewrite:1 acknowledged:1 topics:1 partnership:3 spectrum:10 regime:1 peculiar:1 qualitatively:1 intertwining:18 obviously:1 apparently:1 any:1 paths:1 strength:1 genuine:1 depending:1 thoroughly:1 physique:1 note:2 instance:1 emphasis:2 potential:51 absorbed:1 generalized:2 simplified:1 feshbach:1 even:3 begin:1 unless:1 opposite:1 collaboration:1 decreasing:2 riccati:1 exponentials:1 regular:3 connected:1 successive:1 remarks:4 analytically:2 extremely:1 class:10 soliton:1 laurent:1 consequences:2 clear:1 coincides:2 astonishing:1 part:12 principle:1 exp:14 subsequent:1 physics:6 fact:2 dover:1 fricke:1 connect:1 purely:4 relation:3 solutions:7 miller:1 analogue:1 trivial:3 find:2 partners:1 finally:1 parameters:3 true:1 inserted:1 start:1 should:4 iei:1 analytic:1 only:5 explicitly:3 black:1 subsection:4 factor:1 integrate:1 hamiltonians:20 discuss:3 do:2 di:1 superpotentials:10 2a:1 ones:1 damping:1 reversal:3 despite:1 isaacson:1 dr:2 gen:2 coth:1 normalizable:6 de:1 continuum:2 approach:11 arxiv:1 factorization:7 investigate:3 balantekin:2 common:1 activity:1 analytical:1 αn:2 discussing:1 preserve:2 requirement:3 exists:1 achieved:1 imposing:3 2c:1 outgoing:1 see:4 intertwine:1 discussions:1 terms:9 iu:3 techniques:1 αr:5 eigenfunctions:4 nuclear:4 definite:3 µr:1 state:12 classes:1 various:1 between:11 invariant:7 boundary:2 conditions:10 x4n:2 choose:4 ikr:2 notice:2 restricting:3 recently:2 shabat:3 extend:2 opening:1 attention:2 however:3 jr:1 gratefully:1 vanishing:3 2λg:1 jetp:1 irnerio:1 suggested:1 both:8 x2n:2 last:3 2n:3 clayton:1 many:1 taking:5 parts:1 a5:2 chosen:1 connection:1 sitenko:1 context:2 argue:1 whole:6 schroedinger:7 jersey:1 otherwise:1 among:1 necessary:1 conclude:2 simple:2 asymptotically:3 corresponds:2 ingoing:3 dimensional:3 denis:2 polynomial:7 constant:7 considers:1 superpartner:1 most:1 strong:2 transformations:10 pt:6 basis:1 sl0:1 due:1 been:5 ai:2 cosine:2 combined:1 basic:2 expected:1 αx:3 ph:1 define:1 mccurdy:1 referee:1 corresponding:5 2ǫr:2 itzykson:1 concerning:4 2dr:2 derivative:2 2n1:1 present:2 reverse:1 case:23 exponential:2 tanh:5 plasma:1 ǫi:24 value:3 choices:1 will:9 ǫr:38 while:6 replaced:1 korsch:1 spbu:2 property:5 subsect:3 identical:2 generate:2 bohr:1 phenomenological:1 thus:3 equal:2 sity:1 regularity:1 im:1 susy:20 partner:7 mod:4 vanish:2 k0:5 ig:5 unanyan:1 different:2 italy:1 propagation:1 generic:1 make:2 lett:1 same:2 shifts:1 unity:1 complex:69 quant:1 arguments:4 physical:13 grows:1 conflict:1 higher:4 independent:1 supercharge:3 extended:1 infinity:6 i2:1 absorptive:2 average:1 potentials:48 infinite:1 invariance:5 normalization:1 task:1 supercharges:4 reflection:1 mention:2 expression:2 no:8 well:4 roughly:1 finds:1 severe:1 contact:1 solve:2 reexpressed:1 paris7:2 coordinate:1 model:2 parametric:1 possesses:1 preprints:1 derrick:1 stringent:1 cosh2:1 quoted:1 less:2 able:3 grammaticos:1 obtain:5 detail:2 topic:1 shape:1 formulated:3 aspect:1 alternative:1 reality:1 scattering:8 rotation:1 previous:4 speculate:1 preprint:6 unable:1 application:1 zakharov:3 absorption:1 transparent:11 signals:1 concerns:1 attractive:2 easy:1 iρ:3 mottelson:1 formal:1 solvable:3 transformation:5 build:1 real:49 depends:1 eigenvalue:1 read:1 results:2 possible:6 cf:10 eorique:1 know:1 mol:1 press:2 appearing:1 apart:8 insert:1 intertwined:2 like:6 alternatively:2 reduces:2 performing:1 diderot:2 specific:5 flux:1 imposes:1 yields:1 blencowe:2 arbitrary:5 mentum:1 gluon:1 downward:1 stationary:3 sign:2 therein:2 parity:8 because:9 deal:3 sequence:1 creation:1 some:5 springer:1 deduce:1 growth:2 examples:5 respect:4 ourselves:1 a10:1 separately:1 vol:2 extinction:2 proceeding:1 lead:3 resonances:1 avoid:1 does:2 provides:1 assuming:2 refer:1 inserting:1 considering:1 biology:1 power:1 rep:1 problems:4 equivalent:4 bo:1 agreement:1 illustration:1 constructive:1 although:1 substitution:2 imaginary:10 properties:4 perspectives:1 nishnianidze:1 about:1 amado:1 extension:1 constraint:1 shnerb:1 discussed:6 dependence:1 compatible:4 range:1 involving:1 repulsion:1 done:1 shared:1 illuminating:1 mathematical:1 outlook:2 cambridge:2 letters:1 follows:1 unbounded:1 into:4 within:2 numerically:1 bound:18 three:1 lies:1 appropriate:1 references:3 lively:1 sov:1 isospectral:2 proportional:1 next:1 orsay:1 acknowledgements:1 hep:3 classical:1 few:1 drouffe:1 assumed:2 strictly:2 there:10 limit:5 fast:1 why:3 strict:5 quadratic:1 cond:2 way:2 ψn:4 was:6 naturally:1 function:7 conciseness:1 form:1 jun:1 but:8 cedex:1 construction:4 korte:1 yang:1 ioffe:4 line:11 level:1 dissipative:7 considerable:1 infn:3 made:1 applying:1 levai:1 contradistinction:1 instructive:1 mat:2 smooth:1 us:3 ur:33 below:5 ui:24 ansaetze:1 problem:17 more:4 similar:4 called:5 obtains:4 mechanics:13 interval:2 associated:3 defined:3 u2:1 general:10 exist:1 supersymmetric:1 reflecting:1 formalism:3 check:5 constructed:2 again:3 functions:15 completeness:1 variety:6 whereas:2 vanishes:4 arctan:1 field:3 other:7 role:3 details:1 a6:1 solitons:1 department:1 briefly:1 elements:2 generates:1 respects:1 models:4 become:1 contextually:1 generated:2 a2:10 bounded:3 allowing:3 n1:2 cooper:1 structure:1 jones:1 independently:1 implies:7 faster:1 assume:1 values:4 required:1 turbiner:1 investigated:1 appendix:1 nelson:1 time:4 far:1 4g:5 n2:3 starting:1 having:2 provided:1
|
quant-ph9806020.txt |@word represent:2 sci:1 consider:7 forbidden:1 separates:1 results:7 leads:13 discreteness:1 ge:1 comments:1 expressions:1 hole:3 whose:12 preserves:1 inverse:1 depend:1 technique:13 supported:2 finally:4 those:3 under:2 te:2 worth:1 divergent:1 applied:2 belonging:1 global:2 leeb:1 orthogonal:2 implicitly:1 rise:1 2rb:1 choice:4 suggesting:1 electron:2 witten:1 fam:1 trouble:1 difference:1 exact:2 condition:2 illustrated:1 hussin:2 hamiltonian:31 positions:2 nucl:1 guo:1 solution:15 leave:1 solved:3 elsewhere:2 math:5 indices:1 eigenvalues:16 subindex:2 spiridonov:1 wronskian:1 specially:1 sukhatme:1 ze:1 direct:1 centrifugal:1 jump:1 second:24 ǫm:2 further:5 odd:5 spectral:2 aim:1 letts:2 iterating:1 giving:1 trivial:2 section:14 labeled:2 agrees:1 en:5 above:4 referees:1 new:36 method:18 filled:1 coefficient:1 agreement:1 confluent:2 simultaneously:1 placing:1 here:1 atoms:2 behaviour:3 reported:3 possibility:1 address:1 represented:1 luis:1 equations:14 implicit:2 change:2 arena:1 remark:5 generalizing:1 involved:1 study:2 changed:1 allows:7 example:3 resulting:2 aψ:9 action:3 hospitality:1 narrow:1 makes:2 involves:3 plotted:1 named:1 identification:1 depart:1 besides:2 family:18 f1:3 ipn:2 a22:1 tools:3 linearly:2 use:4 eψ:3 working:1 prove:1 sake:3 positive:2 continuous:2 contains:1 direction:1 charge:1 next:5 comparing:4 harmonics:1 going:4 ψn:2 therefore:5 ψl:3 ψb:5 type:2 historically:1 2ρx:2 more:4 introducing:4 sharing:1 oscar:1 operators:12 apparent:2 odinger:11 validity:1 borisov:1 particular:17 known:11 cases:7 balakrishnan:1 must:1 account:3 r2:2 effectively:1 avoiding:1 equation:46 work:6 oscillator:6 modified:2 mk:5 atypical:2 remain:1 minimum:1 values:8 following:8 making:2 arrive:1 singularities:3 mx:1 asymptotic:1 ions:1 del:2 wang:1 figure:4 process:3 arise:1 suggestions:2 states:3 indicates:1 anihilation:2 caution:1 performed:2 sense:1 unphysical:4 tions:1 hydrogen:27 ylm:1 netherlands:1 notation:3 darboux:4 describes:1 discussion:4 means:12 write:8 how:4 opposite:2 answer:1 instead:1 ordinary:1 parameter:3 isotropic:1 pub:1 simplicity:2 product:3 express:2 intended:1 suppose:2 after:6 derived:14 dx2:3 diagram:1 hence:14 fd:1 studies:1 meaningful:1 excited:1 constants:1 curve:1 andez:13 natural:4 third:2 supersymmetric:3 spectra:5 explicit:2 departure:1 element:1 fraction:1 so:3 allow:1 βk:1 order:73 se:1 typical:1 operations:2 restriction:1 six:1 words:1 mielnik:18 produces:5 indeed:2 produced:1 paper:5 2v:2 thesis:1 mentioned:2 uva:1 satisfies:1 its:3 fis:1 derive:4 thank:1 clk:4 energies:13 interesting:8 solving:2 fruitful:1 forms:1 h2:6 absence:1 choose:1 inspecting:1 mail:1 easier:1 non:9 greater:4 combination:1 propose:1 analitically:1 fig:1 introduce:4 ze2:1 framework:1 ces:5 they:6 singularity:1 now:21 transparent:2 eigenvalue:5 term:6 castilla:1 equality:1 2r:4 level:24 2x:2 labeling:2 grows:1 orthonormal:1 l2:12 radial:7 2l:28 found:7 side:2 characterized:1 homogeneous:1 el:11 domain:4 differential:26 doctrine:1 meaningless:1 energy:36 hypergeometric:3 related:8 isospectral:23 literature:1 quantum:5 our:13 es:1 out:2 try:1 shown:6 rr:1 discrete:2 rep:1 since:4 rev:3 unknown:1 denotes:1 looking:3 rb:1 max:1 denoted:1 formula:1 note:2 shows:3 benefited:1 linear:10 hull:7 ısica:3 departamento:3 standard:7 quart:1 nth:5 reason:1 advantages:1 members:2 beginning:1 c02:1 definition:2 perform:1 benefits:1 derivation:2 language:1 discussing:1 could:3 iterative:2 turn:1 v3:1 due:1 universidad:1 consequence:1 βm:1 teor:1 first:48 origin:2 initial:10 symmetry:2 number:8 linking:1 multiplying:1 embraced:1 preparation:1 clarity:1 electronic:1 angular:2 given:37 rewritten:2 similarly:1 introduction:1 leading:2 eqs:1 behaves:1 system:3 construct:2 their:3 intermediate:1 calculations:1 dealing:1 scheme:1 really:1 final:2 recovered:2 gives:3 free:5 olmo:1 shell:1 way:3 relationship:9 mariano:1 exactly:9 asumption:2 negro:1 nieto:7 authors:2 dutra:1 than:8 coefficients:1 wide:1 kind:1 holland:1 sections:2 iteration:3 zero:4 aims:1 annihilation:1 matter:1 determined:4 providing:1 powers:1 perturbative:2 rend:1 generality:1 rewrite:1 ann:1 spectrum:20 generalization:6 affirmative:1 factorizations:3 close:1 intertwining:36 seen:3 cumbersome:1 recover:1 apparently:1 any:3 option:1 min:1 able:1 isolated:1 εm:12 instance:3 potential:35 generalized:1 subject:1 even:5 added:5 unless:1 shall:10 who:1 satisfy:1 riccati:14 algebraic:2 involving:1 ensure:1 compt:1 successive:1 nothing:1 iterate:1 acknowledgements:1 why:1 exico:2 seshadri:1 constructed:1 fills:1 considered:3 arising:2 clear:6 later:1 km:156 kl:1 traditional:3 exp:3 left:2 fact:2 dover:1 show:6 labels:1 ioffe:1 solutions:35 label:1 d2:12 find:4 ground:17 partners:1 partially:1 resemblance:1 parameters:1 situations:2 only:7 explicitly:3 generators:1 about:1 molecules:1 developed:1 integrable:4 moses:2 hamiltonians:19 oct:1 do:2 viewpoint:1 get:17 samsonov:2 de:6 azimutal:1 ones:2 negative:1 dx:18 during:2 respectively:4 procedures:4 prime:1 evident:1 seldom:1 arxiv:1 βl:6 factorization:43 roy:3 common:1 gotten:1 γl:2 fixed:6 qm:3 valid:1 kernel:3 set:16 exists:1 physically:3 tilde:1 ends:2 up:2 see:17 intertwine:1 result:3 discussions:2 terms:2 particle:1 techniques:2 project:1 said:1 eigenfunctions:14 ul:10 ways:1 definite:1 yet:1 symmetric:1 originated:1 state:20 various:1 between:8 invariant:1 neither:1 previous:1 approach:10 available:1 notice:14 recently:4 missing:3 cinvestav:3 however:7 reproduces:1 le:1 key:6 come:1 junker:2 both:4 essentially:1 last:2 reinterpreted:1 many:1 taking:5 equal:8 against:1 chosen:1 hψ:1 became:1 present:3 filho:1 departing:1 multi:1 whole:3 experimental:1 ansatz:2 ck:1 aa:2 relevant:1 author:3 cm:1 nonrelativistic:1 ca:1 harmonic:4 dimensional:2 concluding:1 simply:1 adding:1 iterations:1 associated:3 considering:2 most:1 transformations:4 capable:1 alves:1 three:3 been:13 int:1 belongs:1 basic:3 ph:4 algebras:4 systems:4 obtained:7 determinant:1 arises:3 families:20 versa:1 x2l:2 concerning:1 subspace:1 ψnl:3 gap:2 coherent:2 roychoudhury:1 determination:1 derivative:1 c0:4 spirit:1 spain:2 case:24 exception:1 look:3 pacs:1 ǫk:3 ǫn:1 value:4 ǫl:46 will:19 eigenproblem:2 while:4 replaced:1 orica:2 procedure:5 remembering:1 detailed:1 mexico:2 almost:16 vi:1 thus:4 them:3 ii:4 itself:1 turns:1 susy:21 partner:4 crum:2 different:23 korolev:1 inc:1 etc:2 generic:1 make:3 belong:1 lett:3 same:12 member:3 strange:1 quant:3 ince:1 avoids:1 finite:1 φl:18 composition:1 higher:3 independent:4 used:6 infinity:1 singapore:1 hand:11 v1:6 v2:1 levels:17 arose:1 potentials:47 changing:1 normalization:1 schr:11 expression:1 well:16 concrete:1 without:1 solve:5 programa:1 coordinate:1 parametric:31 usual:4 spherical:2 just:8 less:2 being:1 exotic:1 2c:1 infeld:7 transforms:1 immediately:3 carrol:1 eigenstates:1 λl:29 elk:2 preprint:2 classification:1 integer:7 field:1 point:4 mathematically:1 quadratures:1 clm:1 add:1 interested:1 conacyt:1 treatment:3 easy:3 theorem:1 input:1 solvable:12 transformation:7 take:5 real:2 aspects:1 eigenfunction:3 represents:5 outermost:1 showing:1 possible:3 resting:1 corresponds:5 increases:1 predetermined:1 valladolid:2 using:13 moreover:3 mod:2 generated:1 factorize:1 intertwined:13 like:21 semi:1 obvious:1 specific:3 intertwiner:1 either:3 arbitrary:1 become:3 works:1 variant:1 reduced:1 mathematical:3 because:7 methods:4 successfully:2 some:13 back:1 algebraically:1 certain:1 acad:2 respect:1 protons:1 erator:1 happens:2 provided:5 describing:1 lead:4 kml:17 integration:5 per:1 conditionally:2 does:5 provides:4 tends:2 proc:1 transmutation:1 presented:2 scientific:1 indicated:1 bl:5 equivalent:2 each:2 rosas:6 broken:2 step:7 although:3 substitution:1 properties:1 takes:2 stone:1 would:4 world:1 rederived:1 basis:1 discussed:2 dependence:2 o:5 page:1 plus:10 glasser:1 introduced:2 slightly:1 op:1 fern:13 unexplored:1 unnoticed:1 previously:5 into:7 formulae:1 andrianov:3 remarks:1 appropriate:2 square:4 references:1 determine:1 operator:18 span:2 additional:2 ortiz:6 strictly:3 there:6 question:1 approximate:2 generation:1 quadratic:1 inner:1 lot:1 labelling:1 was:3 opens:1 naturally:1 function:7 creation:2 north:1 complete:1 form:5 governs:1 but:14 taken:1 construction:8 trum:1 hl:36 atom:8 convergence:1 attainable:1 vl:45 ha:1 coupling:1 absent:1 made:1 cie:1 ordering:2 generating:1 maximum:1 us:17 theoretical:1 placed:2 below:5 limit:2 iterated:2 problem:7 similar:4 called:1 mechanics:3 irish:1 units:1 constant:8 worthwhile:1 ln:8 defined:2 ah:1 abstract:1 refered:1 general:22 continued:1 single:1 right:1 relates:1 corresponding:27 simplest:2 physical:6 again:5 functions:12 nag:1 index:2 wavefunction:1 when:7 detail:1 junta:1 application:4 other:16 khare:1 special:1 becomes:8 test:1 mathematics:1 er:2 sufficient:2 conclude:1 elements:2 denote:1 models:2 convention:1 meaning:1 important:4 nucleus:1 allowing:1 included:1 cooper:1 parities:1 n2:2 abraham:2 factorized:1 algorithm:1 vice:1 holes:2 rule:1 original:1 dr:14 time:2 nuclei:1 having:1 once:4
|
quant-ph9806021.txt |@word represent:1 consider:6 magnetic:5 leads:1 roy:2 cooperative:2 follow:1 causes:1 knill:1 environment:5 charge:1 program:1 those:2 nodes:3 localizations:2 cm2:2 random:1 r12:2 orthogonal:1 far:5 frequencies:2 rise:1 induce:1 wave:6 prog:1 resonant:6 experimentally:1 four:1 vibrational:4 level:8 marry:1 large:2 small:6 optics:1 possibility:1 kz0:1 work:1 computation:9 oscillation:2 deutsch:2 pulse:2 threshold:1 rate:7 enhancement:1 implemented:2 blue:4 interatomic:1 trapping:4 stoof:1 giving:1 localization:2 near:5 below:1 experiment:2 above:4 new:5 avenues:1 d1:1 method:2 3d:3 coefficient:1 condensed:1 full:2 ibid:2 fmax:5 respectively:1 promising:2 here:2 atoms:38 tiesinga:2 free:1 separation:1 others:1 ratio:5 along:1 strong:1 z0:2 naval:1 technical:1 shift:11 vectors:1 allows:1 amount:1 periodic:1 resulting:1 defeat:1 resonance:10 implement:1 studies:1 king:1 via:5 useful:1 scales:3 inducing:1 readout:1 maximizing:1 logical:6 highly:1 brought:1 turchette:1 poyatos:1 total:1 linearly:1 standing:2 plot:2 use:3 preskill:1 jessen:2 army:1 remains:1 mexico:2 tightly:2 phillips:1 few:2 sample:1 type:2 theoretical:1 more:3 separated:2 mol:1 populations:2 apparent:1 emission:3 varying:1 hold:1 producing:1 must:3 γdd:2 keeping:1 mf:7 science:3 r3:1 cat:2 poul:1 values:1 following:2 dec:1 spontaneous:4 example:3 deg:3 control:3 ions:2 transition:4 gordan:1 reasonably:1 figure:4 ann:1 states:12 tag:1 numbers:1 tan:3 times:1 r20:1 lamb:3 cooperativity:2 requirements:1 provide:3 discussion:1 acts:2 ultracold:1 machine:1 very:4 varies:1 monroe:1 influences:1 elliptical:1 opt:1 ensure:1 parameter:3 ensemble:2 massive:1 fmin:1 may:1 max:1 perrin:1 after:1 minimized:1 gardner:1 explored:1 designed:1 waves:2 lat:1 destructive:1 capitalize:1 parallel:3 types:2 diagonal:3 short:1 light:2 register:5 ghz:1 element:2 pax:1 so:1 allow:1 operate:1 realizing:1 prefactor:1 operations:8 gershenfeld:1 executed:2 office:2 produces:1 john:1 over:2 vary:1 major:1 through:3 looks:1 lasers:10 lattices:4 fidelity:3 linewidth:4 its:1 before:1 lg:1 rapidly:1 thank:1 sγ:1 presence:1 unity:1 pulses:3 hz:2 systems:2 constitutes:1 main:1 might:3 lx:1 s1:5 good:1 schematic:2 thereby:3 propose:2 polarizations:3 processes:1 scaling:2 steane:2 detunings:2 effects:4 half:1 rotation:1 inelastic:2 maintaining:1 february:1 goldstein:1 james:1 university:2 hamiltonian:1 sideband:1 appropriate:1 sufficiently:1 trap:1 truth:2 each:5 references:2 entirely:1 quarter:1 interfering:1 side:1 mean:1 homogeneous:1 schemes:1 scheme:2 energy:2 universities:1 reduce:1 gaussian:1 resolvable:1 frequency:2 expect:1 measurement:1 quantum:16 wavelength:5 operation:3 transitions:1 out:6 divincenzo:1 shown:2 matrix:3 gradient:2 rep:1 since:2 rev:15 research:3 increase:2 collisions:3 acting:1 gou:1 foundation:1 induced:4 issue:1 shows:1 gate:7 arizona:1 interactions:5 maintains:1 mechanisms:1 albuquerque:1 governing:1 standard:1 hankel:1 advantages:1 conditioning:2 detecting:1 pairs:3 interaction:8 created:2 geometry:2 widths:1 could:1 computers:2 tolerant:2 silicon:1 khz:3 produce:2 isotropic:1 first:1 ability:1 features:1 number:2 channels:1 done:1 long:2 another:2 carry:2 electronic:2 given:6 perturbation:1 interact:7 system:3 least:1 their:3 cooling:2 1d:2 molecular:2 national:1 gives:1 shifted:1 trapped:10 ih2:1 ih0:1 plane:1 transverse:5 slides:1 optical:12 manipulation:2 eliminated:1 than:3 population:3 distance:1 polarized:6 target:3 zero:1 matter:1 determined:1 intensities:1 were:1 tion:1 function:7 addressing:1 correction:2 turned:1 argument:1 operated:2 seem:1 constrained:1 any:4 relatively:1 chem:1 angle:2 offering:1 depending:1 isolate:1 isolated:1 polarization:5 sciences:1 high:1 potential:8 negligible:3 knobs:1 many:5 hyperfine:3 even:2 play:1 beyond:1 electric:2 though:4 wells:10 most:1 pair:1 extremely:1 class:1 axially:1 especially:1 neighboring:1 calculated:1 drive:1 order:3 kr:2 part:1 principle:1 kt:2 effect:1 physics:2 fact:1 laws:3 shor:1 spaced:2 intensity:2 distances:4 supported:1 merit:3 motional:1 rotating:1 minimizing:1 chuang:1 kx0:1 range:2 d2:2 x0:2 ground:7 ηx:1 based:1 parameters:2 implementation:1 print:1 written:1 should:1 only:7 candidates:1 factor:1 g00:1 achieve:1 legendre:1 goes:1 wide:1 dependent:1 beams:6 zurek:1 expectation:1 joint:2 cannot:1 reading:1 during:4 sisyphus:1 adiabatically:2 evolution:1 resolve:1 densities:1 indicated:1 fields:2 arxiv:1 tuned:2 europhys:1 including:1 qk:1 fixed:1 apparatuses:1 rms:4 set:1 alsing:1 achieved:1 hγ:2 achieves:1 packet:1 clebsch:1 relative:5 see:3 computer:1 enhanced:1 discussions:1 paul:1 techniques:1 onance:1 co2:1 tensor:1 kl:2 nuclear:1 µw:1 currently:1 dipole:26 superradiant:3 symmetric:2 state:21 between:6 pairwise:1 neither:1 caves:1 mainly:1 realizations:1 creating:1 nature:2 qubits:6 weak:4 however:1 implementing:3 subspace:1 longitudinal:8 suppressed:2 ωc:2 both:1 cos:1 zoller:2 fault:2 region:1 according:3 chosen:1 involve:1 logic:8 distinction:1 qubit:6 heart:1 expression:1 experimental:2 generic:1 reside:1 mechanics:1 point:1 cg:1 harmonic:1 dimensional:1 maximize:1 cs:2 table:2 suppressing:1 described:3 second:2 lattice:10 addition:1 twostate:1 been:3 detuning:1 describes:2 pj:1 flexible:1 ph:2 dynamically:1 fig:6 dots:1 direction:3 contribute:1 neutrals:1 sufficient:1 photon:8 coherent:6 confinement:3 external:3 rudimentary:1 stems:1 θr:6 spin:1 present:1 p2:2 p3:4 laser:13 pacs:1 solid:2 value:1 will:3 while:1 hdd:3 error:3 taking:1 unpaired:1 transi:1 identical:1 unitary:2 coupled:1 almost:1 thus:7 characterize:1 technology:1 ig:2 sequentially:1 different:2 unaffected:1 develop:1 combination:1 grant:5 perform:1 make:1 lett:8 same:5 archive:1 stimulated:1 quant:2 widely:1 catalysis:6 several:1 difficult:2 used:1 functions:2 ellipsoidal:1 ion:2 phy:1 levels:2 unpublished:1 potentials:3 entanglement:1 changing:2 recent:2 lower:1 weakly:1 off:4 center:2 no:5 well:8 concrete:2 without:2 components:1 coordinate:2 position:2 arising:1 usual:1 spherical:1 gates:3 proposed:2 minima:1 being:2 thz:1 gavin:1 sources:1 atomic:11 spherically:1 alternative:1 brennen:1 scattering:9 yet:1 adv:1 oriented:1 integer:1 tight:1 excites:1 dicke:4 source:1 spread:1 nor:1 excited:4 resolved:1 saturation:2 κmax:1 depends:1 read:2 couple:1 traps:1 possible:3 lanl:1 entangled:3 background:1 performance:1 confined:2 using:1 bit:2 advanced:1 loss:1 δz:3 particle:1 sublevel:1 alternatively:1 signal:1 alkali:2 deleterious:1 vdd:7 arbitrary:1 ivan:1 reduced:1 cooled:2 accessible:1 because:3 laflamme:1 qed:1 classical:1 sequence:1 conditional:2 polynomial:1 respect:1 closer:1 neglecting:1 scale:2 cooper:1 collaborative:1 lead:1 cavity:1 tube:3 measurements:2 requisite:1 overlap:2 manipulations:2 does:1 connecting:1 dipoles:4 y20:1 propagating:1 proc:2 demonstrated:1 noise:1 nmr:2 reasonable:1 detuned:3 performed:5 radial:1 conventional:1 cycling:1 intense:2 central:2 basis:5 discussed:1 dependence:1 occupation:1 essential:1 nonvanishing:1 carries:1 repulsion:1 greatly:1 neighbor:1 contours:1 sensitively:1 therein:2 soc:2 computational:3 follows:1 wineland:1 into:1 within:2 numerically:1 due:1 services:1 carlton:1 promise:2 determine:2 proportional:1 reducing:1 ηz:1 domokos:1 additional:2 elastic:1 measured:1 question:1 approximate:1 stark:2 occupy:1 much:1 low:1 way:1 was:1 raman:7 kane:1 form:1 but:6 hk:1 neutral:3 contradictory:1 atom:10 line:1 removed:1 proposal:1 auxiliary:2 made:5 applying:2 fluorescence:1 characteristic:1 hamann:1 paired:1 tucson:1 limit:1 problem:1 define:1 strongly:3 storing:1 ac:2 cirac:2 associated:3 describe:1 deep:2 denote:1 substantially:1 single:3 exist:1 periods:1 our:2 controlled:1 az:1 internal:2 jaksch:1 physical:3 mutual:1 compared:4 nm:2 dotted:1 variety:1 whereas:1 generally:2 field:8 other:5 role:1 details:1 department:1 confine:1 elements:2 superposition:1 excitation:2 separate:1 excite:1 problems:1 prepared:2 important:2 individual:1 allowing:2 flushed:1 astronomy:1 meystre:1 regime:1 coupling:4 coulomb:1 corresponding:5 tubes:1 required:1 governed:1 parallelism:1 time:2 retardation:2 decoherence:8 verhaar:1 once:3
|
quant-ph9806022.txt |@word consider:5 results:2 leads:3 ptp:1 whose:1 finally:3 does:1 under:2 tf:2 fermionic:4 sound:4 very:12 wave:2 bjorken:1 electron:1 experimentally:1 exact:2 entire:1 quantized:3 applicable:1 large:5 team:1 small:5 louie:1 smaller:2 smalley:1 imply:1 value:1 further:5 even:1 appear:1 nano:3 section:8 brief:1 version:2 above:3 new:3 net:1 occupation:4 ever:1 loose:1 atoms:2 behaviour:7 others:1 drell:1 strong:1 extreme:2 box:1 technical:2 studied:2 contradiction:6 narrow:1 anticommutators:1 via:2 scales:2 explained:1 replace:2 coinciding:2 inexplicable:1 viz:1 neutrino:1 total:2 unit:2 bastin:1 use:4 would:2 covariant:1 handedness:1 next:2 comparing:1 therefore:3 centre:4 relativistic:1 type:3 more:5 about:1 eν:2 observations:1 known:5 cases:4 iii:1 must:1 states:1 springer:1 mc:1 tokyo:1 science:3 equation:1 lorentz:1 thin:10 wang:1 discussed:2 boseeinstein:2 india:1 high:4 νf:2 degenerate:2 sense:1 sought:1 counting:2 verlag:1 discussion:1 frontiers:1 instead:2 sommerfeld:1 description:1 wiley:1 collection:3 reflect:1 waves:1 society:1 law:2 meaningful:1 liquid:1 correspond:1 thorne:1 so:5 fundamental:1 order:4 wavelengths:1 indeed:4 over:2 years:2 thermal:1 statistical:2 japan:1 still:1 energies:2 interesting:2 relativity:1 exhibits:3 communication:1 mail:1 correspondence:2 freeman:1 non:2 motivated:1 greater:2 material:1 landau:1 they:1 now:6 nor:2 easily:2 term:2 dirac:3 university:1 realistic:2 inequality:4 reasonable:1 2m:10 side:2 mean:2 weyl:1 vanishingly:2 ed:1 energy:18 logz:2 zdp:2 bosonization:7 frequency:4 quantum:8 wavelength:8 beyond:1 space:5 since:2 rev:1 combinatorial:1 hill:2 ref:11 occurs:2 shows:2 meden:1 theory:6 free:1 completely:1 york:2 philip:1 pairs:1 could:3 persists:2 length:5 first:3 hyderabad:1 features:3 number:10 ihm:1 angular:1 given:14 checked:1 temperature:23 introduction:1 behaves:2 confirming:1 assumption:2 stephan:2 fermions:26 bosons:1 speaking:3 gives:2 reversed:2 exactly:2 venema:1 than:6 distance:8 penrose:1 were:2 ktf:2 perspective:1 exhibit:3 lowest:1 motivation:1 san:1 cohen:1 generalization:1 apparently:2 lin:1 able:1 metallic:1 note:2 sciences:1 take:1 coincide:1 mir:1 moscow:1 insulated:1 broglie:4 though:2 jun:1 boltzmann:4 gravitation:1 rationale:1 preliminary:1 extremely:6 why:2 bsc:2 physico:1 dresselhaus:1 richard:1 surprising:1 considered:2 average:4 partition:2 proceedings:1 electrons:1 kt:6 velocity:6 justify:1 tubes:4 fact:5 superfluidity:1 phenomenon:2 show:6 charles:1 converge:2 attempts:2 relation:2 d3:5 ground:4 resemblance:1 conduction:1 commutators:1 should:1 only:4 black:2 notation:1 get:4 dekker:1 de:4 closely:2 international:1 report:2 dp:4 takahashi:2 mattis:1 fields:1 arxiv:1 reif:1 σdp:2 view:2 up:1 observed:1 see:2 computer:1 result:2 recently:1 wire:10 interacting:3 phonons:5 state:4 between:4 fermi:24 neither:2 approach:1 available:1 publishers:1 p2f:1 terms:2 nature:5 p2m:2 however:3 huang:2 bose:3 problem:5 suggested:4 both:4 density:2 according:2 mathematical:2 jin:1 connection:1 context:3 disappears:2 experimental:1 mechanics:2 point:3 had:1 corresponds:4 whatever:2 dimensional:24 carbon:1 considering:1 described:2 hd1:1 basis:1 tomonaga:3 rinzler:1 three:4 been:6 much:6 phononic:2 ph:1 pm:7 obtained:3 corresponding:2 eastern:1 wheeler:1 gas:4 andrew:1 wires:5 hv3:2 spin:2 case:20 ǫf:5 cf:10 ǫm:3 will:4 while:1 suppose:1 remembering:2 larger:2 thus:2 encountered:1 limit:1 fermion:2 different:3 develop:3 occupied:1 make:1 radiation:2 cross:2 same:3 wherein:1 quant:1 arguments:1 compton:2 several:1 development:1 independent:2 extended:1 effect:1 hand:4 insulating:1 levels:5 kim:1 recent:2 weakly:1 scenario:1 nevertheless:1 well:3 analysis:1 academic:1 model:2 dimension:3 usual:2 less:1 being:4 solvability:1 atomic:2 facts:2 alternative:1 λm:8 vσ:4 conclusions:1 character:2 momentum:11 idealization:1 delhi:1 february:1 atomique:1 unification:1 know:1 press:2 using:6 mod:1 like:3 interestingly:2 either:3 mcgraw:2 inter:2 therein:2 because:2 back:1 nagar:1 deduce:2 towards:1 transmutations:2 dimensions:3 shall:1 per:2 behave:1 energie:1 proc:1 conference:1 assembly:5 obey:2 remembered:1 agreement:1 odom:1 although:1 conducting:2 choi:1 anomalous:5 distinct:1 stand:1 addendum:1 bloch:1 lieb:1 considerations:1 cambridge:2 delaney:1 h2:2 h3:4 lieber:1 right:2 references:1 einstein:3 france:1 bosonic:11 statistics:7 few:1 strictly:5 there:4 approximate:2 specifically:2 dispersion:5 mkt:4 quanta:1 low:6 pf:3 misner:1 function:2 denoting:2 but:4 volume:5 nanotubes:1 true:1 2πc:2 he3:1 maximum:8 below:17 ωm:8 distribution:4 define:2 similar:1 display:1 detailed:1 inspite:1 interparticle:4 abstract:1 am:1 general:1 sidharth:5 examine:3 inc:1 again:2 no:3 when:1 detail:2 field:2 other:4 np:7 mathematics:1 conclusion:2 francisco:1 superconductivity:1 osheroff:1 mechanical:2 cooper:1 physics:4 holes:2 together:1 time:1 original:1 bcs:1
|
quant-ph9806023.txt |@word quarks:2 consider:1 less:1 john:1 rest:5 course:1 paper:1 including:1 aspect:2 edu:2 kinetic:3 its:2 galaxy:1 before:1 nevertheless:1 personal:1 explain:2 striking:1 smith:1 ts:1 should:2 h2:2 html:2 transformed:2 th:1 mail:1 hidden:1 momentum:1 real:2 case:1 non:1 psi:1 evaluate:1 zurek:1 spatial:1 walls:3 pegasus:1 effects:1 confined:6 integer:1 part:1 now:1 boundary:1 wiley:1 entire:1 particle:6 bring:1 textbooks:1 arxiv:1 guidry:2 each:1 2m:4 valence:1 page:3 gauge:1 afforded:1 www:2 because:3 says:1 ga:1 ed:1 energy:9 approximation:1 deduce:1 radius:1 us:1 sight:1 measurement:1 quantum:10 our:1 acts:1 really:1 even:1 total:1 space:2 support:1 electromagnetic:1 review:1 since:2 rev:1 uniform:1 models:1 contained:1 does:1 between:3 net:2 questionable:1 who:1 theory:12 found:1 frank:1 contain:1 however:1 jr:1 quark:18 mev:3 illustration:1 although:1 others:2 hadron:2 box:3 about:3 interaction:2 impenetrable:2 many:1 could:1 uncertainty:1 equal:1 o:1 motion:1 urls:1 published:1 action:2 hadrons:9 other:2 experimental:1 first:1 relativity:1 nonrelativistic:12 within:2 into:3 explained:2 objectively:1 references:1 tony:1 apply:1 precisely:1 described:1 usa:1 prove:1 create:1 contains:1 transform:1 been:1 opposed:2 qcd:4 2πnx:1 ph:2 perfectly:2 was:1 empty:3 more:1 free:1 mike:2 wheeler:1 jun:1 but:2 confinement:1 known:1 constituent:1 analogous:1 those:2 applied:2 distance:1 works:1 princeton:1 recall:1 inside:1 work:1 see:1 cau:2 theories:1 considered:1 fermi:1 were:1 identical:1 problem:2 property:2 result:2 separated:1 abstract:1 surprisingly:1 ii:2 seem:1 confirms:2 apparently:1 fermion:5 physical:1 nh:2 confirmed:1 puzzling:1 conversely:1 formulations:2 able:1 enclosure:1 note:1 field:10 high:1 potential:4 quant:2 observe:1 papers:1 mass:2 you:2 effectiveness:6 explains:1 sin:1 picture:1 http:2 may:3 act:1 june:1 most:2 significant:1 variable:1 why:2 structure:1 assume:1 light:5 well:3 electron:2 having:1 bohm:15 reflecting:2 so:1 principle:1 mechanical:1 model:10 section:1 reprinted:1
|
quant-ph9806024.txt |@word consider:4 results:3 ρaµ:3 commute:1 research:1 row:1 whose:4 dimensionality:1 segments:1 tr:5 finally:1 th:2 norm:1 inform:1 overlaps:1 p2:7 orthogonal:3 far:1 choice:1 matrices:6 condition:2 four:5 school:1 fewer:1 deals:1 proposition:1 phase:1 encloses:1 smaller:1 coordinate:1 design:1 substitute:1 theory:5 even:1 what:1 reminiscent:1 experiment:1 above:3 new:3 consisting:1 satisfy:1 respectively:1 concepts:1 component:1 here:1 tangent:2 address:2 represented:2 extreme:10 obtained:6 antisymmetric:1 ellipsoid:3 suitably:1 receive:1 vectors:2 exceptionally:1 drt:1 example:2 resulting:2 usually:1 suitable:2 y12:1 projection:1 convexity:1 outcomes:2 linearly:4 readily:1 use:2 takes:1 would:1 probabilities:8 positive:5 next:1 therefore:2 type:1 more:6 israel:2 outputs:2 operators:2 labelled:1 particular:2 known:1 valued:1 equation:1 work:1 caratheodory:1 values:1 mr:2 following:2 trans:1 institute:1 performed:1 want:2 states:9 sphere:8 numbers:1 hyperplane:4 occur:1 information:2 get:2 write:1 how:2 pure:8 optimal:1 parameter:1 sin:3 may:4 wiley:1 derived:1 applications:1 plane:4 data:4 correspond:1 element:1 generic:3 so:4 asserts:1 gerard:1 order:3 terno:2 indeed:1 satisfied:1 statistical:1 hypersurface:2 still:2 ieee:1 its:3 chosen:1 affine:1 coordinates:2 complex:1 systems:7 non:1 good:1 combination:5 records:1 they:3 now:1 ensemble:2 asher:1 academic:2 reasonable:1 each:4 x11:4 x12:2 constraints:2 2y12:1 related:1 elementary:1 used:2 encouragement:1 measurement:2 quantum:13 our:1 eq:3 rt:1 shown:2 matrix:11 space:10 restricted:1 helstrom:1 denotes:1 daniel:1 linear:3 associate:1 complicated:1 york:3 imagine:1 estimate:3 geometry:1 determining:1 times:1 probability:6 number:5 rank:4 another:2 xp:1 electronic:2 their:2 ξmn:3 meaningful:1 ξmm:1 system:5 needed:2 zeros:1 gives:1 centered:2 exactly:1 x2:1 translation:1 than:4 detection:1 require:1 namely:2 preparation:2 determined:1 outcome:3 vector:5 constrained:1 any:11 lie:4 ρmn:1 efficient:1 note:1 potential:1 generalized:3 interior:5 davies:3 trace:1 opposite:1 x212:1 reach:1 fails:1 most:4 regular:1 eight:1 preparations:1 pair:1 measured:1 parametrize:1 technion:4 dordrecht:1 stronger:1 points:16 physics:2 lying:1 hyper:1 supported:2 notations:1 ξnn:1 spaces:1 relation:1 d2:7 parameters:8 state:4 only:7 explicitly:1 columns:1 ymn:1 do:2 means:1 dependent:1 cannot:1 combinations:1 arxiv:1 acknowledgments:1 mapped:2 bars:1 set:16 testing:1 observed:1 depends:1 radius:1 result:3 best:3 subject:2 phases:1 qµ:5 positivity:1 label:2 symmetric:1 written:5 between:2 boundary:1 available:2 terms:3 however:1 cos:2 last:1 equal:2 estimation:1 expression:1 experimental:4 solving:1 point:11 simple:1 corresponds:1 dimensional:14 maximize:1 proved:1 described:1 leads:1 three:6 strategy:1 povm:9 expected:1 ph:1 pn:1 fig:2 box:2 corresponding:5 photon:1 fund:2 angles:2 spin:2 obtainable:1 present:1 case:5 p3:6 p1:7 p4:5 tetrahedron:1 value:1 remaining:1 will:2 euclidean:1 evaluating:1 error:3 larger:2 vj:2 thus:9 surface:3 itself:1 cone:1 vanish:1 technology:1 swope:1 different:2 open:1 grant:1 il:2 parts:1 quant:1 pauli:1 finite:2 independent:5 extended:1 mutual:1 parametrized:1 running:1 experimenter:2 infinite:1 eigenvectors:1 pµ:22 well:1 analysis:2 obviously:3 concrete:1 components:4 sets:1 kelly:1 dimension:3 just:1 less:1 xρ1:1 obtain:2 rest:1 press:2 shape:2 distant:1 transforms:1 λj:1 eigenstates:2 polarization:1 kluwer:1 density:11 photons:1 weiss:1 signals:1 source:1 valid:1 transformed:1 samples:1 theorem:3 input:1 transformation:2 ought:1 real:5 sytems:1 possible:2 department:1 five:1 confined:2 like:3 arbitrary:4 output:4 because:1 methods:1 convex:14 eiα:1 eiβ:1 dimensions:3 measurements:3 unit:4 refer:1 binomial:1 ratios:1 found:1 imaginary:1 hilbert:3 integers:1 constraint:1 distinct:1 whence:1 mixed:1 bloch:5 considerations:1 ηd:1 into:4 obtaining:1 domain:6 due:1 lies:3 references:1 operator:1 rows:1 assumed:1 there:2 question:2 dispersion:1 quadratic:1 was:2 complete:1 form:3 jun:1 but:2 aµ:8 haifa:1 true:3 embedded:1 whether:3 bounds:1 us:3 ηmn:2 distribution:1 pm:3 nµ:7 ac:2 constant:1 defined:1 likewise:4 abstract:1 measure:1 general:2 peres:3 ap:1 examine:2 functions:2 compared:1 no:2 graduate:1 other:2 test:5 polar:1 elements:4 subspace:4 prepared:1 important:1 ξd:2 sides:1 implies:1 fact:1 n2:1 having:1
|
quant-ph9806025.txt |@word limited:2 world:1 eigen:1 show:2 supported:1 professors:1 course:1 relation:3 woggon:1 grateful:1 using:2 landau:1 before:1 semiconductor:2 based:3 k2:1 solving:2 corrections:2 wavevector:1 company:1 only:1 creations:2 corresponds:1 choose:1 easy:1 republic:1 nodes:1 c4:3 interested:2 momentum:2 real:3 non:5 πl:3 return:1 dk:7 combination:1 get:1 very:1 similar:1 straightforwardly:1 wave:5 zeng:1 increases:2 every:1 instead:1 confined:8 integer:1 discuss:1 projects:1 2ml2:2 term:1 cj:8 particle:4 always:1 university:2 arxiv:1 guo:1 solution:2 large:1 peking:1 l2:3 integrals:1 analytical:1 2m:2 2h:4 inside:1 mathematical:2 differential:3 classical:1 people:1 series:1 energy:10 dots:2 modified:1 zero:1 books:1 static:2 result:2 quantum:6 further:1 chem:1 odd:1 even:2 reviews:1 acknowledgment:1 fang:1 space:3 research:1 particles:11 kun:1 outside:1 optical:1 ren:1 between:1 new:4 approach:1 foundation:1 condensed:1 wavefunctions:1 scientific:1 extend:1 state:2 dow:1 upon:2 ikx:1 however:1 here:1 standard:1 completely:2 china:2 cos2:1 huang:1 wiley:1 region:1 therefore:2 sine:1 equations:4 eik:1 e2:1 obtained:2 cos:1 oj:1 extension:1 most:1 oxford:2 many:1 could:3 so:1 o:7 length:2 products:1 published:1 barriers:2 fourier:1 expression:2 ej2:1 york:2 subset:1 there:2 natural:1 author:2 probability:1 press:2 requiring:1 semiconductors:1 koch:1 obtaining:1 number:2 three:1 dimensional:7 set:2 simply:1 construct:1 national:1 operator:4 table:1 mc2:1 standing:2 dispersion:1 given:2 2k2:1 basis:1 addition:1 ej:4 brus:1 transform:1 been:2 noticed:1 ψj:7 vol:2 a53:1 cosine:1 low:3 way:2 m2:3 free:2 ph:1 john:2 was:1 theoretical:1 pm:1 function:3 corresponding:3 complete:2 ryzhik:1 shang:1 exactly:1 jun:1 odinger:3 but:3 aware:1 gao:1 berlin:1 confinement:2 everywhere:1 normalized:1 known:1 c2:3 cases:1 coefficients:1 must:1 case:1 alivisatos:1 springer:2 look:1 pacs:1 science:3 equation:10 up:2 devices:2 postive:1 will:1 matter:1 zhao:1 ωj:1 values:1 following:1 problem:1 property:2 jπ:2 example:4 stimulating:1 publishing:1 mechanics:2 beijing:1 references:1 tracts:1 wang:1 give:1 almost:1 relativistic:15 abstract:1 modern:1 naturally:2 textbook:1 ii:1 discussions:1 ik:1 properties:1 numbers:1 limit:1 any:1 verlag:1 different:3 straightforward:1 no:3 wavefunction:1 range:1 same:1 materials:2 far:1 potential:3 quant:1 widely:1 program:1 department:1 4j:2 several:1 require:1 sin:1 formulas:1 used:2 see:3 singapore:1 may:1 use:1 problems:1 effect:3 expectation:1 applications:2 plane:2 value:1 waves:1 infinite:2 climbing:1 yuan:1 concerning:1 gradshteyn:1 recent:2 schr:3 nano:1 spectra:3 well:1 kl:2 academic:1 without:1 mass:4 fundamental:1 kelly:1 appl:1 physics:5 having:1 usual:1
|
quant-ph9806026.txt |@word concept:4 consider:3 rev:6 excellent:1 results:3 illustrated:3 generalize:1 computation:1 francesco:1 follow:1 expressions:2 research:1 gk:2 c0:4 depend:1 calculate:1 technique:6 environment:4 finally:2 preserved:1 th:1 under:1 hermann:1 stochastic:40 norm:1 case:1 amplitudes:1 very:2 straße:1 induce:1 wave:20 lecture:2 resonant:1 exact:17 fakult:1 encounter:1 leads:9 presented:7 notes:2 t2:15 solution:9 damped:12 large:2 vector:1 markov:1 trr:2 optics:1 heinz:1 eλt:1 α2n:1 cosh:1 approximation:4 second:4 dynamics:9 implemented:1 odd:1 theory:1 spectral:1 will:4 t2k:1 nonlinear:1 rate:22 contributions:1 section:2 graduiertenkolleg:1 above:2 new:2 ground:3 method:11 contrast:1 respectively:2 realizations:2 equals:2 here:2 agreement:3 desired:1 inverse:1 ansatz:2 sinh:3 consideration:1 strong:1 equations:13 alicki:1 obtained:6 gli:1 remark:1 shift:1 vectors:1 allows:7 poisson:4 usually:1 resonance:1 studi:1 deterministic:4 projection:6 discontinuous:2 castin:1 replace:1 apply:1 total:3 γk:1 use:6 quasi:1 projector:2 eiωs:1 formulated:1 positive:7 h0:3 contains:2 dni:12 γi:4 dnj:1 calculation:2 depicted:1 memory:6 type:2 more:2 γm:2 clearly:1 initial:1 operators:8 odinger:1 tested:1 berlin:2 normalized:1 particular:3 known:2 unraveled:2 cases:3 iii:4 pseudospin:1 evolves:1 springer:1 equation:55 ρr:6 values:4 following:1 making:1 spontaneous:1 example:4 transition:1 process:6 organized:1 states:3 indicates:2 performed:1 want:1 verlag:1 lamb:1 isk:1 end:2 turn:1 rather:1 di:5 write:1 pure:2 parameter:2 ensemble:1 description:5 may:1 demonstrates:1 long:1 freiburg:2 physik:2 summarize:1 choice:1 parallel:1 constants:2 short:1 dynamical:1 explicit:5 chapman:1 element:4 si:3 algorithms:1 correlation:6 definitions:1 order:14 ito:2 reservoir:9 kampen:2 cumulant:1 over:2 displayed:1 symbols:1 course:1 through:2 statistical:2 jaynes:11 differentialgleichungen:1 rapidly:1 thank:2 decay:15 chosen:1 lk:1 li:13 microscopic:3 systems:3 k2n:1 takahashi:1 τr:1 alter:1 eur:1 non:5 good:2 fourth:9 obtaining:1 fig:9 framework:1 effects:6 discuss:2 easily:1 february:1 hamiltonian:4 sin:4 sufficiently:1 mode:3 universit:2 t1:19 mean:3 differential:12 ei:1 significantly:2 dωj:1 unravelling:11 series:1 energy:1 reduce:1 related:2 t3:12 frequency:2 multitime:3 measurement:3 quantum:31 our:1 transitions:3 eq:13 matrix:18 space:9 furthermore:1 since:4 crucial:1 projected:1 denotes:4 nakajima:3 investigation:1 dsk:1 istituto:1 herder:1 dsg:1 induced:1 correct:1 shows:1 linear:6 ory:1 gardiner:1 free:1 standard:1 approaches:3 advantages:1 york:2 milburn:1 definition:1 interaction:6 derivation:3 applications:1 computers:1 times:2 motion:21 ordering:2 anti:1 δij:1 hence:7 onto:1 first:2 major:1 already:2 probability:4 ihs:1 employing:2 done:1 least:1 directly:2 open:8 illustrate:2 given:10 necessarily:1 indicate:1 introduction:1 eqs:1 system:38 construct:1 their:1 master:29 too:1 dt3:3 rates:1 dt1:6 scheme:3 petruccione:5 kolmogorov:1 ih0:4 continuous:3 albert:2 yield:1 dt2:3 dfg:1 coefficients:4 population:5 jump:2 determines:1 breuer:5 namely:2 annihilation:1 computer:1 garraway:1 amplitude:1 result:1 jpn:1 rewrite:2 generalization:3 orders:2 strength:1 latter:1 secs:1 converges:2 note:6 k2:2 take:3 k4:2 finding:2 performance:1 detector:1 bernd:1 channel:1 calculus:2 exactly:2 most:1 germany:1 cummings:11 kappler:2 pair:1 ludwigs:2 observation:1 nonlinearity:1 calculated:1 physica:2 hi:6 exp:7 oscillates:1 physics:3 show:2 timedependent:1 rotating:1 purely:1 find:2 principal:1 postulates:1 based:4 ensembles:1 parameters:3 situations:1 dalibard:1 only:3 local:2 equilibrium:1 means:3 dependent:4 expectation:1 negative:5 dt:7 ds:2 differentiating:1 carmichael:1 evolution:13 chronological:2 continuum:1 arxiv:1 doubled:5 summary:1 analytical:1 ql:1 view:1 kernel:1 parkins:1 undergoes:1 differentials:2 observed:1 depends:1 individual:2 sec:12 descriptions:1 close:1 uncorrelated:1 techniques:1 project:1 αpl:1 federal:1 justifies:1 state:22 closed:1 between:1 geometric:1 approach:4 αl:1 terms:3 extend:1 initially:3 however:3 reproduces:1 ji:7 distinguish:1 article:3 both:3 essentially:1 zoller:1 0t:3 according:1 contribution:3 expense:1 expression:1 otherwise:1 ck:3 ci:5 perturbative:6 point:2 simply:1 moreover:2 expensive:1 semigroups:1 described:6 pw:6 piecewise:2 due:1 been:2 strategy:1 springerverlag:1 detuning:5 describes:4 pg:1 basic:1 degrees:1 ph:1 naples:1 pl:11 define:3 arises:1 corresponding:1 photon:2 covariance:3 fortschr:1 eigenfrequencies:1 determination:1 systematic:4 c1:8 denote:2 present:4 applied:1 exponential:1 expanded:2 value:1 heidelberg:2 employ:1 near:1 procedure:2 real:2 unitary:1 αhi:1 coupled:4 phenomenological:2 formulation:1 thus:2 iv:2 ii:11 im:1 vanish:1 ig:2 containing:1 italy:1 make:1 lett:2 same:1 any:3 shifts:1 quant:1 mølmer:1 modification:1 dimensionless:1 several:1 higher:1 independent:2 used:1 zwanzig:3 see:3 again:1 numerical:1 hand:3 schr:1 center:1 well:2 obviously:2 components:1 model:20 dimension:1 usual:4 λt:11 being:1 obtain:5 arimitsu:1 tcl:11 underlying:1 properties:1 λe:2 generator:8 density:18 iψ:1 interested:1 extends:2 treatment:5 easy:2 wiseman:1 solvable:2 excited:4 generalized:1 identical:1 represents:1 iα:1 possible:3 vacuum:2 using:13 italiano:1 lendi:1 like:2 follows:1 reduces:1 performing:1 specific:2 communications:1 yields:2 either:3 arbitrary:5 become:1 stationary:1 reduced:15 often:1 successfully:2 some:6 stat:1 understood:1 respect:1 oscillations:1 peter:1 separately:1 lead:2 cavity:2 electromagnetic:1 integration:1 per:1 instantaneous:4 eliminate:1 prog:1 inserting:2 slight:1 huber:1 jumps:2 conventional:1 expansion:8 bk:4 hilbert:9 takes:1 would:2 freedom:1 simulation:5 soc:1 computational:2 jθ:3 markovian:7 into:3 within:5 integral:2 three:1 device:2 hermitian:1 operator:8 financial:1 neumann:1 van:2 ψk:2 assumed:1 support:1 there:1 stark:1 way:5 propagator:3 convolutionless:14 function:22 form:18 hs:3 jul:1 applicable:1 volume:2 construction:2 incorporation:1 lindblad:9 level:2 dissipative:1 usefulness:1 compute:1 algorithm:2 born:1 ωs:3 us:1 ur:1 ωk:2 limit:2 continuously:2 percival:1 similar:2 called:1 gisin:1 mechanics:1 constant:1 defined:5 describe:3 general:7 single:1 dψdψ:3 together:3 dθ:1 simulations:1 check:1 regime:1 ni:1 functions:7 compared:5 cos:4 whereas:3 generally:1 vanishes:1 dθdθ:1 field:2 other:4 republic:1 hpb:1 theor:1 deviation:2 picture:2 briefly:1 elements:1 chem:1 important:2 shibata:3 m18:1 structure:1 acknowledgment:1 coupling:9 dψ:3 dφ:2 governed:4 time:36 observables:1 backward:1 chaturvedi:1
|
quant-ph9806027.txt |@word concept:3 consider:4 similarity:1 desirable:1 leads:1 entropy:58 gn:1 gj:2 gi:6 calculate:1 ohya:17 those:1 under:3 sent:1 inform:2 p2:8 g1:1 very:1 geometrical:8 difference:3 fractal:30 condition:3 dim:1 transmission:3 notes:1 discrete:1 vector:6 eigenvalues:1 markov:1 trr:1 concluded:1 application:1 neighborhood:1 measurable:2 zc:1 approximation:1 second:1 further:1 dynamics:2 theory:6 even:2 section:6 expressed:3 sut:2 above:6 sup:11 new:6 led:1 degree:1 respectively:1 here:1 objects:1 represented:2 obtained:2 study:1 amount:1 usually:1 changes:1 uniquely:1 diameter:1 formulated:2 useful:1 classification:1 put:1 total:4 use:3 positive:2 hilbert:4 call:2 therefore:2 criteria:2 taken:1 more:2 becomes:1 operators:1 akashi:3 particular:1 masanori:2 cases:1 md:2 springer:1 valued:1 tokyo:2 science:2 equation:2 radon:2 indicating:1 following:11 trans:1 gqs:3 mx:2 proof:6 control:1 f1:1 nikodym:2 give:2 calculation:1 states:15 minimum:1 numbers:2 verlag:1 information:13 provide:1 discussion:2 holds:1 mµ:4 how:1 criterion:3 instead:1 classify:1 simplicity:2 product:2 max:4 derived:1 mapping:4 applications:1 fg:1 fi:4 fj:2 fn:1 short:4 lemmas:1 sk:12 lemma2:2 complexity:4 so:19 decreasing:2 definitions:1 order:6 feedback:2 paper:3 through:2 y1:1 japan:2 satisfies:3 ieee:1 its:4 sciences:2 actually:1 systems:3 derivative:2 yn:1 framework:1 they:2 compound:4 rµ:2 transmitter:1 several:1 name:1 always:1 university:2 possibilities:1 inequality:4 transmitted:2 each:6 2n:1 traces:1 mean:3 formulate:1 gaussian:34 related:1 measure:23 quantum:6 our:5 shown:1 matrix:3 space:15 rep:2 since:4 contained:1 denoted:2 lecture:1 rn:9 induced:4 math:6 fiber:1 linear:2 monotone:2 limδ:1 ask:1 definition:4 r0:14 geometry:1 could:1 phy:1 hence:1 exhibited:1 first:2 separable:1 xn:1 probability:14 upper:1 variables:8 number:3 channels:3 another:1 precisely:1 open:2 city:2 given:6 similarly:1 introduction:1 adjoint:1 system:9 their:1 assumption:3 scheme:1 mostly:1 continuous:6 direct:2 optical:1 authors:3 x2:3 translation:1 x1:6 than:1 distance:3 depends:2 limiting:1 determined:3 were:2 treated:1 san:1 kossakowski:1 dynamically:1 rat:3 any:7 min:2 lim:9 self:1 chiba:2 instance:1 take:1 coincide:1 channel:22 compa:1 trace:1 shall:1 measures:14 extending:1 class:1 treats:1 clear:1 coincides:1 inoue:1 points:1 exp:3 nλi:1 mailing:1 takashi:1 show:4 random:22 relation:1 q1:9 q2:9 based:1 matsuoka:3 lemma:8 only:4 yanagi:2 constant:3 do:5 notation:1 means:1 dc:2 obtain:5 joint:2 dz:1 dx:6 expresses:1 dt:1 processes:2 determinants:1 covering:1 qx:2 arxiv:1 prokhorov:1 fixed:2 kernel:1 set:11 ser:2 kolmogorov:18 relative:2 ara:4 namely:2 result:1 dµ:10 theoretic:1 satisfying:10 capacity:7 extend:1 review:2 state:35 µh:2 between:3 µg:11 µf:55 approach:3 email:1 petz:2 kei:1 nature:1 jp:2 distinguish:1 amer:3 come:1 equal:1 leibler:1 σx:1 receiver:1 estimation:1 expression:1 otherwise:2 dimensional:6 respect:7 described:3 much:1 pg:1 ph:1 pi:1 topics:1 choose:1 yaglom:2 covariance:4 general:5 present:2 case:6 p1:8 mount:1 value:1 euclidean:1 behavior:1 error:1 property:1 identical:1 chaotic:2 vi:1 metric:1 thus:1 according:1 characterize:4 ij:4 ℑk:1 different:3 formulations:1 same:3 quant:1 proved:1 finite:1 used:3 singapore:1 functions:3 hand:1 running:1 infinite:2 without:1 sets:7 model:1 dimension:24 usual:2 gelfand:2 mandelbrot:4 dφ0:2 sources:1 aspect:1 world:1 λi:7 λn:1 2σx2:1 kluwer:1 density:4 mathematically:1 other:2 theorem:2 input:9 adress:1 transformation:1 real:4 aspects:1 represents:1 using:3 bit:1 moreover:2 pinsker:2 ation:1 follows:3 dµf:6 remind:1 output:10 essential:1 because:1 often:1 classical:6 conditional:1 some:4 b1:2 b2:2 convex:1 describing:1 dimensions:6 theorem1:1 theorem2:1 normal:1 does:1 prof:1 noise:2 scientific:1 bk:1 become:1 properties:1 cδ:8 about:1 carried:1 o:19 introduced:8 soc:3 h2:3 communication:1 h1:4 bound:1 references:1 operator:3 log:46 there:1 borel:3 way:1 analyze:5 was:4 function:6 head:1 form:1 sequel:1 jun:1 but:1 hk:1 hi:3 hn:1 russian:1 irreversible:1 maximum:3 ωk:2 distribution:2 define:1 called:3 entropies:1 ac:2 associated:2 defined:6 certain:2 abstract:1 describe:2 denote:1 transl:1 examine:1 ar:3 exist:1 ax:3 inf:11 ni:1 mutual:11 no:1 when:5 nx:3 field:1 conditions:3 department:2 company:1 briefly:1 francisco:1 noda:4 norm:15 problems:1 variation:4 includes:1 bounded:1 ising:1 variable:9 structure:4 implies:3 dφ:5 baker:3 notion:1 time:1 4a:1
|
quant-ph9806028.txt |@word gw:11 secondly:1 partial:3 consider:5 interference:1 global:3 results:6 holevo:1 eds:1 scalar:7 commute:1 entropy:1 grateful:1 parameterization:1 consists:3 follow:1 expressions:1 gl:2 reasoning:1 soc:6 devoted:2 increase:1 certainly:1 inverse:2 depend:3 calculate:1 tx:2 re:11 tw:4 concerned:1 equivalence:1 tr:22 acting:10 derivations:1 containing:1 alberti:1 finally:4 does:3 present:4 th:1 skip:1 tf:6 geom:1 include:1 takesaki:5 belonging:5 labels:1 presently:2 straightforward:2 orthogonal:11 institute:1 vt:3 rise:1 springer:2 helpful:1 choice:11 valued:3 every:20 entries:1 difference:1 condition:27 dim:4 y1:1 hamiltonian:1 did:1 turns:1 having:1 t2:3 solution:9 large:3 solved:2 vector:10 annihilates:1 small:1 eigenvalues:6 selecting:1 rξ:1 ver:3 possibility:1 application:1 smaller:2 version:1 findings:1 foundation:1 consistent:1 direct:2 literature:1 past:1 go:2 zero:7 further:5 remarkably:1 returned:1 canonical:6 even:2 index:2 what:5 essence:1 power:1 invertible:6 forgetting:1 section:14 selected:1 expressed:3 infinitesimal:1 absolute:1 establishes:2 capital:1 obvious:2 increasing:1 ˆl:4 exercise:1 satisfy:1 supporting:1 evolving:1 ensure:1 respectively:6 calculates:1 here:3 anandan:2 behaviour:1 modular:7 objects:3 tangent:28 free:1 groups:1 fulfill:1 represented:3 path:1 along:8 equations:11 change:3 extreme:1 obtained:10 bibliopolis:1 remark:2 suitably:1 rests:1 involved:1 study:2 vectors:13 allows:2 completely:9 resp:4 prior:1 exemplifies:1 substituted:1 resulting:1 loop:1 action:3 implement:1 suitable:2 regularity:1 relation:6 mutual:1 uniquely:3 mimicked:1 via:2 followed:1 projection:3 extra:1 requiring:1 explained:2 diagonalizable:1 modifying:1 rx:1 texts:1 unitary:2 d35:1 anomalies:1 apply:1 operational:2 tools:3 research:2 vienna:1 use:5 takes:3 might:1 prove:4 remains:4 positive:26 contains:1 rademacher:1 uniqueness:2 next:4 rao:1 comparing:1 live:1 going:1 call:9 therefore:8 associated:1 stage:1 type:2 metric:67 reflects:1 more:11 ψout:1 alg:1 knows:1 started:2 becomes:6 operators:56 under:4 odinger:2 validity:2 monotonicity:1 berlin:2 appendix:2 normalized:6 verlag:1 particular:6 known:7 cases:2 must:3 account:1 monopoles:1 room:1 fulfils:1 skipping:1 rosenthal:1 equation:19 constraint:2 modified:2 london:1 radon:1 erwin:1 remain:2 fock:4 values:3 royal:1 following:11 meet:2 trans:1 root:5 example:5 numbers:2 asymptotic:1 continuity:1 compare:2 cosmological:1 give:2 calculation:1 4t2:1 arise:1 rc:1 states:17 minimum:1 caused:1 reviewing:1 allowed:2 rescaling:3 conversely:1 lifts:7 world:2 axis:2 normalize:1 information:4 needs:1 end:1 g1:4 vjj:1 meanwhile:1 vji:2 orthogonality:1 occur:1 write:2 unitaries:2 varies:1 hor:4 pure:16 answer:1 instead:2 constraints:3 parameter:7 classify:1 belongs:2 map:1 product:10 express:2 blocks:3 algebra:13 may:16 horizontality:10 advice:1 after:1 derived:1 mapping:7 applications:1 physik:3 coming:1 multiplication:2 requirements:1 horizontal:29 unentangled:1 parallel:6 goal:1 period:1 short:2 natural:6 bailey:1 whenever:2 consequently:1 linear:18 sw:10 parameterized:1 purification:25 kosaki:1 perform:1 cannot:1 so:12 expression:3 allow:2 lξ:1 representation:17 words:1 order:5 superscript:1 operations:1 restriction:5 commutator:1 holds:1 interpretation:2 help:6 zee:3 indeed:11 over:7 mainly:2 satisfied:1 equality:1 paper:3 including:1 statistical:2 signs:1 mentioned:2 y0:5 satisfies:6 jochen:1 its:22 roots:2 before:1 horizontally:2 pt:2 group:8 probability:2 maps:1 appropriate:3 interesting:5 fix:6 affine:2 lk:1 conjugation:3 writing:1 forms:3 parts:1 lr:3 choose:6 superoperators:1 mail:1 schmidt:20 defining:1 pointed:1 lx:1 happened:1 correspondence:4 them:3 crucial:1 return:3 integral:2 am:2 budapest:1 functional:2 equating:1 motivates:1 effects:1 they:10 half:1 now:15 discuss:3 yw:1 above:3 2t:4 represents:2 finite:6 dirac:3 solves:1 invariants:5 classified:1 concave:3 identified:2 fs:52 orthonormal:7 sufficiently:1 iff:17 inequality:4 ψin:1 reasonable:2 eigenvalue:5 sophus:1 found:1 universit:3 traces:1 side:4 characterized:2 mean:4 gφk:1 bw1:2 domain:2 holonomy:9 g2:2 arbitrariness:2 independent:5 doing:1 ed:3 reduce:1 related:2 conventions:1 parallelity:5 operator:39 ξj:1 used:5 obtains:4 changed:1 quantum:10 our:28 operation:1 win:8 brings:1 out:5 try:1 rv:1 monographs:1 matrix:8 analytic:3 space:51 restricted:3 furthermore:1 since:3 induces:5 projected:1 converts:1 denotes:4 looking:2 replacing:1 contained:2 multiply:2 wu:3 rb:4 reader:1 denoted:3 formula:1 get:26 induced:10 issue:2 occurs:1 independence:1 shows:2 2fs:1 fiber:5 theory:9 written:2 monotone:21 diagonal:6 governing:2 standard:11 admits:1 indices:1 reason:2 base:6 york:1 ask:7 wanted:1 beginning:1 warszawa:1 rewritten:3 definition:3 fw:1 kubo:1 geometry:2 determining:1 could:1 impose:1 ds2:2 takasaki:1 vjk:11 turn:1 length:4 place:1 loops:1 leading:1 hence:14 onto:2 assign:2 first:11 verifies:1 already:4 lond:1 symmetry:2 assumptions:1 geodesic:1 rank:9 system:1 restrict:2 entanglement:1 multiplying:1 done:4 adopted:1 another:6 enumerate:1 carry:1 reached:3 smoothly:1 several:3 xu:1 wilczek:4 given:20 necessarily:5 publication:1 similarly:1 introduction:1 meaningful:1 adjoint:1 observes:2 amsterdam:1 theoretische:2 least:4 obligatory:1 their:9 returns:1 quadratic:1 manifolds:1 πw:4 statement:1 convention:3 normalization:1 scheme:4 structures:1 1l:4 gives:2 similary:1 commutativity:2 exactly:6 yield:1 assumption:3 part:25 because:4 authors:6 focusing:1 schr:2 x0:2 believe:1 uhlmann:7 than:5 specify:2 center:1 relative:5 determines:1 holland:1 cyclic:6 fuchs:1 split:1 require:2 enes:1 depends:6 kakutani:2 appealing:1 accordance:3 supposed:1 enables:2 distinguished:5 decompose:3 result:3 ansatz:1 purify:2 topics:1 kossakowski:1 rewrite:3 respecting:4 explicit:2 ann:3 mind:2 argument:1 curves:8 affirmative:1 say:2 manner:2 need:13 seen:6 cumbersome:1 element:5 hasegawa:3 any:5 seminar:1 lie:4 genuine:2 mappings:2 der:1 depending:3 lim:5 latter:4 rudolph:6 mills:3 ideas:1 mechanism:1 oriented:1 gφ:1 relatives:2 potential:3 take:1 neither:1 indexed:3 new:1 coincide:1 switching:1 kawaguchi:1 play:2 added:1 multiple:1 appl:1 trace:6 shall:3 singles:1 object:2 systems:1 metrics:25 extending:1 satisfying:4 germany:3 but:10 letter:1 formulae:1 phase:25 probabilistic:1 class:16 tensor:1 dummy:1 enumerating:1 observation:2 samuel:1 considered:5 clear:3 later:1 request:1 traditional:1 braunstein:1 yang:3 kw:2 exp:8 velocity:6 physics:5 sum:4 dot:2 applied:1 λs:2 selection:1 particularly:2 sakai:1 show:4 isomorphisms:1 dittmann:8 recipe:1 marmo:1 notations:3 x2:8 reminder:1 spaces:6 gauge:15 solutions:4 decompositions:2 purifications:2 possibilities:2 subtle:1 determined:1 trivial:4 find:3 principal:1 fibre:1 x1:7 based:3 aφ:1 representing:1 explain:3 enough:2 topological:2 should:8 lemma:1 only:15 bases:1 originally:1 worthwhile:1 equipped:2 acknowledge:1 hopf:1 imposing:1 borrowed:2 do:5 his:2 goes:3 notation:4 means:2 vary:1 µj:1 straightforwardly:2 solvability:2 aim:3 dyn:1 ones:3 instance:1 lifted:1 expresses:1 dw:12 geo:1 boundary:2 differentiating:1 bhatia:1 runs:1 caves:2 addresses:1 densities:2 φk:5 conditions:7 differential:1 think:2 remove:1 whether:5 experiments:1 gram:2 through:3 communicated:1 view:1 riemannian:26 kernel:1 requirement:1 set:8 modulo:1 computed:1 exists:7 achieved:1 physically:1 smooth:6 frame:1 banach:1 respect:6 ends:1 lett:11 grosse:1 connections:12 differentiation:1 see:11 arc:1 merits:1 w2:8 w1:6 existence:2 discussions:1 wc:1 acts:1 points:1 αp:2 phases:8 said:3 wa:6 enlightening:1 ways:1 review:1 definite:1 functionals:1 label:1 symmetric:1 state:13 smallest:1 various:1 closed:5 between:10 without:1 invariant:3 geometric:17 wether:1 numerous:1 petz:9 publishers:1 notice:1 jw:4 terms:3 wb:1 vertical:17 adding:1 fold:1 complement:2 attention:1 transpose:1 however:6 supports:1 wh:1 ww:17 strictly:2 vanishing:3 wt:5 unnormalized:2 jk:2 lb:9 amer:1 come:1 relying:2 motivation:1 wx:6 faced:1 observable:1 essentially:2 last:4 kluwer:1 gratefully:1 spectra:1 taking:1 la:1 equal:3 comment:1 fulfilled:2 chosen:2 connection:38 tout:5 berry:9 camb:1 uni:1 passing:1 estimation:1 adapted:1 guarantee:1 comes:2 otherwise:2 arbitrarily:4 adjusted:1 regulates:1 co:2 abbreviate:1 point:5 reasons:3 seems:2 deviating:1 leipzig:6 corresponds:1 insist:1 dimensional:3 directions:1 non:8 likes:1 moreover:7 mathematical:2 speak:1 considering:1 pp:18 much:1 commutative:2 second:8 basis:4 invert:1 armin:1 been:5 reduction:5 arxiv:1 combined:1 interest:1 basic:1 conjugated:1 ph:2 meeting:1 naples:1 define:5 concentrated:1 tangents:27 relations:4 families:1 both:3 influence:1 concerning:1 degenerates:1 subspace:2 coincides:2 neumann:6 remarks:1 lift:14 understand:1 generalization:1 demand:2 comming:1 irrelevant:1 spirit:1 those:4 case:11 gns:2 main:2 jx:2 look:3 decades:1 appearance:1 bω:1 value:3 remaining:1 will:9 euclidean:1 while:2 suppose:3 augustusplatz:2 behavior:1 aid:3 property:2 procedure:5 enforces:1 remembering:1 maximal:2 purifying:12 larger:5 simons:1 von:5 ir:4 thus:6 instantons:1 iw:1 according:5 rin:1 exchanging:1 reads:3 properties:4 cone:3 vv:2 vx:1 inf:1 chern:1 2g1:1 different:5 null:3 open:2 fibers:2 perhaps:1 arguments:1 belong:1 cross:1 same:7 clearly:1 read:1 complex:4 quant:2 emphasize:1 modification:2 φi:1 φj:18 constructed:2 infer:1 consequence:2 difficult:1 evolve:1 extended:1 entangled:9 bhandari:1 forced:1 effect:2 hand:7 sys:1 principally:1 moment:1 purpose:1 potentials:2 infinite:1 changing:2 invariance:3 identity:3 eigenvectors:7 task:3 off:4 proceed:1 torino:1 acknowledgement:1 nevertheless:2 whole:1 well:12 morandi:1 deal:2 obviously:2 peculiarities:1 bifurcation:1 programm:1 dimension:7 left:5 isometry:2 composed:1 reminding:2 construct:1 manifold:3 just:4 appropriately:1 being:7 able:1 observed:1 λx:2 obtain:6 valuable:2 anti:1 underlying:1 identify:1 immediately:2 λk:10 λj:14 previous:1 note:1 postal:1 preprint:1 generator:1 density:49 tok:1 conclude:4 had:2 except:2 simple:3 add:1 other:6 extends:2 nor:1 versa:1 vik:2 usage:2 extensive:1 transformation:4 measure:2 real:40 aspects:1 haux:4 easily:1 rules:3 decomposed:1 lin:1 possible:4 harmonic:3 interior:1 game:1 philos:1 know:1 using:3 variants:1 unique:10 domains:1 apart:1 insert:2 modifications:1 necessary:3 like:8 tomita:6 follows:4 reduces:1 velocities:1 characterization:1 fubini:1 heart:1 collect:1 yields:5 either:3 arbitrary:3 defects:1 become:5 canonically:2 conclusion:3 continuation:1 essential:3 terminology:1 fulfil:2 deviation:3 right:8 often:1 namely:1 stiefel:1 bull:2 acan:11 confused:1 some:15 back:3 acad:1 examples:4 choosing:2 specified:1 proper:1 ohya:1 little:1 classes:1 ourselves:2 transport:12 provided:1 dabrowski:1 dimensions:2 positivity:1 decision:1 though:2 thank:3 protocol:1 wout:6 asking:1 decomposition:9 provides:1 heidelberg:1 respects:1 proc:3 tk:2 minimal:2 inserting:1 varying:1 noise:4 xw:3 computation:1 indicated:1 rep:3 performed:1 problems:1 equivalent:6 stefan:1 ando:1 how:2 step:2 bw:3 convex:3 sandwiching:1 although:1 sesquilinear:1 relating:1 stay:1 super:1 hilbert:28 submanifold:2 gained:5 a1:1 about:2 would:2 extension:2 most:1 rev:6 freedom:2 completing:1 metrical:3 introduces:1 factors:1 assertion:2 compatible:4 mutually:2 extensions:1 mixed:2 ru:5 introduced:5 slightly:1 ubner:3 block:5 considerations:1 equally:1 own:1 letters:1 publishing:2 inclusion:2 into:9 within:6 definitely:1 isomorphic:2 down:3 pair:2 hermitian:50 square:3 references:2 einstein:1 elementary:2 factor:1 math:14 physical:2 methods:1 choosen:1 rely:1 forth:1 institut:4 additional:3 few:1 assumed:4 support:5 there:28 question:5 transform:2 initial:3 start:8 accordingly:2 describes:1 way:6 discontinuities:1 scientific:2 was:1 jy:1 treat:1 function:30 complexified:1 north:1 complete:5 form:39 shapere:1 something:1 hs:6 identities:1 jun:1 hw:3 encodes:1 neutral:6 construction:1 link:1 gain:3 encoded:1 line:3 true:2 bures:24 especially:1 extend:3 constitute:1 made:1 ruskai:1 versions:1 fulfilling:7 ut:6 de:1 attached:1 up:3 us:12 international:2 below:2 limit:2 submanifolds:1 continuously:1 problem:5 similar:5 called:10 eigenvector:2 distance:4 interval:1 constant:1 ad:3 pin:6 computing:1 defined:15 certain:7 abstract:1 describe:3 linearity:1 general:5 separating:2 single:1 au:1 dλ:1 aw:1 corresponding:2 exist:1 formalism:2 commuting:6 check:3 defines:3 functions:15 expect:1 faithful:5 no:5 mathematik:1 commutes:4 generally:4 detail:1 field:2 tin:11 setting:5 role:1 details:1 papers:1 sufficient:4 arithmetic:1 nw:16 mathematisches:2 polar:3 draw:1 elements:4 star:1 generates:1 calculating:3 living:2 preceding:1 june:1 shown:1 bundle:7 transported:1 deriving:2 a0:2 meaning:2 important:5 bounded:1 allowing:1 additionally:1 antilinear:2 variable:1 fisher:4 solving:1 gerd:1 gets:3 structure:3 stodolsky:1 simon:2 algebraic:1 implies:4 auxiliary:6 calls:2 vice:1 assume:9 transports:1 unital:2 curve:20 ppp:1 overload:1 donoghue:1 equivalently:6 time:5 observables:3 dm:3 starting:3 original:1
|
quant-ph9806029.txt |@word logarithm:1 represent:3 logarithms:1 gt:4 partial:3 consider:4 gv:1 induces:1 results:6 δi1:2 leads:1 gf:8 scalar:1 commute:1 generalize:1 ηi2:2 computation:26 consists:2 gs:1 research:2 gj:3 issues:2 compact:2 whose:1 dimensionality:2 indices:2 graph:11 deterministic:7 tr:14 factoring:2 finally:1 program:1 tj:2 present:1 th:3 stable:1 nodes:3 gb:11 norm:27 case:9 g5:1 g4:1 g3:1 string:7 advantage:1 orthogonal:7 very:6 implicitly:2 springer:1 geometrical:1 corollary:1 fan:3 summarized:1 bounding:1 affect:1 ga:11 matrices:30 dim:7 obvious:4 immediately:1 trn:1 νi1:2 turns:6 having:1 t2:11 solution:1 culminating:1 trf:8 try:1 discrete:1 vector:7 universal:1 dealt:1 small:2 eigenvalues:3 path:5 accumulation:2 configurations:1 upper:1 aρa:2 ηi1:2 deutsch:4 dealing:2 grover:1 measurable:2 suffices:1 sign:1 go:1 likely:1 infimum:2 follow:1 further:2 machines:4 theory:4 even:2 what:7 errors:5 tensoring:1 stands:1 brackets:1 d2:1 section:6 labeled:3 uniform:1 current:3 version:1 gi:14 above:5 scientists:2 new:5 acknowledgments:1 compactness:1 y2:3 full:1 notions:1 degree:5 respectively:2 never:1 equals:1 here:9 understanding:1 desired:1 objects:2 operating:4 possibility:1 others:1 represented:4 causality:3 principle:1 respect:3 appears:3 change:1 simulating:1 box:1 sending:1 property:3 tx:1 institute:2 larger:3 allows:1 completely:5 ρik:4 p2:1 schumacher:2 usually:2 dorit:1 changes:1 helps:1 involves:1 useful:3 projection:6 family:2 danger:1 ug:20 outcomes:1 till:1 boolean:3 analyzing:1 apply:5 orderings:1 total:3 establish:1 unit:2 alamitos:1 use:16 additive:1 superpositions:4 working:1 prove:9 probabilities:1 positive:12 contains:1 hilbert:15 few:2 call:1 therefore:2 vi:3 taken:2 noisy:1 type:1 theoretical:4 more:13 sort:6 israel:2 diamond:3 door:1 started:1 outputs:8 operators:19 infinitesimal:1 problem:5 quantity:2 berlin:1 particular:3 known:1 foundations:2 cases:1 conditioned:2 effort:1 vj:2 must:5 alexei:1 kraus:3 account:1 stabilized:1 defines:1 ρi:5 science:6 work:3 2d:2 remain:1 ij:2 values:1 ρw:1 tracing:1 following:13 example:8 def:1 proof:21 control:3 claim:2 impose:1 give:2 process:2 preserving:5 states:37 contradicts:1 numbers:1 allowed:8 every:1 keep:2 νi:8 calculated:1 g2:11 needs:1 end:3 g1:13 awkward:1 rather:1 means:3 feature:1 machine:1 how:2 subroutines:25 ens:1 pair:2 ig:9 pure:25 gate:26 ψij:12 verlag:1 ba:1 inputs:5 product:10 description:5 algebra:1 may:5 turing:7 after:3 applications:1 fundamental:1 plane:2 distances:1 fi:9 yes:4 efficiently:1 transposed:1 acyclic:1 natural:13 imply:1 computations:2 lemmas:1 grant:1 correspond:2 provide:4 complexity:5 algorithms:3 expression:1 allow:1 correlation:9 definitions:4 operate:5 make:1 operations:12 restriction:2 a400:1 interpretation:2 words:1 produces:2 over:12 pρ2:1 choose:3 years:1 paper:6 through:2 thesis:1 signs:1 mentioned:1 satisfies:4 still:2 put:2 its:2 before:3 write:3 garbage:12 maps:2 summands:1 actually:1 better:1 h2:5 fq:2 systems:1 annual:1 fij:8 main:5 might:2 maximal:5 non:9 incompleteness:1 affected:1 copying:2 combination:2 uv0:2 propose:1 largest:1 qs:4 landau:2 effects:2 37th:1 instead:1 trm:4 now:9 association:1 fi2:4 easily:2 february:1 gets:1 dirac:1 2r:1 intuitively:1 coping:1 always:1 university:2 traced:1 uρu:2 hermitian:6 simplicity:2 iff:1 inequality:5 brassard:1 each:12 2n:11 polynomially:2 2i:4 characterized:1 referred:2 subset:3 νi2:2 map:3 michael:1 enables:1 idea:3 slowdown:1 extended:3 computable:1 connect:1 measurement:14 quantum:106 our:11 operation:13 t1:11 logk:3 special:5 out:13 leave:1 shown:4 matrix:34 space:24 since:3 crucial:1 ry:3 bennet:1 denotes:2 particles:1 similarly:1 reader:2 denoted:8 induced:3 cause:1 correct:1 shows:2 foundation:2 weaknesses:1 linear:11 maintains:1 diagonal:2 undo:1 standard:13 vazirani:2 difficulty:1 reason:4 1r:1 advantages:3 term:1 besides:1 usual:1 ask:1 cornerstone:1 log:1 definition:19 benefits:1 language:3 could:2 computers:5 correctness:1 tolerant:3 thing:1 circuit:45 hence:7 onto:4 assign:1 first:10 initial:1 probability:20 omitted:2 powerful:1 number:2 oracles:1 restrict:1 randomized:3 done:2 specifically:2 another:2 blank:6 impossible:3 clarity:1 aharonov:2 size:1 manuscript:1 given:4 necessarily:2 reference:1 changing:2 their:5 introduction:2 xz:2 system:14 needed:2 returns:1 assumption:1 california:1 calculations:1 inconvenient:1 bits:14 final:6 permutation:1 inner:2 relies:1 imperfect:1 lot:1 moscow:1 observable:1 proving:1 next:1 part:1 simulate:2 x2:3 ancilla:4 copy:3 herself:1 than:7 specify:1 distance:11 subroutine:13 unfortunately:1 1m:2 behaved:1 require:1 enabled:1 namely:4 euclidean:2 project:1 symposium:2 determined:1 pairwise:1 were:2 outcome:1 russia:1 projections:1 generality:1 strengthen:3 correction:1 modern:2 measure:2 kitaev:3 say:3 manner:1 conjugate:1 need:7 seen:1 null:1 knill:1 any:17 viewed:1 tρ:1 paths:3 generalizes:1 built:1 zero:1 sj:3 studying:1 latter:1 able:3 lǫ:2 primed:1 note:4 k1:1 maxi:1 gσ:3 take:4 gρ:2 bailey:1 so:9 strengths:1 tool:1 accuracy:1 1n:2 needle:1 sm:4 trace:20 normal:1 track:3 sets:2 metrics:5 most:7 connected:1 representation:3 device:2 probabilistic:41 why:1 registers:2 considered:1 clear:2 sometimes:1 vertices:1 order:5 feynman:3 proceedings:1 h2n:7 error:15 inaccuracies:1 hellwig:2 physics:11 notion:3 fact:3 laws:2 shor:5 hyper:1 show:10 reductions:1 supported:1 speedup:1 notations:2 bring:1 spaces:8 relation:1 substituting:1 trivial:3 find:4 x1:3 based:1 knowledge:1 distributed:1 written:5 topological:6 should:2 lemma:31 only:9 explicitly:1 black:2 stated:1 bernstein:2 local:2 hope:1 do:1 mixture:4 subspaces:4 notation:4 get:3 zurek:1 sup:4 overall:2 satisfied:1 joint:1 october:4 valuable:1 dx:1 international:1 during:2 quantifies:1 sorts:2 stoc:1 qp:7 regarding:2 consist:1 conditions:1 arxiv:1 roy:1 34th:1 though:1 controlled:2 fortunately:1 remains:1 counterexample:1 set:20 computed:9 exists:5 achieved:2 physically:7 generally:1 j1:17 j2:14 operates:5 observed:1 y1:3 depends:3 computer:9 result:14 close:2 institutes:1 λi:2 incorporating:1 satisfying:1 tensor:9 channels:1 ieee:1 positivity:1 siam:4 definite:3 state:45 cooperation:1 between:15 conceptual:2 αk:2 c2n:1 αl:7 preserve:1 extend:2 qubits:39 confusion:1 restricting:1 however:7 jl:4 implementing:1 ji:4 key:4 jk:2 interface:1 relying:2 originates:1 0r:1 both:4 essentially:1 realizable:2 last:3 fault:3 taking:1 infinitely:1 according:5 attributed:1 agree:1 etc:1 embedding:4 qubit:6 whole:2 ci:10 point:2 simple:5 corresponds:9 dimensional:4 pm:7 ab:3 simply:3 spans:1 church:2 polynomial:3 associated:2 pr:7 lv:2 pp:5 described:8 transformations:1 second:3 basis:11 union:1 af:4 ben:2 due:3 been:1 ker:2 yao:1 describes:1 complicated:2 basic:13 pj:4 applying:1 ph:4 pi:4 meeting:1 formalized:1 pl:4 define:15 addison:1 direction:2 contribute:1 corresponding:9 commutes:1 subspace:3 precision:3 gap:1 generalization:1 fuctions:1 c2:1 c1:1 denote:6 those:1 applied:3 semidefinite:1 exponential:2 ǫj:1 value:2 will:23 technical:1 replaced:2 bounds:1 behavior:1 many:4 2k:1 procedure:3 yi:4 unitary:43 laflamme:1 vol:6 averaging:1 metric:12 thus:7 them:1 equal:3 middle:3 ik:2 good:2 im:2 avi:1 dual:2 hebrew:2 ready:1 ib:2 chi:1 disappear:2 binary:1 different:7 polygon:1 perform:1 realizing:1 trg:2 same:9 clearly:3 read:1 complex:4 quant:4 schematic:1 mixtures:1 modification:1 several:2 difficult:3 used:9 gc:6 see:5 somewhere:1 i1:26 i2:26 upon:1 hand:2 v0:3 action:1 edges:1 uses:7 entanglement:1 recall:2 identity:7 recent:1 eigenvectors:2 lower:7 task:1 vα:5 edition:1 0n:4 obstacles:1 well:5 vβ:2 without:1 norms:3 edge:2 simulated:1 organization:1 model:35 kv:2 dimension:1 left:4 gates:43 noam:1 just:1 being:5 captures:2 rest:4 isolated:1 completed:1 questions:1 using:24 alternative:2 yet:1 adding:1 density:56 extra:1 seems:6 reasons:1 add:3 other:3 lett:1 easy:1 theorem:10 input:17 haystack:1 transformation:2 real:1 aspects:1 rev:1 eigenvalue:1 rules:2 possible:4 spanned:1 possibly:1 boxes:1 fi1:6 pages:3 background:2 press:1 world:1 bit:6 unique:4 formal:3 semi:3 particle:2 follows:14 unnecessary:1 serves:1 discarded:2 communications:1 yields:3 δk:1 arbitrary:9 become:1 reduced:5 mathematical:2 exceed:1 because:5 often:2 deal:5 sequence:1 sends:4 belonged:1 conditional:1 phenomena:1 back:3 understood:1 specified:2 proofs:3 happens:2 orthonormal:1 choi:1 tools:1 measurements:5 thank:1 does:7 provides:4 steps:1 proc:1 prob:3 minimal:1 measuring:2 bf:4 noise:5 run:1 inaccurate:1 power:4 wigderson:1 equivalent:10 δi:1 continuing:1 wesley:1 step:3 convex:1 output:8 super:32 properties:4 proceed:1 integers:1 about:1 central:1 would:2 universe:1 theorems:2 discussed:1 generated:1 o:17 side:1 practical:1 mutually:3 extensions:2 act:1 mixed:17 discard:1 discusses:1 undoing:1 soc:1 computational:9 computes:7 previously:1 into:2 within:2 bound:9 ηi:13 lies:1 appropriate:3 references:1 operator:30 jerusalem:2 theoretically:1 span:2 classical:10 measured:3 there:26 question:2 lond:1 long:1 class:1 los:1 much:1 physicists:2 way:5 was:8 naturally:2 function:23 revised:1 form:5 enough:3 some:12 jun:1 but:7 searching:1 volume:1 link:1 pk:2 russian:1 line:1 true:2 copied:1 directed:5 inverse:2 made:1 compute:3 nisan:1 versions:1 circuits:13 inside:1 variations:2 up:1 devices:1 po:2 below:1 ui:7 sum:2 ud:5 distribution:11 generalises:1 called:10 mechanics:3 separated:1 later:2 constant:2 worthwhile:1 computing:10 defined:17 certain:1 abstract:1 describe:1 linearity:2 life:1 general:18 proves:1 exist:1 journal:1 formally:2 inf:1 formalism:1 distributions:4 check:2 physical:9 functions:20 completeness:1 us:19 no:18 whereas:3 when:6 disjoint:1 interested:1 remarks:1 becomes:4 naive:1 nice:2 node:3 picture:1 elements:1 simon:1 superposition:2 models:6 finite:3 time:2 problems:3 variation:3 includes:1 ξi:5 meaning:1 important:3 bounded:1 vectors:5 variable:1 seeing:1 urged:1 max:6 correlated:3 implies:1 longer:1 algorithm:3 assume:3 original:2 depth:8 passed:1 incomplete:1 ρv:3 remarked:1 observables:1 decoherence:4 augmented:1 strings:2 once:1
|
quant-ph9806030.txt |@word consider:9 jatkar:1 leads:1 roy:3 consists:1 chair:1 worked:1 whose:1 depend:1 calculate:4 bx3:3 technique:1 finally:1 those:1 th:1 worth:1 orthogonal:1 far:1 3ab:1 wave:19 witten:1 exact:3 condition:9 hamiltonian:5 solution:7 solved:3 eigenvalues:2 zh:2 sukhatme:2 dutra:1 sign:1 zero:7 pass:1 ǫx2:2 linear:6 tkachuk:3 section:1 poles:1 3b:7 method:9 contrast:1 satisfy:6 full:1 respectively:1 here:2 behaviour:1 ansatz:1 sinh:2 nonsingular:1 obtained:3 institute:1 study:1 studied:1 superpotential:8 varshni:1 bx2:10 elaborated:1 use:2 reflected:1 commun:1 quasi:5 properties:3 calculation:2 ψn:6 therefore:1 theoretical:1 more:1 walczak:1 duality:1 pisma:1 odinger:2 berlin:1 4ab:1 known:9 must:8 kumar:1 springer:1 equation:14 oscillator:6 reviews:2 following:9 razavy:2 example:2 dxw:3 states:4 junker:3 numbers:1 orthogonality:1 parameter:1 de:1 description:1 may:2 earlier:1 derived:1 dx2:1 yanov:1 stress:2 supersymmetric:8 explicit:5 correspond:1 so:2 subsequently:1 order:4 nizk:2 indeed:1 paper:5 through:1 statistical:1 existence:1 satisfies:5 its:3 energies:2 interesting:2 vicinity:1 systems:2 mail:1 supersymmetry:1 propose:1 franko:2 ces:4 souza:1 easily:2 february:1 several:1 university:1 level:1 appropriate:1 2a:4 2b:1 found:2 referred:1 differential:1 generation:2 energy:16 w12:1 related:1 isospectral:2 literature:1 quantum:12 our:1 special:3 out:1 space:1 rep:1 since:1 rev:2 denotes:1 math:1 theory:1 singularities:2 8a:1 free:2 khare:5 put:1 e1:4 e0:4 consequence:1 teor:3 first:10 number:1 restrict:1 directly:1 given:7 similarly:1 introduction:1 construct:2 zaslavsky:1 zeros:1 convention:1 bagrov:2 unbroken:4 gives:1 continuous:1 x2:2 x0:9 x6:1 x4:1 18b:3 require:1 integrability:2 str:1 were:3 ktf:1 dutta:1 treated:1 rewrite:2 spectrum:4 jour:1 latter:2 note:9 potential:23 square:6 generalized:1 finding:1 singh:1 canonical:1 exactly:10 shall:3 riccati:1 simplify:1 nagaraja:1 pair:1 bǫ:1 class:1 considered:4 calculated:2 exp:11 physics:3 8a2:1 fact:1 12b:1 discovered:1 relation:2 solutions:1 keywords:1 substituting:2 d2:1 find:1 ground:14 based:1 knowledge:1 parameters:1 written:2 only:3 explicitly:3 subsection:3 integrable:4 hamiltonians:6 do:3 eksp:2 samsonov:2 superpotentials:5 lviv:3 dx:6 new:8 dw:1 ushveridze:3 arxiv:1 factorization:1 view:1 coefficient:1 constructing:2 exists:1 see:10 result:6 w1:19 said:1 eigenfunctions:4 αx:1 review:2 state:20 various:2 between:2 invariant:2 boundary:1 conditions:2 recently:2 biswas:1 suggested:1 many:1 taking:1 equal:1 fiz:5 bristol:1 expression:1 mechanics:10 point:3 corresponds:6 pole:1 anti:2 polynomial:2 respect:7 described:2 transformations:2 addition:1 due:1 been:2 pb:1 basic:1 ph:4 choose:2 ukraine:1 generating:2 corresponding:5 dxφ:3 c1:6 c0:8 spin:1 present:2 case:14 pacs:1 transformation:7 suppose:4 cancelled:1 ǫx:3 thus:3 reads:1 susy:20 partner:5 different:3 develop:2 belong:1 same:5 zaslavskii:2 quant:4 finite:1 used:4 ulyanov:2 monotonic:1 levels:5 purpose:1 potentials:20 normalization:2 schr:2 whole:1 well:1 model:1 proposed:1 when:1 aǫ:3 obtain:12 shape:2 immediately:1 eigenstates:8 previous:1 preprint:4 4a3:2 except:1 belongs:1 lett:8 versa:1 mandal:1 solvable:7 excited:10 5b:1 real:1 eigenfunction:1 read:2 harmonic:6 know:2 using:10 mod:3 follows:3 arbitrary:2 ivan:1 node:2 because:3 methods:3 some:3 qes:28 b1:4 b2:3 ourselves:1 cooper:1 integration:1 conditionally:1 does:1 obey:1 bx:5 hilbert:1 publishing:1 discussed:1 o:3 αx0:1 introduced:1 previously:2 into:3 three:1 hermitian:1 en:5 references:1 operator:1 hep:1 initial:2 was:6 function:19 form:10 jun:1 idea:1 construction:2 line:1 24a2:1 applying:1 temp:2 mat:1 us:9 ul:1 below:1 shifman:1 problem:1 ua:2 called:3 examples:3 detailed:1 ab:1 constant:4 choosing:3 int:1 certain:1 abstract:1 am:1 general:4 relates:1 ax:3 eigenstate:1 functions:16 generally:1 application:1 book:1 details:1 papers:1 conclusion:1 conclude:1 generates:1 models:1 a2:1 included:1 vice:1 turbiner:2 starting:1 4a:2
|
quant-ph9806031.txt |@word since:3 consider:3 global:2 results:1 illustrated:1 andre:2 commute:1 montr:5 computation:10 edu:2 denotes:1 reasoning:1 inverse:3 exist:1 superpositions:1 alamos:4 concerned:1 technique:1 send:3 environment:1 init:2 permanently:1 present:1 under:1 include:1 sent:1 ingredient:2 string:3 advantage:1 orthogonal:1 very:2 pages:2 keeping:1 unfamiliar:1 choice:1 every:1 trouble:2 difference:3 exact:1 rn:4 entire:2 school:1 level:18 did:1 louis:1 notes:1 mb:6 bright:1 ri:5 try:1 vector:2 rj:1 small:2 enhance:1 optics:1 ville:1 force:7 direct:2 second:4 design:1 pass:3 initialized:1 implemented:1 even:4 index:1 what:8 xor:2 trapping:1 apparatus:3 chicago:1 section:3 ov:5 contributed:1 brief:1 shares:1 kent:2 henceforth:1 version:1 goes:1 new:6 ever:1 public:2 revealing:1 full:1 hash:2 exchange:1 respectively:1 applies:2 gilles:1 understanding:2 behaviour:1 test:4 them:7 twentieth:1 strategies:1 november:4 strong:1 change:2 knowledge:3 box:1 sending:1 convert:1 provably:2 ctr:1 clarify:1 inspired:1 goldwasser:3 allows:3 completely:3 amount:3 published:4 correct:2 bob:34 apart:1 involves:1 mutual:1 uniquely:1 deterministic:1 useful:3 secure:23 extra:1 namely:1 explained:4 outcomes:1 chaum:1 flexibility:1 unitary:2 analyzing:1 1st:1 apply:1 venkatesan:1 use:8 cheating:6 proceed:1 would:7 prove:3 probabilities:1 beginning:3 contains:2 chooses:1 next:1 classically:3 ψi:2 m1:10 therefore:5 centre:1 recommend:1 encode:1 care:1 tell:2 more:6 separated:1 flaw:1 clever:1 formally:1 knows:3 successful:1 binding:6 limitation:1 appendix:3 particular:1 foundations:1 cases:2 must:14 ii:1 account:1 shared:2 defeats:1 science:6 originally:1 work:2 column:1 easier:1 minimum:1 values:1 publications:1 learn:1 following:4 making:1 spontaneous:1 example:4 proof:10 control:3 august:3 process:2 relativistic:1 permutations:1 share:3 ps:1 states:5 really:1 assumptions:4 something:1 want:2 allowed:1 made:1 occur:1 verlag:5 information:16 needs:2 end:1 viewpoint:2 thing:1 rather:2 verify:3 discussion:4 breaking:1 how:2 extended:1 pair:2 fourth:1 place:2 brassard:10 simplicity:1 may:9 after:16 variant:1 containing:1 applications:4 coming:1 verified:1 arhus:2 efficiently:2 realized:1 short:1 elusive:1 remember:1 third:1 light:1 goal:3 register:5 perhaps:1 si:2 so:12 realizes:1 mcgill:3 keeps:1 subsequently:1 ostrovsky:4 order:4 rue:1 restriction:1 least:1 help:4 essence:1 choose:2 years:1 course:1 attitude:1 paper:5 including:2 berthiaume:1 committed:9 y1:14 y0:14 still:5 ieee:2 its:3 before:3 perfect:2 discloses:5 maps:1 personal:1 lo:9 fix:1 cryptology:7 actually:3 better:1 systems:2 annual:3 mail:4 main:1 might:1 into:2 split:2 non:2 combination:1 irreversible:1 practice:1 randomness:5 introduce:1 bound:2 break:1 yz:3 effects:1 they:8 symposium:3 now:7 realize:4 ebec:2 february:1 2p:8 intuitively:2 always:3 university:6 drop:1 unbreakable:1 crypto:3 orthonormal:1 sufficiently:1 reasonable:2 each:2 found:2 universit:2 difficult:1 side:1 referred:1 schemes:3 another:3 generation:1 hard:1 reduce:1 idea:4 used:16 measurement:9 quantum:89 our:8 operation:2 special:1 out:2 canada:2 large:1 shown:5 restricted:2 epeau:9 research:2 participants:2 performs:6 reader:1 denoted:1 lecture:1 get:5 issue:4 occurs:1 announced:1 common:1 counterpart:1 foundation:1 provide:1 theory:5 easily:3 commits:1 cre:2 possibility:2 standard:2 difficulty:2 approaches:2 base:1 hand:1 remainder:1 additional:2 definition:2 r0:2 r1:6 could:6 computers:1 honest:12 creates:3 turn:1 expecting:1 exponentially:3 βc:1 think:5 first:6 already:1 probability:8 variables:1 xa:2 number:1 restrict:2 2a7:1 done:1 long:3 directly:4 impossible:6 precisely:1 miss:1 between:2 illustrate:1 passes:2 given:4 los:4 introduction:2 system:3 construct:1 their:5 attack:27 assumption:6 passed:1 scheme:11 bits:2 final:3 store:1 danish:1 sigact:1 exactly:1 part:4 x0:11 x1:11 bennett:4 than:6 december:4 distance:1 kind:3 perfectly:1 ben:3 unfortunately:1 showed:1 princeton:4 fuchs:1 require:1 computes:5 aau:1 future:1 crepeau:1 letters:2 were:7 identical:1 india:1 outcome:7 interactive:1 generality:1 boston:1 modern:1 measure:3 bitwise:2 say:3 manner:1 archive:4 seen:1 recover:3 apparently:1 any:11 complete:2 computationally:8 zero:2 efficient:2 able:1 ideas:3 note:4 sciences:1 ideal:1 take:2 objective:2 algorithms:1 techniques:3 sn:1 se:1 criteria:1 entanglement:1 fundamental:1 advances:4 though:2 inverter:1 ıve:2 measures:9 talk:1 most:2 preliminary:1 phase:16 coin:2 measured:3 why:6 pseudorandomness:1 volume:1 don:1 takes:1 consequences:1 salvail:7 considered:2 international:2 clear:1 later:4 defeating:2 proceedings:8 hi:9 principle:2 normally:1 notion:3 fact:13 langlois:1 gz:1 show:1 cheat:3 random:16 discovered:1 bring:1 attempts:3 registers:23 solutions:2 possibilities:1 subtle:1 fine:1 find:1 make:1 impact:1 execution:1 finally:1 based:3 just:2 title:1 claude:1 situations:1 explain:4 state:30 should:2 only:10 going:3 tape:9 indeed:1 hope:4 regularly:1 do:6 his:4 dk:2 cryptography:8 means:1 de:2 overall:3 preferred:1 truly:2 cannot:11 despite:4 report:1 during:9 him:3 qu:2 held:1 denmark:1 arxiv:1 remove:1 negligeable:1 she:22 mapped:1 fixed:8 valid:2 wrote:1 temporarily:1 computed:1 exists:2 achieved:1 physically:3 problem:2 national:1 see:4 computer:9 result:16 existence:1 fail:1 unveils:3 particle:1 subject:2 appear:1 satisfying:1 cheaters:1 review:4 commitments:3 written:1 determined:1 identification:2 iro:2 approach:8 checks:4 discovery:1 available:1 notice:1 never:2 recently:2 creating:1 nature:1 initially:1 weak:1 attention:1 focus:2 however:9 analyzes:1 untouched:1 here:5 key:2 news:1 relying:2 34th:1 both:9 2n:3 many:3 conclusions:1 3j7:1 against:6 moni:1 etc:2 context:1 interesting:1 whole:1 experimental:1 otherwise:2 unitarily:1 unnormalized:1 point:2 ca:2 wonder:1 corresponds:3 simply:3 cs:3 oblivious:6 conference:2 wigderson:3 pp:12 described:2 basis:2 create:1 been:6 strategy:5 reduction:5 describes:2 basic:3 ph:6 define:1 obtained:6 disclosing:1 corresponding:2 retrospective:1 attacked:1 mind:2 sufficient:2 reaching:1 else:1 attacker:1 coherent:1 observe:2 understand:1 epartement:1 denote:1 irrelevant:1 protocols:13 case:1 explicitly:1 multi:1 look:1 value:7 remaining:1 will:5 complexity:2 suppose:2 promising:1 situation:3 dominic:1 cages:1 unlikely:1 h3c:1 h3a:1 vol:6 thus:2 surprisingly:2 defeated:1 encountered:1 couples:1 aspects:1 technology:3 disappear:1 binary:1 different:3 participant:8 unveiling:6 anymore:4 author:1 perform:7 arguments:1 began:1 concealing:11 same:9 clearly:1 ya:3 quant:6 emphasize:2 big:1 modification:1 yung:4 undoes:1 literature:1 temporary:3 initialization:1 permutation:4 functions:1 possible:3 eurocrypt:1 levels:1 uses:2 purpose:2 prague:1 munkegade:1 randomized:1 wholeness:1 thoughts:1 keep:1 safe:1 kept:1 scenario:3 nevertheless:2 unconditionally:13 game:1 analysis:1 picks:6 thought:1 without:6 solve:2 endfor:2 sets:4 model:4 researchers:1 know:3 protocol:70 proposed:7 tossing:2 λx:3 obtain:8 mor:1 world:5 regardless:1 alternative:1 speed:1 previous:3 dropped:1 preprint:4 ny:1 photons:1 had:2 except:2 mcconnell:1 discuss:1 interested:2 easy:2 theorem:3 reason:1 input:2 disadvantage:1 transformation:2 real:2 march:2 depends:1 αc:1 checking:1 replaced:2 papers:1 unlimited:2 term:3 unveil:3 transmit:1 increases:1 entangled:1 using:6 bit:73 unique:2 moreover:1 ruled:1 necessary:1 like:1 success:1 obvious:1 reduces:1 alice:69 specific:3 yields:1 either:2 follows:1 output:1 security:9 works:2 signal:1 shed:1 because:12 often:1 deal:2 sends:2 creation:1 some:11 back:3 fixing:1 erase:2 examples:2 cr:9 proper:1 indirect:3 proofs:2 intractability:1 provided:2 announces:11 measurements:12 everything:1 kilian:3 does:11 demonstrated:1 measuring:3 says:2 who:1 run:3 power:7 bc:7 performed:7 equivalent:3 processing:1 communicate:4 mayers:22 step:1 np:2 become:1 bangalore:1 finding:1 entirely:2 stage:1 about:3 attacks:3 discussed:2 acm:2 practical:1 commit:24 mean:1 naor:6 disclosure:1 computational:6 statements:1 previously:2 communication:14 umontreal:1 indirectly:1 commitment:60 prepares:2 references:1 determine:3 parties:2 lesson:1 reducing:2 rely:1 forth:1 classical:46 her:7 area:1 transfer:5 springer:5 there:9 question:1 yao:2 fast:1 noticed:1 start:1 workshop:2 editor:1 way:13 discard:2 analyze:2 was:23 m0:8 function:2 building:1 successfully:1 eal:5 enough:1 phenomena:2 smolin:1 regard:1 jun:1 but:7 principles:1 hj:1 taken:1 construction:2 encoded:1 true:4 he:9 october:3 compute:6 whether:1 up:3 us:3 until:1 ωi:3 faraday:1 jozsa:1 demonstrate:1 distribution:7 similar:3 called:1 mechanics:1 lanl:1 associated:7 computing:3 defined:1 abstract:2 describe:4 proven:1 general:11 prover:4 initial:5 rule:1 chau:9 journal:3 encompass:2 check:2 physical:2 again:1 nj:1 no:15 na:2 whereas:1 when:6 illinois:1 application:1 other:13 0n:2 becomes:1 department:2 you:1 forcing:1 conclusion:1 requested:3 briefly:1 superposition:5 separate:1 class:1 26th:1 generated:2 important:4 variable:3 sides:1 cryptographic:3 independently:1 algorithm:10 assume:3 physics:1 tricks:1 required:2 pseudo:1 together:3 attacking:1 impossibility:5 cheater:21 came:1 time:1 far:3 http:1 decoherence:1 requires:2 original:5
|
quant-ph9806032.txt |@word represent:2 code:64 consider:4 pth:1 caused:1 results:1 ary:2 eds:1 commute:7 concerning:1 comments:1 computation:7 go:4 follow:1 gj:2 gi:15 forget:3 whose:15 inverse:4 leung:1 alamos:4 finally:11 present:1 th:6 under:2 government:1 include:2 preskill:1 applied:2 g3:4 g2:4 g1:4 orthogonal:2 very:1 dholakia:1 choice:2 corollary:3 replaces:1 every:3 mpq:5 zi2:1 bringing:1 condition:7 arrange:1 notations:2 swapping:1 immediately:1 bring:2 transmission:1 suffices:1 solution:1 occurs:1 large:2 discrete:2 vector:2 science:2 small:3 generalize:1 markov:1 caltech:1 added:1 bd:2 zn:14 approximately:1 says:1 29th:1 det:1 consistent:2 direct:2 grant:1 zero:3 cost:10 qeccs:3 manipulating:1 implemented:2 columns:1 spreading:1 even:1 trick:1 what:1 errors:11 appear:1 invertible:3 d2:11 sum:6 expressed:10 decoding:39 version:1 localized:1 above:8 3c:3 3b:2 3a:2 row:3 method:3 3d:2 body:3 slotine:1 excludes:1 respectively:7 error:40 equals:7 here:1 hku:2 reported:1 address:2 represented:6 path:2 quite:1 importantly:1 change:1 obtained:3 sending:1 convert:2 generalizing:1 divisor:2 suitably:1 involved:2 mx:1 p2:31 amount:1 permutation:1 tolerantly:2 suitable:2 involves:1 york:1 control:2 useful:6 projection:3 subtracts:1 scales:1 timestep:1 namely:3 replace:1 brought:1 cij:2 sloane:3 1st:1 summation:1 apply:1 manipulate:3 use:2 takes:1 would:2 codewords:5 probabilities:2 next:2 qcc:46 going:4 call:1 therefore:2 criteria:2 encode:4 associated:2 type:1 until:2 more:9 convolutional:34 introducing:1 multiplying:1 becomes:3 operators:24 apparent:1 occurred:1 surprisingly:1 reversible:1 particular:2 known:3 iv:1 iii:1 must:5 me:8 respected:2 ma:2 quantized:1 zi1:1 recall:4 work:5 mi:3 paragraph:2 obvious:2 stabilizer:37 concepts:2 following:7 trans:8 root:1 example:9 numbers:1 f0:9 f1:3 compare:3 spiller:1 abelian:2 process:11 share:1 boston:1 implementations:4 states:4 minimum:9 reviewing:1 sense:1 distinct:1 keep:1 conversely:1 information:13 ti:2 redundancy:1 end:1 recovery:19 rather:1 verify:1 discussion:1 acts:4 feature:1 write:7 located:2 vital:1 criterion:2 fourth:2 answer:1 optimal:2 hi:8 divides:1 proof:18 belongs:3 fp:4 simplicity:1 product:10 blocks:9 flip:18 transforming:3 after:11 different:3 consequence:1 tries:2 lot:1 gottesman:7 multiplication:4 fi:8 law:1 unencoded:6 eighth:1 lar:1 syndrome:5 stress:1 branches:5 remember:1 effective:1 whenever:4 lemmas:3 register:16 summing:1 element:3 perform:3 si:2 ones:2 algorithms:3 block:23 keeps:2 order:1 operations:14 holds:1 submatrices:1 ith:4 produces:1 essence:1 over:5 move:2 kong:3 symbols:1 paper:1 including:1 same:4 finitely:1 during:1 existence:1 still:2 ieee:9 its:8 before:2 massey:4 delay:1 group:7 probability:6 maps:1 chosen:3 matrices:8 lm:1 actually:1 forms:1 according:1 choose:3 annual:1 mail:1 wellknown:1 syndromes:8 yi:2 them:4 good:5 affected:1 greater:1 eiθ2:1 auto:1 practice:2 introduce:2 22b:1 steane:2 they:2 instead:1 dealing:1 now:8 yu:1 fi2:1 eigenvalue:1 february:1 finite:41 exits:1 always:4 university:1 tran:1 xy:1 each:28 found:1 domain:3 ei:2 directly:5 weight:2 map:2 series:2 4b:1 faulttolerant:3 elementary:2 used:2 gates:2 knill:2 measure:2 quantum:146 http:1 operation:4 extract:2 out:5 category:1 fano:1 shown:1 dij:8 matrix:21 space:4 furthermore:4 since:14 rev:13 denotes:2 may:7 acting:7 multiply:2 performs:2 adaptive:1 ref:8 correct:2 math:1 reck:1 theory:4 plication:1 seventh:1 given:13 free:1 minimized:1 applications:1 int:1 besides:9 org:1 likelihood:1 generate:2 care:1 definition:5 paz:1 retained:1 her:1 4a:1 trices:1 starts:2 impose:1 wrong:1 tolerant:15 length:9 place:1 exponentially:1 circuit:22 enough:1 hence:19 facilitate:1 eqs:2 first:35 xj:3 xk:1 note:1 surviving:1 encoding:26 u1:8 coding:3 number:38 restrict:2 entanglement:1 erroneous:3 done:1 u3:6 another:3 diagonal:4 ring:5 precisely:4 aharonov:1 idea:1 differ:2 similarly:7 introduction:3 unknown:1 xij:10 construct:4 their:6 normalization:1 statement:2 time:1 scheme:4 bits:4 final:2 recovered:1 gives:2 terminates:1 proving:1 manipulation:1 x2:5 x1:5 than:1 intrinsically:1 18b:2 distance:14 kind:4 18a:2 ben:1 third:5 showed:2 prevent:1 df1:6 computes:1 xi1:2 xi2:2 future:1 represents:1 tion:1 decompose:2 bertani:1 xin:1 false:1 generality:1 viterbi:7 correction:2 mind:1 argument:1 kitaev:1 needs:1 randomly:1 miquel:1 say:3 archive:4 need:1 my:5 recover:2 clearly:6 paths:2 generalizes:1 mij:10 resultant:3 k3:6 k2:15 k1:18 internal:1 generalized:3 gets:1 ancillary:9 so:11 channel:10 greatest:1 begin:1 regard:2 a3:1 shall:3 measures:1 satisfy:2 surv:1 most:2 preset:12 propagate:5 encodes:2 codeword:10 phase:22 measured:1 class:1 prove:3 observation:2 kk:1 kj:1 clear:5 cover:1 km:1 kl:1 braunstein:1 qbc:4 zurek:2 hamming:19 sain:4 left:2 physics:1 fact:5 shor:5 selection:1 index:2 show:9 supported:1 terminate:1 discovered:1 ki:27 registers:38 lloyd:1 carefully:4 conclusion:1 careful:1 data:2 find:8 fifth:1 calderbank:2 q1:16 q3:16 q2:26 based:1 knowledge:1 spite:2 implementation:2 explain:1 written:6 should:1 lemma:12 only:16 sequential:3 generators:10 constant:1 bernstein:1 local:7 sure:1 jth:2 dn:5 do:3 dm:2 gains:1 notation:4 means:1 df:1 dd:1 overall:1 truly:1 nevertheless:2 cannot:2 rest:1 words:2 new:1 report:5 reconstruct:1 tips:1 dp:2 prime:11 acm:2 singapore:1 hardin:1 initial:8 upper:1 transposition:1 arxiv:1 fixes:1 borrow:2 summary:2 investigate:1 common:3 mapped:1 qi:8 through:3 fixed:7 shl:1 remains:4 fault:17 requirement:1 set:9 modulo:1 thesis:1 exists:7 catastrophic:31 tech:1 lett:6 up:3 achieves:1 depends:4 result:7 discussions:3 close:1 definitely:1 instance:3 phases:1 said:2 parent:1 ways:2 subsequent:1 bi1:1 materials:1 symmetric:2 rgc:1 state:37 smallest:1 permutes:1 closed:1 between:12 αi:6 consecutive:2 αj:2 discovery:1 concatenate:1 ends:1 loose:1 recently:3 ability:2 extend:2 nature:2 qubits:11 comp:3 however:1 jr:2 comm:2 tum:1 key:3 subgroup:2 ket:5 thank:1 both:5 protect:2 many:8 readers:2 correctable:1 agree:1 propagation:3 involve:1 σx:31 efficiently:1 lo:2 qubit:5 los:4 otherwise:3 unitarily:3 among:1 forney:2 relevant:2 conclude:2 simple:2 sciencemag:1 simply:8 spans:2 polynomial:5 moreover:9 throughout:1 considers:1 pr:1 eiθ1:3 aij:6 described:3 commutative:5 second:4 capable:1 addition:8 skew:1 locally:1 ai1:2 due:2 ai3:1 ai2:2 pb:4 ai:3 reduction:1 much:2 interest:1 pe:4 expected:1 ph:6 pi:13 define:7 determinant:1 corresponding:5 turned:1 subjecting:1 search:1 zeilinger:1 observe:2 optimality:3 denote:4 spin:19 those:7 case:11 p3:18 myself:2 p1:16 pacs:1 indefinitely:1 straight:1 chap:1 ǫl:1 will:4 euclidean:3 while:2 suppose:8 behavior:1 applies:2 property:1 procedure:1 inherits:1 theo:7 concurrently:1 unitary:14 examines:1 laflamme:2 memoryless:7 ip:3 refs:1 thus:11 non:31 sym:1 equal:4 ii:1 ij:6 conf:1 ax:2 ready:2 shift:12 binary:4 hong:3 qecc:4 σz:41 lengths:1 acknowledgments:1 make:3 belong:5 wiring:2 σy:3 arbitrarily:1 any:5 unity:1 quant:7 pauli:5 units:1 several:2 composition:2 independent:1 extended:2 infinity:1 see:5 again:1 effect:4 times:1 hand:1 action:3 running:1 levels:2 uses:1 infinite:8 identity:2 fourier:6 kept:3 possibly:2 minimize:1 nonetheless:1 well:9 increases:1 analysis:1 without:2 costs:2 ωni:2 cj2:2 cj3:2 model:1 cj1:2 dimension:2 researchers:1 usual:1 distances:6 kkk:1 popescu:1 transmitting:1 generally:1 actions:1 questions:1 ωn2:1 regardless:1 alternative:1 bi2:1 previous:3 adding:2 preprint:4 family:5 kluwer:1 infinitely:8 bir:1 regarded:3 except:1 mathematically:1 signals:11 add:2 valid:2 omura:1 location:2 easy:6 theorem:9 input:12 formal:2 transformation:5 take:1 available:2 bij:3 easily:2 checking:1 replaced:3 showing:1 decomposed:3 sums:1 possible:13 spanned:1 department:1 suffering:1 five:1 know:3 performance:1 average:1 using:11 bit:1 unique:1 correcting:4 usually:2 preparatory:1 meaning:1 necessary:6 like:2 lost:1 identifying:1 follows:2 signal:32 vda:8 steps:2 either:4 arbitrary:1 output:12 security:1 works:1 essential:1 terminology:1 twelve:1 www:1 right:2 classical:35 sequence:1 sends:1 some:6 supplementary:1 n2:5 repeat:2 examples:1 specified:1 separately:1 mmp:1 amongst:1 memories:1 per:5 does:3 decomposition:1 linearly:1 tends:1 compute:3 proc:2 symbol:1 measuring:3 noise:1 run:1 scientific:1 power:14 performed:1 sixth:1 equivalent:3 processing:1 bi:1 how:8 np:3 although:1 eiφ:3 pokfulam:1 hilbert:2 noisy:1 about:3 carried:1 world:4 column:5 basis:1 discussed:1 generated:5 o:3 mutually:2 carries:2 involving:1 plus:2 rule:1 act:2 eight:1 introduced:2 consequently:7 road:1 wire:1 primitive:1 own:1 statements:1 followed:1 presence:1 previously:2 into:11 iden:1 22a:1 three:5 nothing:1 because:2 operator:30 proportional:1 additions:1 conceptually:1 mm0:1 rows:1 span:1 prepare:1 u4:2 there:13 question:2 transform:9 long:4 u2:9 decode:10 start:1 accordingly:1 ψi:2 way:16 forward:1 was:1 a2:1 debbie:1 function:1 decoded:5 complete:5 form:16 dummy:2 something:1 memory:15 jun:1 but:7 encoder:1 hk:1 repeated:2 construction:2 related:1 encoded:48 enlarging:1 he:1 xi:9 applying:1 places:1 characteristic:1 probabilistic:1 maximum:1 us:1 relabeling:1 below:2 ui:5 union:1 ωn:12 sides:1 russ:1 distribution:1 similar:7 called:3 his:2 proved:3 ad:2 computing:1 defined:4 certain:5 measurement:2 am:4 general:4 single:3 exist:4 trix:1 chau:8 controlled:2 inf:7 formalism:1 check:3 metric:1 constructed:4 ni:6 inductively:2 codes:37 no:3 rains:3 eq:19 when:8 field:3 other:8 branch:2 test:2 tie:1 really:1 tity:1 sufficient:6 2dk:1 nice:1 briefly:2 elements:17 la:1 separate:1 why:1 mechanical:1 polynomials:1 includes:1 a1:1 chance:1 important:1 variable:1 needed:1 independently:1 implies:1 algorithm:7 starting:1 required:3 together:1 nasa:1 affects:1 n1:7 decoherence:2 backward:1 requires:3 original:5 provided:3 once:3
|
quant-ph9806033.txt |@word represent:3 concept:1 consider:1 similarity:1 rev:1 global:1 results:2 four:3 gf:2 bohm:1 consists:3 expressions:3 research:1 contributions:3 carpet:4 compact:1 depend:1 alamos:1 p2:2 consequently:1 very:1 rise:3 differently:1 wave:29 decide:1 hannay:1 nieto:1 difference:7 fractal:1 condition:1 leads:1 immediately:1 hamiltonian:3 ref:3 large:2 indices:2 enhance:1 optics:3 degeneracy:5 neighborhood:1 hillery:1 go:1 second:1 enhancement:1 dynamics:1 odd:4 gm:3 substitute:2 theory:2 even:4 nonlinear:1 appear:1 brackets:4 section:6 uniform:1 above:1 new:7 contrast:4 coefficient:1 eikn:1 eikm:1 led:1 here:9 understanding:1 free:2 separation:1 hkm:1 canals:5 equations:1 appears:1 box:11 institute:1 involved:1 allows:4 eberly:1 suggests:1 poisson:3 published:1 fourier:1 involves:1 carpets:11 emerge:1 useful:1 replace:3 scaled:1 summation:11 apply:1 ipy:2 standing:1 use:7 takes:3 usa:1 ψr:1 ψs:1 negative:1 substitutions:2 bialynicki:2 ψn:6 therefore:5 ψm:20 themselves:1 theoretical:1 flat:1 brings:3 distribution:3 appendix:10 particular:1 cases:2 aligned:1 iii:1 md:1 ρf:2 pursue:1 recall:2 equation:1 values:3 publications:1 ulm:3 following:1 making:1 arrive:4 example:2 compare:1 figure:1 give:2 relativistic:8 arise:1 organized:1 topic:1 numbers:14 allowed:1 train:1 axis:1 lamb:3 information:1 eng:1 rather:2 range:1 located:1 pair:1 acta:1 verlag:1 sin:1 product:4 express:2 replacing:1 after:1 derived:4 stroud:1 hence:3 physik:1 waves:4 multiplication:2 representations:3 summarize:1 bratislava:1 fm:6 natural:1 third:1 light:1 counter:1 lines:13 correspond:4 green:1 sect:5 allow:1 lξ:9 representation:12 order:2 2sl:1 wigner:15 eigen:1 laboratory:1 indeed:4 over:8 insight:1 paper:4 satisfies:2 excitations:1 its:3 before:1 derive:3 symmetry:1 energies:3 interesting:1 conjugation:1 fruitful:1 fig:3 mail:1 main:2 image:1 emphasize:1 non:4 introduce:2 walls:1 kiss:1 symposium:1 now:5 hall:2 2t:4 term:2 2r:2 2s:9 university:2 l2:1 each:1 2l:17 2m:9 universit:1 traces:1 em:3 square:3 tilted:1 weight:1 ed:3 energy:16 idea:2 related:1 fs:2 quantum:29 our:2 operation:1 eq:20 special:1 out:8 shown:4 space:10 rep:1 since:1 interference:1 denotes:1 print:1 formula:9 issue:1 ree:2 mπ:1 written:1 possibility:1 completely:1 narosa:1 e1:1 definition:5 pairs:1 lighthill:1 derivation:1 thread:1 applications:1 woven:2 stiftung:1 creates:1 length:1 consequence:1 uses:1 eqs:5 first:1 origin:1 already:1 humboldt:1 probability:22 striking:2 relate:1 variables:1 number:3 exact:1 another:2 horizontal:1 revival:3 start:1 introduction:3 top:1 their:3 structures:12 gives:2 fraction:1 enhancing:1 centered:1 continuous:2 coefficients:10 determines:1 double:5 determined:2 amplitude:2 steep:1 topics:1 argument:5 conjugate:2 sas:1 curved:2 clearly:3 warsaw:1 lie:1 built:1 latter:1 governs:1 connell:1 note:4 fundamentals:1 take:2 kaplan:3 finding:1 formulas:1 play:1 differences:1 scripta:1 asymmetric:1 most:3 propagate:1 but:3 multiply:1 eigenfunctions:1 surprising:1 average:1 kn:12 km:16 proceedings:3 points:1 exp:37 physics:4 sum:13 phenomenon:1 show:2 hnr:3 discovered:1 bring:2 relation:9 find:11 fifth:1 ground:1 ratio:1 state:2 only:2 summarizing:1 factor:2 local:1 do:2 klein:1 de:1 dx:9 dy:4 steepness:3 areas:2 arxiv:1 expansions:1 factorization:2 summary:1 contain:3 explanations:2 leeuwen:2 packet:9 see:2 individual:1 result:1 discussions:1 dµ:1 saif:1 phases:1 evaluation:1 extend:1 review:1 symmetric:1 outside:2 future:1 cambridge:1 between:2 propagated:1 prentice:1 conditions:1 terms:13 creating:1 vertical:1 comp:1 wl:3 focus:1 however:3 jr:4 jl:6 key:1 distinguish:1 ikn:3 ikm:5 thank:1 both:5 last:2 many:2 conclusions:1 according:2 conference:2 jin:1 berry:4 uni:1 hπ:1 expression:11 los:1 co:1 conclude:6 simple:6 address:1 corresponds:1 dimensional:1 scully:1 wider:1 moreover:3 schleich:8 considering:1 hω1:1 publishing:1 puts:1 three:2 much:1 electr:1 pj:2 ph:2 define:1 obtained:1 arises:1 corresponding:1 deeper:1 restrictions:1 quantities:1 understand:1 c2:1 present:6 case:6 multi:2 laser:1 straight:5 kimble:1 will:1 cast:1 freely:1 property:2 real:1 vol:1 them:1 ii:3 reads:3 obstacle:1 theta:1 different:6 develop:1 perform:1 same:2 any:1 complex:3 quant:2 arguments:2 kn2:2 φm:4 development:1 used:3 trajectories:4 sudarshan:1 moving:1 purpose:1 along:6 relies:1 intermode:1 schr:1 center:1 acknowledgement:1 nevertheless:1 whole:1 poland:1 no:1 analysis:1 thought:1 contact:1 position:5 left:2 appropriately:1 rest:1 shape:4 identify:1 using:2 eigenstates:1 heuristic:2 enters:2 integer:1 density:13 help:2 combine:3 location:1 rost:2 iπ:1 momentum:4 generalized:1 identical:1 sums:5 kinzel:1 dark:1 press:4 world:11 depicts:1 mod:1 particle:12 follows:3 dept:1 yields:1 either:1 integrals:2 essential:1 right:2 classical:4 certain:1 mirror:1 excitation:1 icl:6 integration:7 contributing:1 quantenphysik:1 does:1 connecting:1 provides:2 propagating:2 gratitude:1 shaker:1 scientific:2 bl:1 equivalent:2 expansion:9 wesley:1 step:1 abteilung:1 approximating:1 properties:1 integers:1 extension:3 hopkins:1 theorems:1 o:6 cancelation:1 ow:1 germany:1 introduced:2 slightly:4 computational:1 ridges:4 noting:1 into:7 johns:1 integral:2 due:1 phase:4 appropriate:2 extending:3 references:1 proportional:1 iπm:3 jubilee:1 forth:1 van:2 support:1 initial:9 question:1 dispersion:2 width:2 quadratic:2 slovakia:1 low:1 way:6 house:1 was:1 opens:1 function:23 lotnik:1 form:5 offer:1 hr:1 gauss:1 m2:3 jun:1 ht:5 gaussian:5 delta:1 made:8 zhu:1 2πi:1 inside:1 maximum:1 us:7 ur:1 um:5 limit:1 mk1:1 problem:3 jπ:1 clear:1 iqc:6 mechanics:1 constant:1 addison:1 defined:2 recognize:2 single:1 physica:3 marklof:3 archive:1 physical:1 functions:8 ingredients:1 slovaca:1 whereas:6 when:12 vanishes:2 2πiµ:1 application:1 other:3 role:1 briefly:1 superposition:6 χj:4 iπµ:5 preceding:1 june:1 odinger:1 deriving:1 important:2 suppression:1 variable:3 birula:2 lang:1 algebraic:1 dσ:1 rule:1 dρ:11 4l:1 4m:1 mass:2 presenting:1 time:10 starting:1 original:2
|
quant-ph9806034.txt |@word consider:2 results:2 leads:3 gf:8 cooperative:2 research:1 devoted:1 whose:1 analogous:1 worth:2 very:2 frequencies:1 engineered:1 wave:1 chaichian:2 affect:1 exact:1 condition:2 quantized:1 level:5 bonifacio:1 developing:1 large:2 convenience:1 leninsky:1 small:2 eigenvalues:2 c02:1 upper:1 smaller:1 approximation:3 zero:1 spontaneously:2 aim:1 what:2 nonlinear:4 3n:2 international:1 increasing:2 3f:1 coefficient:1 respectively:1 here:1 atoms:20 groups:1 berkeley:1 strong:2 equations:3 change:1 buck:1 great:1 institute:1 study:2 studied:1 allows:1 vibrating:1 commonly:1 amount:1 action:1 resonance:1 changes:1 via:1 plenum:1 highly:1 modulated:1 mataloni:1 unit:1 seligman:1 use:2 takes:5 mexico:1 almost:1 noting:2 therefore:1 means:1 possible:2 lowering:1 becomes:3 operators:2 ellinas:1 odinger:3 normalized:1 particular:2 known:2 cases:3 iii:1 high:1 graphic:1 vladimir:1 permits:1 deformed:7 decay:1 equation:3 work:2 oscillator:4 remain:1 fock:1 values:6 chumakov:6 making:1 spontaneous:7 initial:2 figure:1 discussed:2 sample:1 performed:1 arise:1 occur:1 provide:1 buzek:1 get:1 located:1 zaccaria:3 influences:1 acta:1 parameter:5 sin:5 l873:1 oscillatory:1 simplicity:1 description:1 algebra:1 may:4 oscillators:5 different:3 collection:2 stefano:1 date:1 choice:2 response:1 types:1 man:4 kulish:2 whenever:1 spectra:1 sj:6 shore:1 fundamental:1 martini:1 saturated:1 tavis:1 electromagnetic:1 over:1 soon:1 course:1 mathematicians:1 paper:1 captions:1 jaynes:2 its:3 group:2 how:2 interesting:1 choose:1 might:1 deformation:15 motivated:1 fourth:1 introduce:2 framework:4 walls:1 equidistant:1 effects:3 they:1 symposium:1 now:2 represents:2 february:1 hamiltonian:1 2f:2 2g:1 mode:5 knight:2 references:1 universit:1 characterized:1 referred:1 subsystem:1 24f:3 financial:1 energy:4 barnett:1 inverted:1 frequency:3 quantum:4 our:4 eq:4 really:1 shown:3 tombesi:1 matrix:1 furthermore:2 since:3 rev:15 denotes:2 fx:1 istituto:1 induced:1 math:1 shows:1 linear:2 fisica:2 possibility:1 standard:2 approaches:1 asj:1 log:2 interaction:3 could:3 transition:1 times:1 unexcited:1 turn:1 place:1 hence:1 neglect:1 first:1 2if:1 already:3 probability:2 nc0:1 nc1:1 number:1 restrict:1 clear:1 another:1 given:3 introduction:2 dipartimento:1 system:8 least:1 their:1 3gf:1 structures:1 infm:1 way:1 moscow:1 exactly:3 part:1 july:1 than:1 coefficients:1 distance:1 18f:1 intensity:3 annihilation:1 amplitude:2 were:2 treated:2 russia:1 klimov:1 biedenharn:1 generalization:1 conjugate:1 seen:1 any:1 relatively:1 strength:1 latter:1 resembling:1 2c12:1 formulas:1 towards:1 scripta:1 shall:2 algebraic:1 cummings:4 revivals:3 acknowledgements:1 extremely:1 32f:1 nonlinearity:8 considered:1 into:1 ko:4 physica:2 typeset:1 proceedings:2 oscillates:1 quantity:1 drastically:1 lebedev:1 phenomenon:3 show:1 rotating:1 solutions:4 wigner:1 written:4 collapses:3 only:7 acknowledge:1 do:1 di:3 dependent:4 de:1 expectation:1 ones:1 lossless:1 evolution:4 arxiv:1 release:1 view:1 enhances:1 physically:1 up:1 depends:1 result:1 enhanced:1 macfarlane:1 radiates:1 interacting:3 marmo:3 tend:1 symmetric:1 state:4 various:1 jth:1 between:1 terms:1 nature:2 initially:3 emitted:1 weak:1 however:1 incommensurate:2 comm:1 russ:1 ket:1 suppressed:2 c22:1 received:1 cos:6 conclusions:1 equal:1 figures:1 regimes:1 whole:1 otherwise:1 sinh:2 point:1 16f:2 corresponds:1 atakishiyev:1 barakat:1 considering:2 described:3 basis:1 due:2 been:6 much:1 treat:1 interest:2 ph:1 fig:4 quantities:1 photon:2 essentially:1 c3:3 c2:7 c1:8 c0:8 spin:1 present:2 case:8 laser:1 pacs:1 beats:2 value:4 excited:3 will:2 while:3 replaced:1 behavior:3 losses:1 coupled:1 phenomenological:1 characteristics:1 thus:2 iv:1 ii:1 vq:8 ic:9 disappear:1 1c2:1 1c1:1 italy:1 considerable:1 generic:1 radiation:9 same:2 quant:1 several:1 sukumar:1 development:1 used:2 eds:1 see:4 singapore:1 numerical:1 sudarshan:1 hand:3 recent:1 lower:1 schr:3 modes:1 nucleare:1 disappears:1 well:2 analysis:2 concrete:1 inhibition:1 solve:1 2gf:3 model:16 drinfeld:1 atomic:7 world:1 field:16 absorption:1 photons:3 character:2 dicke:12 valid:2 lett:6 solvable:2 eigenstate:1 opt:2 read:1 inversion:7 period:3 increases:1 vibrations:4 vacuum:1 press:1 using:1 innocenti:1 9f:1 mod:1 like:1 follows:2 collective:6 camerino:2 specific:1 become:2 reduces:1 methods:1 creation:1 phenomena:1 examples:1 oscillations:5 indirect:1 vol:1 scale:2 lead:2 cavity:6 affects:1 investigations:1 extensively:1 does:2 tends:2 beating:2 pr:1 assembly:1 scientific:1 revtex:1 properties:1 analysing:1 introduces:1 reduced:1 nonvanishing:1 wolf:1 introduced:1 presence:1 h0:2 within:2 obtaining:1 three:1 hermitian:1 rising:1 operator:4 additional:2 few:1 assumed:1 support:1 there:2 specifically:1 start:1 fraction:1 preparata:1 was:1 function:4 form:1 jun:1 but:5 matematica:1 atom:5 eat:3 faster:1 paolo:1 wish:1 ωt:3 us:3 placed:1 limit:2 demonstrate:1 problem:1 called:1 ωf:3 strongly:1 constant:1 af:1 int:1 48f:1 abstract:1 jex:1 influence:1 aq:1 substantially:1 single:2 exist:1 wavelength:1 nazionale:1 physical:3 no:1 nonlinearities:1 when:3 application:1 other:6 coded:1 conclusion:1 picture:1 elements:1 congress:1 models:2 emission:8 important:1 vectors:1 jimbo:1 structure:1 reabsorption:1 implies:1 coupling:5 assume:1 pseudo:1 mancini:1 time:6 4f:2
|
quant-ph9806035.txt |@word represent:1 concept:2 partial:2 consider:11 results:3 four:9 eds:1 scalar:1 grateful:1 go:1 follow:1 referring:1 quasi:2 under:5 case:8 belonging:2 subject:1 choice:1 dzdt:1 husimi:2 condition:6 smithey:1 immediately:1 hamiltonian:1 evaluation:1 t2:3 solution:3 leninsky:1 manifestly:1 markov:1 optics:1 der:1 degeneracy:1 miller:1 perspectives:1 second:1 hopefully:1 canonical:1 aim:1 analogously:2 above:6 new:2 boost:1 consisting:1 satisfy:1 led:2 measurements:1 respectively:2 here:1 beck:1 separation:4 galileo:2 along:8 standard:1 equations:2 galilei:2 obtained:3 thirty:1 institute:2 shift:1 study:3 studied:2 ravndal:1 characterizing:2 hospitality:1 fourier:1 york:1 useful:1 projection:3 merwe:1 marginal:17 ask:1 addressed:1 immediatly:1 total:1 unit:3 additive:1 takes:3 would:1 probabilities:4 finally:1 therefore:2 scope:1 means:1 cahill:1 becomes:3 correspondingly:1 particular:3 cases:1 states:1 account:1 defines:1 vladimir:1 equation:11 work:1 oscillator:13 values:1 following:4 making:2 example:2 performed:1 νv:1 νp:4 give:1 relativistic:12 reconstructed:1 indicates:1 lorentz:12 βz:1 degenerate:1 νi:3 quark:1 axis:2 information:1 end:1 invoke:1 describes:1 get:1 write:2 located:1 opt:2 instead:2 constraints:1 parameter:1 sin:1 isotropic:1 product:1 intended:1 may:3 ζi:4 after:1 derived:1 stefano:1 consequence:1 plane:1 ipµ:1 wave:13 man:3 natural:1 whenever:1 light:1 goal:1 sp:2 lost:1 so:2 fundamental:1 enter:1 definitions:1 order:2 restriction:1 wigner:9 vary:1 course:2 paper:2 japan:1 marginalization:2 its:2 boosts:1 group:3 render:1 interesting:1 relativity:1 coordinates:4 systems:3 deformation:1 non:1 affected:1 combination:1 introduce:2 they:2 rotation:1 now:2 maintaining:1 shadows:1 represents:2 several:1 always:1 applied:1 theory:2 mode:1 found:1 universit:1 2i:1 characterized:1 mean:1 differential:6 financial:1 due:2 hadronic:4 energy:5 hard:1 gaussian:3 related:3 elementary:2 extended:2 measure:1 quantum:13 laboratory:1 beyond:2 eq:11 tombesi:3 matrix:2 space:20 nuovo:1 since:7 rev:11 research:1 particles:2 vector:1 dxdy:1 istituto:1 ref:3 math:2 bz:1 foundation:1 linear:1 sudarshan:2 fisica:2 pub:1 quite:1 imaging:1 thrust:1 βt:1 definition:3 applications:1 could:5 omit:1 m20:3 used:2 gordon:1 hence:3 onto:1 eqs:1 first:4 separable:3 probability:6 xb:6 variables:13 xa:6 number:1 construct:1 given:4 cartesian:1 rewritten:1 glauber:3 introduction:1 dipartimento:1 system:6 least:2 their:3 too:2 relations:1 moscow:1 transverse:1 optical:1 x2:4 x1:3 specify:1 kind:1 nucleare:1 cimento:1 zero:3 tomographic:1 limiting:2 project:1 determined:2 russia:1 result:1 generality:1 spectrum:2 correspond:1 manner:1 raymer:1 conjugate:2 need:1 apparently:1 strength:1 genuine:1 depending:3 studying:1 latter:1 high:1 potential:1 take:2 tp0:1 concern:1 measures:1 simplify:1 drummond:1 representation:5 phase:18 measured:1 xµ:4 considered:2 clear:1 ko:3 face:1 exp:13 velocity:3 physics:1 fact:1 dover:1 lebedev:2 russian:1 attempts:1 spaces:1 solutions:3 interpretation:2 trivial:1 ground:2 q1:1 q2:1 parameters:6 state:6 should:3 only:2 factor:4 x2µ:3 do:3 goes:1 klein:1 di:4 familiar:1 simplest:1 infm:1 cannot:1 combinations:1 during:1 du:1 dp:5 dq:3 normalizable:2 dpv:1 processes:1 approach:1 arxiv:1 acknowledgments:1 contain:1 set:3 reference:2 undergoes:1 frame:5 relative:1 see:1 projections:1 w0:1 techniques:1 satisfying:1 commutation:1 excitations:1 µq:4 written:1 future:1 µi:4 xµa:2 between:3 invariant:2 boundary:1 conditions:1 terms:3 ability:1 nature:1 w00:2 analogues:1 however:1 wv:1 problem:3 thank:1 cos:1 xµ2:1 many:3 conclusions:1 equal:1 connection:1 symplectic:4 expression:1 otherwise:1 among:1 feynmann:2 nonrelativistic:1 simple:2 ca:1 harmonic:5 dimensional:6 exploit:1 polynomial:1 moreover:1 pv:12 transformations:3 pu:12 pz:2 three:2 been:2 pb:3 much:1 interest:1 basic:1 marginals:3 ph:1 define:2 ariano:1 direction:5 arises:1 quantities:1 subspace:2 covariance:2 kalnins:1 θp:1 θq:1 present:3 p2:2 p0:2 p1:2 pacs:1 straight:1 value:1 excited:1 will:5 while:2 procedure:1 identical:1 orientation:1 vogel:1 almost:1 characteristics:1 thus:4 them:2 nazionale:1 vt:3 cone:1 different:5 italy:1 generic:1 lett:3 same:2 poincar:1 quant:1 units:1 finite:2 higher:1 literature:1 singapore:1 boosted:2 upon:1 v2:1 moving:3 kim:4 angle:1 invariance:1 pµ:2 com:1 well:3 without:2 components:2 coordinate:7 position:1 model:6 parametrically:1 ψ0n:2 noz:3 perugia:1 obtain:3 rest:3 transforms:9 questions:1 integer:1 momenta:1 renewed:1 infinitely:2 except:1 passive:1 internal:3 transformed:2 treatment:1 easy:1 hermite:2 transformation:8 momentum:8 build:1 real:2 yukawa:1 eigenvalue:2 measurement:1 possible:4 corresponds:1 increases:1 know:1 using:3 bertrand:2 like:2 particle:2 prospekt:1 exploiting:1 camerino:2 specific:1 sezione:1 follows:1 become:1 works:1 reduced:1 specifies:1 reidel:1 classical:4 some:1 oscillations:1 provided:1 describing:2 dimensions:1 lead:1 avoid:1 quarks:4 mesons:1 connecting:1 proc:1 scientific:1 rescale:1 equivalent:1 agreement:1 properties:11 hadron:8 stage:1 integers:1 about:1 world:1 most:2 discussed:1 dependence:1 essential:1 covariant:7 continous:1 efforts:1 introduced:2 soc:1 into:2 integral:2 bound:1 ηi:3 combine:1 lies:1 references:1 wβ:4 operator:1 mere:1 van:1 deal:1 assumed:1 support:2 there:5 question:2 transform:2 u2:1 doing:1 pa:3 way:2 was:1 naturally:2 function:16 form:6 jun:1 but:4 hk:1 repeated:1 hn:4 matematica:1 hb:3 line:3 ha:3 considerable:1 he:1 paolo:1 instructive:1 supp:1 uv:1 up:1 us:5 dordrecht:1 projecting:1 dv:1 distribution:9 semiclass:2 called:2 mechanics:5 defined:2 certain:1 abstract:1 describe:1 frames:3 general:2 exist:1 formulation:1 tomography:2 moves:2 distributions:10 physical:3 functions:2 no:1 when:2 reality:1 field:1 other:4 conclusion:1 picture:3 primed:2 polynomials:1 faridani:1 variable:4 risken:1 needed:1 structure:1 independently:1 practically:4 factors:1 mancini:3 mass:4 time:7 observables:2 having:2 once:1
|
quant-ph9806036.txt |@word concept:1 allowed:1 results:5 four:1 mild:1 fortiori:2 localized:16 tr:3 yngvason:1 james:1 gromes:1 finally:1 under:1 ingredient:2 applied:3 already:1 seemingly:1 wave:3 putting:1 stays:5 continued:3 clouds:1 hamiltonian:1 notes:1 t2:1 solution:1 large:1 vector:1 small:2 noted:1 gerlach:1 upper:1 smaller:1 imply:2 pass:1 even:1 will:7 nonlinear:1 appear:1 clock:1 section:3 localization:15 current:2 version:1 above:3 replaced:1 slabs:1 edited:2 full:1 never:1 component:1 equals:1 here:2 atoms:2 tachyons:1 possibility:1 alone:2 causality:16 standard:1 equations:1 remark:1 technical:1 spontaneous:1 larger:2 suggests:1 amount:1 makes:2 formulated:1 highly:1 apply:2 causal:2 ψz:1 use:1 hegerfeldt:7 proceed:2 would:12 prove:2 remains:2 positive:7 contains:2 negative:1 ψt:11 hilbert:2 vol:1 a52:1 therefore:4 more:8 separated:1 composite:1 becomes:2 operators:3 apparent:1 emission:1 berlin:1 everywhere:1 particular:3 known:2 hold:3 must:4 states:10 springer:2 deformed:1 originally:1 values:5 ρt:2 following:1 making:1 root:1 example:2 proof:2 relativistic:7 arise:1 high:1 application:1 sense:3 conversely:1 evidently:1 axis:1 preferably:1 requirements:1 distinguishable:1 discussion:2 holds:3 write:1 how:1 nontrivial:1 pure:1 instead:1 absolute:3 prohibits:1 superluminal:5 may:4 after:1 treatments:1 vieweg:1 hence:3 plane:2 inst:1 physik:1 d10:1 ψi0:6 advocated:1 light:2 ones:1 so:2 d22:1 order:1 wigner:2 indeed:3 over:6 move:1 n0c:3 paper:2 through:2 mentioned:1 existence:1 satisfies:2 still:1 its:4 envisage:1 before:2 regions:1 decay:1 ln:1 matrices:1 temporal:1 relativity:2 82a:1 writing:1 detected:1 permanent:2 systems:4 unbounded:1 redhead:1 main:2 might:5 variables:1 framework:1 tails:13 they:1 identically:1 now:8 day:1 easily:2 finite:13 dirac:5 always:1 drop:2 sufficiently:2 inequality:1 fφ:17 each:1 found:2 universit:1 characterized:1 domain:2 square:1 evolve:1 ed:1 energy:6 gaussian:1 used:5 expect:1 measure:2 quantum:9 our:2 happen:1 eq:6 special:2 out:2 shown:5 space:5 nuovo:1 since:8 rev:9 particles:12 contained:1 lecture:1 cause:1 shows:1 theory:12 reformulated:1 interactions:1 given:5 free:4 quite:2 causally:2 york:1 put:1 ruijsenaars:2 care:1 skagerstam:1 could:12 times:7 motion:2 length:1 isn:1 consequence:4 passante:1 onto:1 support:2 ihz:3 initial:2 probability:15 thereafter:2 disregarded:1 iht:2 theoretische:1 intuitively:1 fast:2 directly:1 precisely:1 open:3 little:1 necessarily:1 hyperbolic:1 introduction:1 eqs:1 behaves:1 system:11 relations:1 needed:3 assumption:1 upshot:1 speaking:1 adopts:1 holden:1 petzold:1 fraction:1 reversed:1 continuous:3 immediate:3 released:1 part:3 somewhat:1 schlieder:1 translation:4 than:1 distance:2 showed:1 approximations:1 zero:3 were:6 exhibit:1 san:1 electrodynamics:1 half:2 mind:1 argument:2 generalization:1 pedestrian:1 say:1 need:1 null:1 any:4 bohm:1 latter:2 note:1 potential:1 simultaneity:1 tool:1 accuracy:1 spectral:1 begin:2 towards:1 unless:2 algebraic:3 connected:1 nothing:1 analytically:2 class:1 localizable:1 χv:1 subtracted:1 considered:2 calculated:1 later:2 flow:1 principle:1 exp:4 levinson:1 velocity:2 physics:1 notion:5 fact:2 phenomenon:2 show:3 violation:1 fleming:1 spaces:1 solutions:1 earth:1 find:3 ground:2 based:1 irreversible:1 should:1 analytic:5 only:2 experiment:1 schweber:1 local:3 continuity:2 do:1 means:2 expectation:5 synchronization:2 new:1 dt:1 neither:1 densities:1 conditions:1 arxiv:1 wightman:1 yield:1 d16:1 fixed:1 require:1 set:4 dobrev:1 exists:1 argued:2 individual:1 result:5 theoretic:2 concern:1 satisfying:1 commutation:1 doebner:2 ways:1 nuclear:1 positivity:8 boundaries:1 state:7 closed:1 between:2 αi:3 invariant:1 boundary:2 buchholz:1 approach:1 counterexample:1 initially:9 complement:2 weak:1 however:9 suggested:1 observable:1 essentially:1 last:1 region:16 attributed:1 propagation:4 connection:3 became:1 und:1 poincar:1 context:2 argue:2 arbitrarily:2 strongly:1 fields:2 conclude:3 simple:2 seems:2 asymptotically:2 corresponds:1 werner:1 simply:2 likes:1 proved:2 speak:1 selfadjoint:3 strong:2 second:2 due:3 been:3 int:2 pa:9 ph:1 ann:2 define:2 nattermann:1 ottingen:2 persist:1 photon:1 spectrum:1 observe:1 external:2 denote:1 spin:1 present:4 case:2 noncommuting:1 indefinitely:1 appearance:1 value:1 employ:1 suppose:1 behavior:2 rigged:1 gerhard:1 iy:2 almost:3 ir:3 thus:9 ii:3 ih:1 im:5 il:1 vanish:2 containing:1 develop:3 projector:2 author:4 make:2 same:3 clearly:1 complex:1 quant:1 arguments:1 mixtures:1 several:1 events:1 conflict:3 difficult:1 development:1 independent:2 investigated:1 infinity:2 singapore:1 lie:1 effect:1 hand:1 v0:21 purpose:2 braunschweig:1 potentials:1 infinite:12 invariance:3 felder:1 francisco:1 recent:1 lower:1 off:2 center:1 well:3 thought:1 academic:1 components:1 position:6 model:1 usual:1 world:1 just:1 being:1 generally:1 newton:2 obtain:2 detail:1 press:1 clocks:1 using:1 alternative:6 speed:6 previous:1 lebesgue:1 density:2 photons:2 nonrelativistic:2 had:6 except:2 signals:2 spread:2 lett:4 theorem:12 redheffer:1 excited:2 real:3 aspects:1 around:1 eigenvalue:1 possible:1 cf:1 early:1 possibly:1 overlooks:1 vacuum:2 confined:1 immediately:7 milonni:1 necessary:1 like:1 particle:27 follows:2 signal:2 velocities:1 cannot:3 either:4 arbitrary:3 conclusion:1 mathematical:2 satisfactory:1 often:2 sequence:1 some:5 understood:2 sure:1 garnett:1 nonzero:3 provided:1 dense:4 lead:3 avoid:2 recorded:1 moon:1 does:2 decomposition:1 tends:1 schwarz:1 semigroups:1 noise:1 scientific:1 bacry:1 restrictive:1 wilde:1 inherent:1 standpoint:1 approximating:1 properties:1 takes:2 about:1 carried:2 extension:2 discussed:3 recognized:2 ensure:1 introduced:1 therein:1 previously:1 reflexion:1 spreading:5 integral:1 bound:1 contrasts:1 references:2 einstein:4 operator:11 existed:1 detectors:1 institut:1 anticommutation:1 assumed:2 strictly:11 there:8 question:2 equation:5 way:3 exceptional:1 was:17 function:6 irreversibility:1 jun:1 but:3 volume:1 atom:3 highest:1 true:2 he:1 made:1 whether:1 characteristic:1 inside:2 us:3 ur:1 below:1 fermi:7 fluctuations:2 problem:4 similar:1 called:1 obtains:1 mechanics:2 sometimes:1 ae:1 defined:2 certain:1 abstract:3 general:3 proves:1 exist:4 perez:1 fearn:1 check:1 defines:1 again:1 functions:3 analyticity:4 cim:1 no:5 dressed:1 when:1 vanishes:4 virtual:2 field:8 other:2 eiht:1 theor:2 revision:1 repeat:1 urr:1 excitation:6 models:1 problems:1 a1:6 develops:2 bounded:11 describing:1 implies:3 assume:2 interval:2 holes:2 equivalently:1 mass:1 time:4 n0:7 original:1 thaller:3
|
quant-ph9806037.txt |@word monte:1 partial:1 consider:8 rev:22 results:2 four:1 expressions:2 faster:2 gk:2 causes:2 ρss:11 inverse:1 tr:7 groundstate:2 finally:1 according:2 th:1 under:1 decomposition:2 analogous:2 must:2 norm:2 applied:3 very:4 frequencies:2 account:1 wave:3 experimentally:1 difference:3 matrices:1 condition:1 gg:2 ρs1:2 level:25 tra:1 positions:1 notes:1 t2:13 t1:21 large:7 vector:1 small:29 trr:1 optics:3 upper:2 smaller:3 force:1 literature:1 approximation:2 rate:6 evaluated:1 further:2 steadystate:2 carlo:1 even:1 will:3 ˆr:4 sub:3 advantageous:1 section:5 kus:1 uniform:5 waiting:3 goes:3 new:5 3a:1 consisting:1 coefficient:2 edited:1 ρaa:2 exchange:2 respectively:3 here:4 understanding:2 plenio:1 cos2:1 groups:1 alone:1 strong:6 equations:10 eik:1 change:4 obtained:5 remark:1 drops:1 antisymmetric:2 dividing:1 shift:3 larger:10 allows:1 approaches:4 prior:2 repel:1 walther:1 identity:1 resonance:5 interact:1 studies:1 involves:1 plotted:1 yamada:1 useful:1 ratios:5 suddenly:2 proportion:6 castin:1 explained:2 coinciding:2 unitary:1 decrease:1 apply:1 tools:1 use:1 hegerfeldt:4 figure:4 commun:2 probabilities:1 positive:1 contains:2 next:6 few:1 depicted:1 going:1 call:2 therefore:7 taken:1 type:1 until:4 minor:1 more:5 populations:20 becomes:5 operators:1 inherited:1 emission:62 berlin:2 appendix:9 normalized:11 particular:3 known:9 cases:2 iii:2 r1:1 keeping:1 quantized:2 recall:1 work:1 modified:1 ρr:3 obvious:1 ficek:4 following:1 making:1 arrive:1 weaker:1 indicated:3 give:3 calculation:2 neglected:1 states:32 numbers:1 degenerate:1 sense:1 counting:2 verlag:1 respective:4 rather:2 s2:7 discussion:1 holds:1 recovers:1 far:2 lam:1 ens:1 adapted:1 pure:6 instead:2 ensemble:7 simplicity:3 product:1 description:1 may:1 after:33 derived:3 needs:1 ρee:1 physik:1 parallel:2 constants:10 diagonal:7 short:3 outline:1 sets:2 ss:22 counter:1 explicit:1 cascade:1 si:6 so:10 correlation:8 order:8 wigner:1 over:7 move:3 vary:1 cohen:1 paper:3 through:2 wolf:1 still:2 its:9 tendency:1 before:6 rapidly:1 decay:16 decreases:1 better:1 wineland:1 detected:4 complex:1 itano:1 systems:9 rabi:3 main:2 wellknown:1 bunching:26 s1:7 non:8 affected:1 ρs2:2 mølmer:1 fig:11 investigated:2 band:1 walls:1 effects:3 they:1 half:2 now:6 discuss:2 easily:3 instances:1 james:1 university:1 hamiltonian:7 radiance:1 hermitian:2 traj:9 sufficiently:2 magnitude:10 2a:4 each:7 found:2 universit:3 quarter:3 decreasing:3 2i:1 el:1 ei:2 directly:3 populated:1 ee:3 energy:1 frequency:6 static:1 obtains:6 changed:1 quantum:8 wavelength:3 operation:2 eq:19 event:1 out:4 travels:1 shown:1 mediates:1 matrix:27 driving:14 space:7 jump:2 since:16 squared:1 denotes:1 increase:1 re:29 denoted:2 lecture:1 get:1 ref:6 ri:3 theory:2 written:3 little:1 quite:4 reason:3 perturbation:2 put:1 e0:2 pairs:2 interaction:16 derivation:2 r2:1 iss:15 could:2 transition:8 times:4 turn:1 hence:11 saxena:1 onto:2 eqs:5 first:10 rand:1 there:8 probability:22 number:6 system:32 intuitively:2 2a2:2 another:2 knight:2 carry:1 slower:1 precisely:1 open:1 size:1 given:13 necessarily:1 checked:1 similarly:2 introduction:1 antibunching:16 achieved:1 theoretische:1 approximately:1 1a:2 their:7 intermediate:5 master:1 observations:2 dt2:6 dt1:6 gives:6 explanation:2 acquire:1 part:2 too:1 kept:3 july:1 than:18 population:32 l43:1 distance:16 require:1 transferred:3 symposium:1 determined:2 treated:3 result:1 tracts:1 sees:1 unchanged:1 modern:1 argument:4 spelled:1 say:1 need:1 seen:5 clearly:1 viewed:1 angle:1 zero:2 efficient:1 lim:4 latter:8 responsible:1 downwards:1 mechanism:4 oliveira:1 k0:7 absorbed:2 take:4 finding:3 negligible:2 detector:3 tannoudji:1 play:1 electric:1 trace:5 normal:1 measures:1 twolevel:1 involving:1 germany:1 position:2 phase:3 why:2 appear:2 considered:1 clear:1 steady:21 shortly:1 kl:1 proceedings:1 optical:5 principle:3 exp:1 physics:2 away:2 fact:3 phenomenon:2 detection:3 appearing:1 rotating:2 relation:2 ground:22 feng:1 ha:1 based:2 ensembles:2 parameters:2 distributed:1 state:67 should:1 dalibard:2 only:4 explicitly:3 factor:4 emitting:2 he:1 pointed:1 do:1 above:3 means:12 dependent:4 aim:1 ones:1 international:1 combinations:2 during:1 dt:2 carmichael:2 processes:1 evident:1 dissertation:2 arxiv:1 tuned:2 europhys:1 fixed:6 wodkiewicz:1 ik0:2 observes:1 acquired:1 relative:6 depends:2 individual:2 changes:1 w1:4 sooner:1 closer:1 ergodicity:1 hilbert:1 interacting:6 doebner:1 review:3 dipole:31 tend:1 symmetric:2 enough:2 hendriks:1 between:7 ui:5 approach:7 checks:1 multiplied:2 terms:2 emitted:4 weak:6 however:1 efficiency:2 comm:1 twophoton:1 distinguish:1 atoms:42 come:1 ikl:1 both:8 c21:8 last:1 brown:1 solely:1 conclusions:1 equal:3 attributed:2 agree:1 connection:1 exceeds:1 disappears:2 among:1 point:1 simple:5 cf:1 dimensional:1 throughout:1 factors:1 configuration:1 described:2 second:5 basis:6 addition:1 trajectory:5 narducci:3 due:5 been:7 detuning:2 much:9 combined:3 rates:4 ph:1 ak:1 define:2 sanders:1 corresponding:6 coherence:1 photon:48 observe:1 understand:1 c12:10 denote:5 irrelevant:1 former:2 those:6 case:12 p0:3 traced:1 laser:14 pacs:1 ǫk:1 appearance:2 kimble:1 value:1 employ:2 while:13 behavior:1 situation:1 gerhard:1 procedure:1 opt:8 vectors:1 brewer:2 vol:1 ip:5 refs:4 formulation:1 thus:8 iv:1 ii:5 im:11 ie:1 different:2 agarwal:6 lengthy:1 develop:1 d12:4 radiation:4 same:8 any:1 noninteracting:2 quant:1 arguments:1 none:1 grows:1 higher:5 development:4 independent:7 used:2 see:8 singapore:1 trajectories:4 effect:1 hand:1 driven:7 average:2 moment:1 levels:5 purpose:1 kim:1 changing:1 ωk:2 normalization:6 recent:1 lower:2 off:2 expression:3 well:4 analysis:2 without:3 components:1 convenient:2 quantitative:1 usual:1 distances:13 world:1 just:2 less:3 moments:6 generally:1 obtain:1 underlying:2 atomic:32 immediately:6 facts:1 previous:3 letting:1 doctoral:2 density:32 irradiated:1 photons:6 conclude:1 had:1 dicke:9 lett:6 ω0t:1 diagonalization:1 role:1 mod:3 excited:20 real:1 acta:2 increased:5 read:2 increases:2 makes:1 press:1 using:3 coincide:1 apart:1 necessary:1 follows:5 qualitative:1 discarded:2 detections:1 yields:2 either:1 become:2 right:15 classical:2 conditional:4 some:3 draw:1 understood:3 gilmore:1 extended:1 pronounced:1 proceeding:1 broadband:1 broad:1 though:1 does:8 connecting:2 l3:1 inserting:1 denominator:1 eiϕ:1 scientific:1 detuned:1 elucidate:1 equivalent:1 disappeared:2 step:4 although:3 super:1 properties:1 projector:2 about:3 carried:1 anything:1 numerator:2 dependence:1 plus:1 beige:2 connected:1 slightly:3 bloch:10 considerations:1 cambridge:1 h2:1 into:1 numerically:1 three:2 down:5 appropriate:1 references:1 scherer:1 determine:1 einstein:2 operator:5 statistics:1 institut:1 classically:1 springer:3 initial:3 start:1 describes:1 mandel:2 way:3 was:7 damping:2 function:6 considerably:1 2d12:1 complete:1 form:3 forming:1 jun:1 but:3 hi:3 hl:4 atom:12 line:2 highest:2 longer:3 reset:18 made:2 intuitive:1 instructive:1 whether:2 cij:2 us:2 ur:1 ωi:3 below:2 decays:1 limit:1 emissions:4 pumped:1 distribution:5 semiclass:1 similar:12 called:1 aa:1 constant:3 defined:2 stronger:1 abstract:1 contribute:4 moved:2 general:9 single:9 ar:1 ensuing:2 simulations:2 ottingen:4 distributions:1 check:1 again:1 functions:5 compared:5 no:7 dressed:2 when:11 power:1 field:9 other:11 compares:1 picture:2 briefly:2 elements:2 preceding:2 berman:2 uniformly:1 develops:1 a2:10 included:3 coupling:2 fluorescence:5 starting:1 interval:1 time:23 retardation:3 requires:1 once:1
|
quant-ph9806038.txt |@word localized:11 whose:1 calculate:3 extrapolate:1 γt:2 γn:1 under:8 rise:2 distort:1 figs:1 affect:2 fractal:1 ref:3 solution:13 convenience:1 vector:11 plete:1 markov:5 deutsch:2 consistent:1 pulse:1 approximation:14 likely:1 street:1 j22:1 j21:24 qualitatively:1 bandgaps:1 haake:2 even:4 interatomic:1 trapping:2 κ2p:1 selected:1 above:7 new:9 net:2 consisting:1 agreement:4 behavior:6 equals:1 here:9 atoms:56 active:2 κp:1 interpret:1 obtained:9 study:2 completely:1 fourier:2 changes:1 elaborated:1 replace:3 counts:1 total:3 bra:1 plot:3 would:5 jozsa:1 negative:4 noting:1 therefore:7 survive:1 type:2 must:5 springer:1 mc:1 permits:1 work:1 straddle:1 temperatures:1 concepts:1 vlasov:1 root:2 example:2 wang:1 give:3 relativistic:1 preserving:1 organized:2 involve:1 indicates:1 feasible:1 provide:4 department:1 how:2 ens:14 w21:1 ordinary:1 oscillatory:2 description:6 modulation:1 after:2 memorial:1 meaningful:1 excited:19 effective:15 green:8 ultimate:1 correlation:7 acknowledges:1 order:20 over:17 satisfied:3 experimentally:1 japan:1 satisfies:2 linewidth:3 before:2 directional:1 exhibits:10 distinguishing:1 fig:30 persist:3 overcome:1 affected:1 ergy:1 band:160 effects:14 they:2 singularity:5 represents:2 each:10 mean:21 schemes:1 series:2 driving:1 crucial:2 george:1 re:9 encourage:1 goy:1 numerical:2 linear:6 associate:2 little:1 free:38 standard:1 gλ2:1 created:1 corrections:1 condensate:1 speeds:1 industrial:1 features:2 rydberg:1 clarity:1 appl:3 glauber:1 master:1 observations:1 john:14 simulates:2 centered:4 tool:1 toronto:2 uning:1 approximations:2 rate:9 kth:1 iωc:4 perturbative:1 spectrum:10 manner:3 polaritonic:1 seen:2 strength:1 latter:1 responsible:2 causing:2 absorbed:1 mondragon:1 twolevel:1 simplify:1 involving:1 phase:33 calculated:5 sum:1 dot:1 dover:2 random:23 infrared:2 implying:1 solutions:1 substituting:4 analogue:2 d2:1 proposed:1 oca:1 ekert:1 rich:1 constant:7 rice:2 do:2 dk:2 despite:2 dt:35 dr:1 dq:1 fields:1 bay:2 nγ:1 reference:1 sensitivity:1 pushed:1 depends:2 result:13 discussions:1 techniques:1 yamamoto:1 away:7 artificial:1 simplest:2 approach:7 terms:5 plicitly:1 extend:3 nature:13 overestimates:1 weak:1 however:12 extent:1 bose:1 cos:6 raimond:1 distinction:2 contribution:2 expense:1 com:1 royal:1 2nd:2 factorize:1 applicability:1 broadening:4 basis:1 simplification:1 radiative:2 three:6 been:9 quickly:3 trigger:1 interest:3 repelled:2 deeper:2 quantities:2 coherent:3 applied:4 transformation:2 near:68 property:2 elaborate:1 procedure:1 brewer:1 phenomenological:2 iv:7 ii:4 im:5 ia:2 agarwal:1 containing:2 weinfurter:1 quang:5 suggest:2 make:2 complex:2 quant:1 louisell:1 dimensionless:1 showing:1 spectively:1 i1:7 i2:4 possible:2 centred:1 academic:4 materials:4 simulated:4 paradigm:1 possesses:2 yeh:1 just:2 rotated:1 photonic:53 identify:1 transforms:3 rotates:1 scattering:3 previous:3 adding:2 enters:1 character:2 5n:1 evidenced:1 iπ:6 opt:1 insensitive:2 bands:1 dφp:2 highly:3 performing:1 specific:4 arbitrary:7 cooled:1 scatterers:1 right:1 born:3 indirect:1 electromagnetic:20 microwave:1 unstable:1 predicting:1 illustration:1 substitution:1 super:1 properties:12 takes:2 o:9 slightly:2 considerations:1 raised:1 markovian:16 presence:1 gradshteyn:1 bound:3 lies:4 raises:1 reducing:1 methods:6 support:1 initial:42 transform:8 width:7 accordingly:1 fraction:7 wax:1 was:7 medium:1 forn:1 form:21 differences:1 j12:65 j11:1 absent:1 b5:2 prevents:1 inside:3 devices:1 crystal:6 stages:1 evidence:1 dκ:4 simulations:8 distributions:4 physical:2 radically:1 dotted:5 no:6 na:1 whereas:3 when:5 vanishes:3 schwinger:2 role:3 papers:1 test:1 picture:5 savage:1 models:4 dies:1 uniformly:3 variable:1 longer:2 dω:1 dφ:2 salt:1 dτ:5 packets:1 governed:3 resonances:1 observables:1 n2:2 lett:20 varying:4 focus:1 leads:4 computation:2 inverse:3 zone:1 technique:1 finally:1 analogous:1 division:1 broadly:1 zhang:1 frequencies:10 choice:6 exact:4 level:13 labels:1 solved:2 upper:5 slower:1 oscillation:1 dealing:1 measurable:1 sign:1 spectral:5 resurgence:1 uniform:2 reminiscent:1 unrestricted:1 satisfy:1 realizations:6 understanding:1 change:5 shift:2 vectors:2 eberly:1 resonance:5 studies:3 plotted:2 useful:2 convolution:1 lending:1 positive:3 predictions:1 hilbert:2 memory:12 theoretical:2 today:1 validity:1 appendix:8 eλ:2 emitting:2 cases:4 k02:2 valued:1 sphere:2 oscillator:5 modified:2 renders:1 hope:1 following:1 making:4 arrive:1 numbers:2 figure:20 predict:1 sample:4 council:1 conversely:1 occur:4 verlag:1 azquez:1 discussion:3 write:10 parameter:4 product:1 may:41 applications:2 produce:1 natural:3 dynamical:2 explicit:1 st:1 si:1 so:2 representation:1 sumner:1 pulled:1 haus:1 typical:1 wavelengths:1 acts:2 schwartz:1 indeed:1 soc:1 years:1 statistical:4 differs:1 cold:1 still:1 aλ:25 solitary:1 interesting:3 jij:2 vicinity:9 decreases:1 forms:1 non:29 mølmer:2 evolution:27 introduce:2 polder:1 identically:1 discuss:2 nor:2 possess:3 inversion:32 equality:2 possibilities:1 realistic:3 domain:1 en:1 ei:2 significantly:5 ek:1 ed:2 gaussian:6 gaps:2 ex:1 wavelength:1 approximated:1 es:1 canada:2 emerges:1 shown:23 space:50 furthermore:4 interference:4 increase:1 collisions:1 bragg:6 correct:5 shows:3 theory:6 state:90 pumping:4 possibility:4 statistics:13 derivation:1 transition:11 motion:5 turn:2 place:1 neglect:3 first:9 sanchez:1 symmetry:2 striking:1 opez:1 4re:2 variables:2 approximate:1 simplified:2 directly:3 comprises:1 angular:4 size:1 given:11 1t:9 barabasi:1 structured:1 realization:3 structures:1 speaking:2 gives:13 ryzhik:1 transverse:1 x2:3 x3:1 x1:3 representing:1 than:14 population:26 third:2 require:2 computes:1 were:3 biedenharn:1 generalization:1 crossover:6 allen:1 recover:1 any:2 kolobov:1 computationally:4 note:8 sciences:1 potential:2 begin:1 opposite:1 multiply:1 considered:1 average:13 later:2 steady:41 drive:1 typically:1 drastically:1 show:11 atom:38 threshold:4 ground:3 aπ:1 ratio:1 ith:1 true:2 pump:1 considerable:2 analytic:5 only:14 explicitly:1 developed:1 coherences:1 expectation:10 expects:1 unimportant:1 cannot:3 nearly:3 symmetrically:1 adiabatically:1 regarding:1 yield:2 paper:5 pang:1 prokofiev:1 kernel:6 j3:40 relative:2 corre:1 stanley:1 fails:2 satisfying:2 subsequent:4 outside:9 between:15 bianco:1 fluctuations:55 suppressed:1 x2j:3 many:6 region:3 propagation:3 expression:2 soukoulis:1 period:1 exploit:1 scully:1 cancel:1 moreover:1 considering:2 peng:1 unusual:2 locally:1 oder:1 markedly:1 ωmax:2 superradiance:22 direction:4 enable:1 formed:1 photon:28 external:8 wavevectors:1 those:3 case:11 processes:3 variances:1 single:7 bogomolov:1 squeezed:1 investigating:1 polymer:1 coupled:3 characteristics:1 yj:1 technology:1 different:6 same:6 shifts:7 verifies:1 regime:12 breakdown:1 extended:1 driven:4 edges:4 changing:1 recapture:1 modes:9 roughly:1 without:1 solve:3 components:1 model:43 dimension:1 transmitting:1 rest:2 relevant:5 zoller:1 photons:6 conclude:1 dicke:3 wavevector:10 treatment:2 δpq:1 momentum:2 real:4 moy:1 early:12 dipolar:1 vacuum:32 using:13 fractionally:1 particle:1 collective:48 integrals:2 output:1 inter:2 stationary:2 reduced:2 provided:1 dimensions:1 confirm:1 cavity:7 langevin:3 provides:1 fabre:1 propagating:1 process:2 power:4 retains:1 equivalent:2 eiπ:3 refers:1 comparison:1 central:1 smear:1 discussed:3 meaning:3 sensitively:1 recaptured:1 eval:1 numerically:2 dissipation:1 gomes:1 references:1 determine:3 operator:18 area:1 assumed:1 strictly:2 there:8 stark:7 dispersion:23 low:12 complete:5 jun:1 illuminates:1 promote:1 dissipative:2 proposal:1 applying:2 assume:3 ωk:19 ωl:5 ωn:3 organize:1 ωc:43 agree:1 regimes:2 strongly:3 cirac:1 ad:1 certain:1 ak:2 aj:1 moved:1 deep:1 general:3 aq:1 controlled:4 moves:2 again:7 extending:1 storage:1 slusher:1 acknowledgments:1 valid:4 spatial:2 deviation:1 polar:1 separate:1 time:45 drift:1 hwa:1 a1:4 commutator:2 a3:3 a2:2 a5:2 a4:2 a7:1 a6:1 included:4 a8:3 d21:10 curve:1 mimic:1 mass:17 ultrafast:1 starting:7 externally:1 consider:7 forbidden:2 splitting:6 cooperative:2 expressions:1 denotes:5 causes:1 reynaud:1 fellowship:1 ts:4 tp:3 dressing:2 stochastic:12 lations:1 very:6 fabricated:2 dispersions:1 difference:1 condition:9 eβ1:2 treating:1 hamiltonian:2 t2:1 applicable:3 t0:34 large:13 pbg:29 microlaser:1 small:11 grateful:1 zero:15 design:1 further:6 what:2 nonlinear:2 sub:2 brackets:1 section:22 issues:2 fractional:8 method:10 contrast:4 edited:3 full:11 modify:1 operating:3 ansatz:2 directions:1 strong:3 equations:25 colored:5 allows:2 experience:2 prior:2 published:1 action:1 via:2 requiring:1 vii:1 conventional:8 proceed:2 lasing:6 contains:1 comparing:1 taken:4 more:23 initiated:1 operators:19 infinitesimal:6 emission:56 particular:7 uation:1 equation:36 remain:1 spontaneous:14 pushes:1 neglected:3 states:21 collision:2 attain:1 information:1 goal:1 rather:2 breaking:1 ensemble:22 simplicity:1 fx:1 wiley:1 derived:2 sprik:1 waves:1 2γc:1 short:4 negligibly:1 quoted:1 spectra:5 fundamental:1 reservoir:20 essence:2 held:1 already:1 through:6 lasers:1 y2:1 excitations:1 its:10 1a7:1 rapidly:4 kardar:1 energies:1 solving:1 scribed:1 boson:1 late:1 absence:8 microscopic:1 systems:10 good:4 propose:1 framework:1 walls:1 oxford:1 yu:1 finite:2 2p:1 fully:7 presented:1 2c:1 found:8 2n:1 referred:2 generation:3 energy:8 reduce:2 expect:4 quantum:55 dominates:1 since:11 research:2 induced:2 evaluation:2 occurs:7 localization:17 difficulty:1 deπ:1 asi:1 generate:1 pairs:1 consequence:1 exhibited:1 integrand:1 probability:7 prevent:1 relate:1 number:9 nacl:1 done:1 tf0:2 equating:1 differ:2 perturbation:2 introduction:1 leading:1 sargent:2 lagendijk:1 passed:1 superscript:1 scheme:2 loudon:1 shifted:1 calculations:3 relationship:1 optical:10 schr:1 diffusion:1 king:1 determines:1 double:3 annihilation:1 determined:4 treated:4 defect:1 randomly:1 conjugate:1 confirms:1 lie:1 self:6 onset:2 k0:29 build:3 analogy:1 finding:4 play:1 towards:1 electric:2 most:1 experiences:1 significant:3 extremely:1 kk:1 clear:3 part:2 exp:1 physics:4 lying:2 particularly:1 relation:16 carefully:1 find:10 occupation:2 impact:2 distributed:6 being:6 integrable:1 peaked:1 notation:1 spurious:2 valuable:2 during:2 exhibiting:2 continuum:4 m5s:1 arxiv:1 factorization:5 set:6 see:10 bare:2 mechanically:1 currently:1 dipole:7 fano:1 various:8 conditions:5 pictured:2 available:1 recently:4 initially:11 both:18 last:1 sensitive:4 context:5 microcavity:1 experimental:3 point:7 simple:4 asymptotically:1 corresponds:2 ultrashort:1 2i1:1 dimensional:8 simply:1 throughout:4 kernels:1 pq:3 described:6 due:15 detuning:21 describes:2 contained:1 anisotropic:23 ωloc:3 ph:1 walter:1 addison:1 generating:2 gap:43 understand:1 imhof:1 exponential:4 pacs:1 solid:12 expanded:3 evaluated:3 while:7 evaluating:1 error:2 credence:1 vol:1 encountered:1 vos:1 busch:1 vanish:2 emphasize:1 products:6 higher:1 development:1 used:6 lambropoulos:2 moment:3 levels:2 recent:2 lower:3 analysis:7 edge:155 organization:4 atomic:151 spatially:1 kluwer:1 conclusions:1 source:2 theorem:1 input:2 remaining:1 evaluate:4 couple:1 integrations:1 meseguer:1 emergence:1 semi:14 follows:3 separately:1 yields:3 reduces:1 mathematical:2 often:2 creation:1 some:2 back:2 b4:1 understood:1 b6:2 experienced:1 b1:5 b2:13 b3:1 oscillations:9 giacobino:1 pronounced:2 scale:6 describing:1 affects:2 measurements:2 integration:6 per:3 behave:1 eliminate:1 proc:1 bg:4 detuned:3 bi:7 step:4 intense:1 constraint:1 exaggerated:1 simulation:3 range:8 consequently:1 bloch:7 cutoff:2 computational:1 into:22 within:9 integral:6 appropriate:1 proportional:5 ontario:2 measured:8 question:2 lond:1 long:10 bosons:1 sections:4 elsewhere:2 delta:1 line:27 collapses:1 raising:1 characteristic:2 up:3 us:3 paired:1 autocorrelation:8 ud:2 similar:6 laplace:11 associated:1 defined:8 likewise:1 influence:11 engineering:1 associates:2 dashed:15 invalid:1 priori:2 hove:1 elements:1 excitation:11 gross:2 problems:3 medina:1 prepared:6 generated:3 suppression:3 structure:1 implies:2 algorithm:2 required:4 phonon:2 presenting:1 broad:1 far:1 meystre:1 gr:1 bandgap:4 results:11 ga:7 stochastically:1 gi:7 leung:1 stable:1 include:4 dramatically:1 probe:2 2re:1 engineered:1 wave:1 electron:3 resonant:26 entire:2 incoherent:2 integro:1 optics:1 dynamics:21 plays:1 lehman:1 giving:4 slight:1 expressed:4 3t:2 experiment:2 values:17 midgap:1 chose:1 degree:3 respectively:7 desired:4 ıguez:1 wesley:1 larger:1 suggests:4 resulting:6 implement:1 makes:2 involves:2 scales:7 δc3:1 sgn:3 buildup:2 apply:1 use:7 asymptotic:2 remains:5 seamless:1 next:2 few:1 simpler:2 bethe:1 formally:1 becomes:3 normalized:3 sharply:1 iii:4 account:5 integrating:1 tunnel:1 averaged:6 anywhere:1 obvious:1 rabinowitz:1 averages:6 control:2 coincident:2 calculation:6 haroche:2 high:10 tan:1 lamb:1 decaying:3 holds:1 delay:6 located:1 varies:1 instead:4 profile:2 singular:2 collection:1 realized:2 light:25 lines:4 correspond:2 allow:1 insight:1 interpreted:1 produced:1 cambridge:1 including:4 facilitates:1 lc:1 decay:22 chosen:3 temporal:11 choose:1 rabi:8 13c:1 13b:1 13a:1 greater:3 13d:1 polarizations:1 material:9 rotation:1 transparent:1 dielectric:1 university:3 tran:1 imamoglu:1 sufficiently:1 magnitude:5 transmitted:1 mode:7 accompanied:2 lorentzian:2 homogeneous:2 inverted:12 decays:2 interplay:1 measure:2 our:28 transitions:2 out:7 fundamentally:1 rep:1 rev:34 wick:1 cause:4 ree:2 interactions:2 maintains:1 approaches:1 york:6 likelihood:1 interaction:10 determining:1 re0:1 times:7 counterpart:1 isotropic:55 davis:1 retain:1 possessing:1 precisely:1 πa:1 ordering:2 adjoint:1 πn:1 system:62 their:7 intermediate:1 exactly:1 simulate:4 constituent:1 outline:1 submitted:2 amplitude:24 exhibit:4 unchanged:1 need:1 constrained:1 clearly:5 angle:9 fractionalized:2 polarization:67 subject:2 heisenberg:6 gλ:9 petrov:1 propagate:1 preliminary:2 device:1 consequences:1 stronger:2 face:1 artificially:1 mechanical:1 prefactor:1 fact:7 supported:1 rotating:1 agrees:1 should:1 employed:1 achieve:1 equilibrium:1 means:2 brillouin:1 words:1 polariton:1 qs:1 precession:4 differential:1 tuned:2 pulses:1 view:1 computed:1 notational:1 correlations:6 intensity:7 closer:1 phases:3 superradiant:24 written:6 neither:1 barenco:1 importance:2 emitted:3 hypothesis:1 sleator:1 problem:2 taking:2 equal:2 attributed:1 figures:2 detailed:2 unclear:1 cl:5 poissonian:4 harmonic:5 table:2 second:4 addition:2 trajectory:1 slowly:4 treat:2 enlarging:1 define:2 field:57 asymmetrically:1 describe:4 corresponding:6 coherence:6 bulk:1 c3:2 improved:1 present:6 multi:1 novel:7 laser:22 unlike:5 balachandran:1 value:24 choices:2 will:10 dephasing:9 havlin:1 almost:1 vi:5 refs:1 thus:9 surface:2 radiation:15 indistinguishable:1 precessional:2 units:11 φk:5 φl:4 φn:4 difficult:1 infinity:2 cubic:1 effect:16 variance:1 identity:2 recourse:1 reflection:1 nevertheless:1 modeled:1 well:8 usual:3 less:3 moments:2 half:1 obtain:12 underlying:1 macroscopic:13 rapid:1 density:13 absorption:1 nato:1 adj:2 identical:1 increased:1 term:6 increases:2 press:5 loss:2 displaced:2 like:3 lost:2 exploiting:1 qualitative:2 δp:1 δi:2 become:2 δc:80 therein:2 because:7 classical:24 phenomena:2 growth:2 lead:4 demonstrates:2 does:5 dipoles:3 demonstrated:4 blaaderen:1 noise:26 reaching:1 expansion:2 cλ:6 hǫ:1 prohibited:1 although:1 cγ:1 stage:1 about:9 extension:1 introduces:1 dependence:9 important:4 introduced:1 peak:4 own:2 attains:1 square:2 van:2 vac:6 much:6 mandel:3 garraway:1 function:36 triggered:2 kronecker:1 but:5 volume:1 gain:1 partially:1 made:3 evident:2 instructive:2 whether:1 variations:1 below:3 frequency:52 limit:8 demonstrate:1 distribution:26 contribute:1 denote:5 periods:1 crystals:3 functions:3 compared:2 dressed:19 detail:3 other:7 details:3 june:1 sustains:1 variation:3 matrix:1 coupling:4 photonics:1
|
quant-ph9806041.txt |@word represent:1 concept:3 consider:1 rev:5 particular:3 results:2 four:1 grateful:1 subjects:1 causes:1 whose:2 aug:1 subjected:1 equivalence:7 finally:1 okada:1 include:1 division:1 straightforward:2 very:3 could:1 induce:1 wave:17 exact:1 condition:3 having:1 solution:2 convenience:1 small:4 noted:1 consistent:1 japanese:1 kopietz:1 zero:5 evaluated:1 rigorous:1 reine:1 quite:1 trivial:3 expressed:1 version:1 above:1 replaced:1 contrast:2 body:10 dictates:1 lee:1 ibid:2 exchange:5 respectively:2 here:1 understanding:1 ansatz:1 strong:3 equations:2 appears:1 obtained:1 antisymmetric:2 technical:2 study:1 allows:1 controversy:1 suggests:1 amount:1 periodic:2 krohn:1 permutation:2 makes:1 perelomov:1 yamada:1 useful:2 inducing:1 univ:1 unit:1 use:1 eψ:3 would:2 prove:1 positive:2 negative:2 call:1 therefore:3 type:1 theoretical:1 more:1 duality:3 becomes:1 naive:1 odinger:2 separates:1 cases:1 fermionic:11 states:1 springer:2 equation:2 work:2 oscillator:1 values:2 following:1 example:1 calculation:1 choice:1 bessis:1 high:1 lorentz:1 numbers:2 dxi:1 sharp:1 absolute:1 nonvanishing:1 rather:4 acts:1 write:1 nontrivial:1 coleman:1 parameter:2 sin:1 massive:1 profile:1 description:1 information:1 replacing:1 thermodynamic:1 dx2:2 unfamiliar:1 representations:1 fk:1 meaningful:1 parallel:1 constants:1 short:3 liquid:1 bind:1 counter:1 explicit:2 fundamental:1 keeps:1 representation:2 legitimate:1 xj:18 least:1 words:1 indeed:1 over:1 displayed:1 paper:2 through:5 iachello:1 japan:3 satisfies:2 excitations:1 its:11 group:1 chosen:1 interesting:1 boson:6 degrees:1 fig:7 inspecting:1 derivative:1 emphasize:1 non:8 combination:1 elementary:1 mezincescu:1 repulsive:2 now:4 manybody:1 nos:1 represents:1 several:2 dirac:1 always:1 university:2 appropriate:1 realistic:1 l2:2 2c:3 side:1 square:1 accelerator:1 due:1 energy:5 related:2 bosonization:3 quantum:4 laboratory:1 eq:17 shown:1 matrix:1 space:2 rep:2 since:3 induces:1 research:1 particles:9 acting:2 recently:1 math:6 takayanagi:1 theory:5 interactions:3 b36:1 discontinuity:5 free:2 standard:1 admits:1 xpn:1 definition:1 interaction:21 ministry:1 followings:1 impose:1 length:1 place:4 gordon:1 top:1 origin:1 intuition:1 xi:25 xn:20 symmetry:3 number:5 linger:1 specifically:1 another:1 sutherland:2 given:3 long:1 rewritten:2 anyons:1 start:1 ordering:2 eqs:1 achieved:1 system:17 relations:1 fermions:5 calculations:1 e55:1 loudon:1 gives:2 holden:1 progr:1 reversed:2 exactly:2 artifact:1 calogero:2 part:1 x2:21 x1:29 than:1 roles:1 cyclic:2 second:1 tsutsui:1 aesthetic:1 contrasted:1 cheon:1 perturbative:1 function:14 saitama:2 raw:1 say:2 a30:1 any:2 subsystems:1 strength:1 lim:2 self:1 aside:1 thorough:1 contact:2 note:2 sciences:1 recognizing:1 potential:9 generalized:3 new:1 strengths:2 allow:1 olshanetsky:1 object:1 systems:4 nuisance:1 luttinger:2 eigenfunctions:1 constructed:1 especially:1 clear:1 sometimes:1 yang:1 physics:2 fact:1 show:2 supported:1 relation:6 subtle:1 d2:6 ground:2 based:1 should:4 only:2 høegh:1 rich:1 local:1 means:2 kochi:2 dx:3 despite:1 dr:1 mattis:1 arxiv:1 investigate:1 mapped:2 reveals:1 set:2 exists:2 dx2i:1 blurred:1 relative:4 namely:3 computer:1 βa2:1 discussions:1 kek:1 subject:1 interacting:6 enlightening:1 ranged:1 symmetric:2 state:1 between:3 limit:9 boundary:5 semiconductor:1 approach:2 discovery:1 attention:1 terms:3 august:1 extend:1 nature:1 adjoint:1 weak:3 however:2 vanishing:4 bose:1 amer:1 xp1:1 both:5 x2i:2 limits:1 tractable:1 many:4 connection:1 figures:2 context:1 ibaraki:1 relevant:1 supply:1 simple:1 each:2 harmonic:3 height:1 dimensional:6 coordinates:3 applicability:1 sensible:1 complication:1 light:1 described:1 basis:1 tomonaga:3 three:1 been:2 balian:1 interest:1 ph:1 pn:1 attractive:2 gesztesy:2 corresponding:1 easy:1 antiperiodic:1 relevance:1 prescription:1 albeverio:1 spin:2 those:1 case:6 p1:1 look:2 pacs:1 contexts:1 admissibility:1 appearance:1 value:2 heidelberg:2 p2:1 suppose:3 promising:1 aid:1 property:2 couplings:2 procedure:1 real:3 full:1 phenomenological:1 characteristics:1 drawbacks:1 thus:2 obeying:1 middle:1 reads:1 itself:2 confining:1 ramifications:1 technology:1 fermion:7 different:1 education:1 d11:1 grant:1 perform:1 lett:2 same:3 angew:1 antisymmetry:1 quant:1 arguments:1 finite:3 residing:1 status:1 see:2 singapore:1 numerical:1 effect:5 moment:1 depict:1 purpose:1 workings:1 identity:1 recent:1 lower:2 schr:2 center:2 onedimensional:1 kirsch:1 well:2 analysis:2 without:1 machinery:1 sets:2 firstly:1 organization:1 model:15 dimension:11 usual:3 kawai:1 precedence:1 solvability:1 valuable:1 thanks:1 aspect:1 eigenstates:2 readers:1 haldane:1 had:1 other:6 extends:1 treatment:1 versa:1 evidenced:1 solvable:4 transformation:2 c14:1 identical:1 spinless:1 around:1 devised:1 b51:1 possible:1 corresponds:2 historic:1 vδ:1 press:1 world:1 like:1 particle:2 alternatively:1 communications:1 imposes:1 lose:1 become:1 reduced:1 replacement:1 mathematical:2 parity:1 classical:1 czech:1 some:2 examples:2 specified:1 scale:1 tsukuba:1 dimensions:2 lead:1 bottom:1 eiλ:1 comments:1 does:2 prof:4 scientific:1 equivalent:3 arbitrary:2 step:1 properties:2 actual:1 extension:1 constraint:1 freedom:1 discussed:2 practical:1 range:12 block:1 op:1 lieb:2 unexplored:1 cambridge:2 into:2 within:1 bound:1 latter:1 hermitian:1 formidable:1 operator:1 bosonic:11 statistics:3 formulate:1 seba:2 there:3 u0:2 signifies:1 strict:2 bosons:3 low:1 way:1 analyze:1 lowest:3 complete:1 form:3 relaxed:1 arima:1 but:4 construction:3 delta:1 ha:1 true:1 intuitive:2 instructive:1 minkowski:1 us:3 bethe:1 ul:1 fermi:3 problem:7 define:1 mechanics:1 worthwhile:1 defined:2 denote:1 diverse:1 exist:1 our:2 tosa:1 physical:2 functions:9 thermodynamical:1 no:4 when:2 detail:1 field:1 setting:2 role:1 spatial:3 department:1 theor:1 elements:1 models:3 thirring:1 meaning:2 implies:1 coupling:8 pointlike:1 vice:1 describable:1 original:1 depth:1 mass:3 time:1 requires:1 4c:1
|
quant-ph9806042.txt |@word code:1 consider:1 equalities:1 results:1 chaos:1 schatten:11 entropy:72 computation:2 compact:1 depend:1 ohya:19 send:1 th:1 sent:4 case:6 orthogonal:7 electron:1 every:1 fractal:4 condition:2 partitions:1 did:1 proc:1 correct:1 markov:1 der:1 degeneracy:1 application:1 says:1 occurrence:1 estimates:1 measurable:3 pulse:1 second:1 further:3 dynamics:4 targets:1 peredachi:1 theory:12 spectral:2 what:2 nonlinear:1 stands:1 complexities:1 section:2 expressed:5 decoding:6 above:8 sup:14 international:2 satisfy:3 respectively:2 equals:3 here:5 objects:1 others:1 represented:1 strong:1 change:4 remark:1 study:5 amount:3 makes:1 accardi:1 projection:3 explained:1 matsuoka:1 put:2 univ:1 use:3 asymptotic:1 prove:1 positive:4 contains:2 properties:1 calculation:1 therefore:4 taken:3 type:1 more:2 becomes:3 operators:4 akashi:1 berlin:1 carrying:1 known:1 cases:2 springer:4 tokyo:1 science:1 ρk:13 ρj:3 obvious:1 norm:1 concepts:1 following:8 trans:1 example:1 theorems:1 process:9 ann:1 states:10 want:1 sense:1 occur:1 verlag:1 information:35 eng:1 holds:1 how:4 criterion:1 pure:1 instead:2 map:6 product:1 description:1 algebra:1 may:1 after:1 mapping:3 applications:2 types:1 fo:3 dynamical:1 computations:1 element:1 their:3 baire:1 so:9 ultimate:1 fundamental:1 correlation:1 definitions:2 order:3 s0:7 wigner:1 over:4 years:1 held:1 including:4 mentioned:1 japan:1 satisfies:2 ieee:1 its:4 before:1 sciences:1 monotonicity:1 maps:1 expectations:1 lect:1 systems:10 main:1 dyson:1 non:1 combination:1 mention:1 compound:6 misuse:1 discuss:2 matched:2 eigenvalue:4 finite:6 equality:3 fully:1 university:1 transmission:12 iff:1 inequality:3 transmitted:2 each:4 fω:1 interpolation:1 ek:11 ej:4 reduce:1 related:1 operator:4 extended:1 measure:8 quantum:82 our:1 event:1 shannon:7 out:1 category:1 watanabe:3 space:17 furthermore:1 since:1 rev:1 holevo:2 contained:1 denoted:6 occurs:2 math:11 gate:1 wiley:1 linear:1 free:1 completely:3 ask:1 anal:2 milburn:1 care:1 definition:3 masanori:1 starts:2 messages:5 times:1 hence:2 repeats:1 first:1 probability:18 coding:24 number:1 channels:4 done:2 another:3 message:14 precisely:2 open:4 ser:1 1q:3 city:1 given:5 similarly:1 introduction:1 system:19 yuen:1 indicate:1 moscow:1 continuous:1 direct:1 optical:1 authors:1 alphabets:2 translation:1 uhlmann:3 than:1 kind:1 cimento:1 depends:2 determined:1 kth:1 treated:1 minus:1 decompose:1 kossakowski:1 nuovo:1 topics:2 need:3 any:5 generalizes:1 efficient:1 complexity:2 note:5 instance:4 generalized:1 sufficiency:1 degenerated:3 channel:42 even:1 converse:2 unless:1 electric:3 trρ:3 measures:2 most:1 device:1 appear:2 considered:5 clear:2 partition:1 physica:2 inoue:1 reflecting:1 tech:1 mechanical:1 physics:1 quantity:1 random:1 purely:2 spaces:1 radio:1 decompositions:4 trivial:1 find:2 aρ:1 explain:1 state:44 should:1 only:2 going:1 attained:1 araki:3 do:1 his:4 means:4 between:1 joint:3 words:1 processes:6 die:1 arxiv:1 calling:1 through:6 set:12 computed:2 exists:1 kolmogorov:3 relative:10 namely:5 sec:4 projections:3 sem:1 dµ:1 theoretic:1 belavkin:2 concern:1 billingsley:1 said:1 capacity:29 inequalities:1 review:2 functionals:1 written:9 correctly:1 µj:6 conditions:3 petz:4 publishers:1 ability:4 rims:1 muraki:2 however:1 teleportation:1 amer:2 σk:9 both:1 last:1 taking:1 according:1 σe:3 leibler:1 receiver:4 expression:3 otherwise:1 point:2 corresponds:2 dimensional:4 cs:1 associated:3 cp:1 conference:1 described:6 transformations:1 basis:1 three:1 been:2 much:1 basic:2 pk:3 ph:1 algebras:2 po:1 misunderstandings:2 ergodic:2 describe:1 corresponding:3 yaglom:2 coherent:1 denote:2 applied:2 p0:11 bσ:1 quantenmechanik:1 kodai:1 forgetting:1 optimization:1 viii:1 behavior:1 grundlagen:1 mistake:1 almost:1 ip:2 von:8 thus:2 iv:1 itself:4 dual:2 supremum:9 id:1 binary:1 different:1 author:2 make:3 lett:1 concavity:1 quant:1 several:6 events:1 difficult:1 used:1 see:1 singapore:1 numerical:1 mutual:46 publ:1 infinite:1 identity:2 mentioning:1 whole:3 well:3 academic:1 sets:1 ccd:4 model:1 usual:4 gelfand:3 less:1 being:1 when:12 resp:4 ozawa:1 world:1 λk:38 σnk:1 stratonovich:1 chiba:1 kluwer:1 density:3 characterization:2 mathematically:1 signals:1 priori:1 treatment:1 input:19 take:2 aspects:1 easily:2 capacities:4 decomposed:2 measurement:1 know:2 using:1 unique:5 moreover:1 like:5 follows:5 signal:3 communications:1 either:1 arbitrary:1 output:17 reduces:1 terminology:1 mathematical:4 because:5 often:3 classical:31 sequence:3 sends:1 conditional:3 some:4 stat:1 ideals:1 understood:1 respect:1 proper:3 describing:1 dimensions:3 measurements:1 extensively:1 does:1 decomposition:16 chains:1 δk:8 object:6 scientific:1 rep:4 kyoto:1 processing:1 bj:2 bk:1 found:1 hilbert:5 about:1 algebraic:1 commun:2 discussed:2 range:1 important:1 introduced:5 lieb:1 soc:2 letters:1 levitin:1 communication:7 into:4 numerically:1 bound:2 due:1 references:1 elementary:1 next:1 neumann:8 statistics:1 log:11 transfer:1 there:3 start:3 appl:2 way:1 was:6 sinai:1 function:4 decoded:2 yanase:1 form:2 fundamentals:1 sequel:1 jun:1 but:4 delta:1 russian:1 lindblad:2 irreversible:1 he:6 made:1 compute:3 characteristic:1 us:1 below:1 limit:2 distribution:5 define:4 called:4 bell:1 ab:1 proved:1 defined:9 certain:1 ak:11 aj:3 general:6 transl:1 exist:1 dλ:3 formulation:1 az:1 distributions:3 physical:3 functions:1 nk:1 no:5 generally:2 ny:1 other:3 coded:10 department:1 theor:2 kullback:1 briefly:1 noda:1 problemy:1 symbol:1 prepared:2 a1:1 a2:1 bounded:1 ising:1 mathematischen:1 implies:1 codings:2 pseudo:3 simplicity:1 starting:2 having:1
|
quant-ph9806043.txt |@word limited:1 rev:30 results:1 knbo3:2 avalanche:1 higher:1 computation:1 particles:1 depend:1 calculate:2 technique:1 nonlocal:3 removal:1 compensate:1 caused:1 exit:1 silicon:1 case:3 belonging:1 supported:1 advantage:1 sitting:1 far:3 choice:4 spool:1 difficult:1 stays:1 affect:1 difference:5 splitter:3 europhys:1 swapping:1 modulator:1 presented:2 did:1 pacs:1 proposals:1 large:1 coincidences:10 small:2 optics:1 inertial:1 smaller:2 direct:1 feasibility:1 second:3 dordrecht:1 pass:2 further:1 implemented:1 port:3 quite:1 telecommunication:1 even:3 will:1 nel:1 sub:1 apparatus:2 sum:3 remain:1 access:1 experiment:20 establishes:1 new:3 net:1 d1:8 3e:1 counters:1 coefficient:2 edited:1 full:1 simultaneously:2 degree:1 exchange:1 respectively:3 promising:1 circulator:1 residual:1 agreement:2 following:1 focused:2 possibility:1 others:1 directions:1 path:2 strong:1 observing:1 change:2 obtained:1 incoming:1 unproven:1 technical:2 losses:5 marrone:1 contradiction:1 leaving:1 implementation:1 amount:1 simultaneous:4 contr:1 involves:1 pearle:1 emerge:1 explained:1 polarizers:1 outcomes:1 counts:3 total:1 scarani:1 use:5 working:1 remains:1 scan:1 arms:4 next:3 comparing:1 sample:1 program:1 therefore:3 type:5 theoretical:1 more:4 separated:1 door:1 ecole:1 becomes:1 holt:1 odinger:2 visibility:9 excellent:1 known:1 foundations:1 cases:1 high:3 mc:1 tokyo:1 setup:4 work:1 theories:4 mw:1 values:5 already:1 closing:1 jds:1 sinusoidal:3 control:1 boschi:1 indicated:3 mirrors:1 bennett:1 franson:4 abner:1 assumptions:2 numbers:1 degenerate:1 counting:1 fnrs:1 information:3 end:2 varied:1 holds:1 differences:2 feature:1 located:2 low:1 significance:1 parameter:5 tension:3 description:2 superluminal:1 overall:1 after:2 santos:3 reflect:1 applications:1 wrong:1 10mhz:1 demonstrating:1 date:2 grangier:2 data:1 compatibility:1 short:2 natural:1 third:1 famous:1 light:7 summing:1 ones:1 so:5 fundamental:1 correlation:14 order:3 se:1 typical:1 wavelengths:2 serving:1 help:1 indeed:2 over:5 satisfied:1 produced:1 experiments:5 pulses:4 nitrogen:1 experimentally:1 mentioned:1 japan:1 still:3 accidentals:2 before:2 perfect:1 group:1 thank:1 la:1 interesting:3 relativity:4 decreases:2 actually:1 better:2 window:3 fig:5 mail:1 hidden:3 imbalance:1 loophole:5 weber:1 emphasize:1 maximal:1 them:2 affected:1 greater:1 wolfgang:1 anticipated:1 kamefuchi:1 effects:1 they:1 half:1 now:4 ghirardi:1 february:1 name:1 stabilize:1 always:1 university:2 podolsky:1 huelga:1 lettere:1 gautier:1 infer:3 possibilities:2 transmission:1 inequality:10 visibilities:2 mode:1 each:3 found:3 soc:1 european:1 ports:2 mean:1 schemes:2 directly:6 ed:1 energy:3 related:1 interferometer:12 obtains:1 measurement:2 quantum:30 our:13 beyond:1 eq:3 out:2 rp:1 network:3 electronic:1 nuovo:1 since:6 interference:2 bennet:2 denotes:1 semiconductor:1 rg:1 reader:1 mattle:2 ri:2 shows:1 fiber:10 theory:4 state:1 birefringence:1 fondation:1 ntu:1 free:2 standard:5 qua:1 reason:1 caro:1 besides:2 estimate:1 prefered:1 pairs:8 created:2 determining:1 could:8 times:1 filter:1 length:6 produce:1 including:1 chiao:1 hence:7 think:1 speeds:1 first:8 origin:1 owens:1 placing:1 symmetry:2 variables:2 reflected:1 huttner:1 channels:2 fits:1 employing:1 done:1 fast:2 another:5 robust:1 impossible:1 precisely:1 open:1 michelson:1 size:1 passes:1 given:2 temperature:1 introduction:1 leading:4 least:3 fm:5 priority:1 needed:1 confirming:2 assumption:2 rates:12 show:3 john:1 bits:2 mandel:1 geneva:6 ratio:2 villages:1 prediction:1 tapster:2 optical:2 number:4 than:8 coefficients:3 distance:4 scheme:1 liquid:1 fuchs:1 bother:1 cimento:1 rate:4 rarity:2 collinear:1 determined:2 assumes:1 enables:1 rimini:1 cohen:1 argument:1 randomly:2 raw:4 idler:1 close:4 weinfurter:4 clearly:1 zero:1 analyzers:3 latter:1 arm:2 polarization:1 martinelli:1 potential:1 absorbed:1 performance:1 detector:6 switching:3 channel:4 accuracy:1 exactly:1 allow:2 though:2 probed:1 jun:1 measures:1 most:1 involving:1 connected:7 letter:1 phase:5 measured:6 why:1 deviations:4 loopholes:3 considered:1 detectors:7 km:18 traditional:1 points:2 mechanical:1 physics:5 away:2 horne:4 violation:10 text:1 detection:4 random:5 infrared:1 d2:12 find:7 subtracting:6 based:9 ment:1 behind:1 should:2 dalibard:1 only:7 going:1 factor:1 thompson:1 local:5 guided:1 do:1 his:2 above:1 cryptography:9 di:1 dependent:1 de:3 db:1 truly:1 beam:3 cannot:2 despite:1 report:1 during:1 freedman:1 increasing:1 qu:1 settings:1 suarez:1 arxiv:1 motion:1 yield:1 wiesner:1 investigate:1 paper:2 roger:3 contrast:1 switzerland:1 through:3 us:1 scanning:1 requirement:1 set:1 questions:1 fascinating:1 quenched:1 correlations:2 observed:4 see:2 sec:1 result:4 led:1 uncorrelated:2 nonlocality:1 best:1 phases:4 exploited:1 inequalities:10 placed:1 nondegenerate:1 shimony:3 label:1 naturwissenschaften:1 pump:2 symmetrie:1 between:8 tens:1 probably:1 experi:1 recently:1 nature:3 importance:1 weak:4 however:7 analyzer:2 teleportation:1 tum:1 opposition:1 configuration:1 aim:1 motivations:2 both:11 cos:1 last:1 han:1 reported:1 mohler:2 attributed:1 agree:1 operating:1 passing:1 argue:1 safely:1 experimental:1 nearby:1 among:2 adjusted:1 ch:4 key:1 bell:22 steinberg:1 aspect:4 kilometers:1 coexistence:1 coincidence:16 maintained:1 qber:6 adding:1 faraday:2 li:1 telecommunications:1 ps:2 pp:1 described:3 basis:1 addition:2 create:1 three:1 been:3 peaceful:1 expected:1 ph:1 systems:1 direction:1 tittel:4 coherence:3 photon:19 zeilinger:5 ensuring:1 external:1 fl:1 applied:2 laser:2 look:1 reciprocal:1 brendel:3 value:3 choices:1 employ:1 while:3 replaced:1 error:1 situation:1 photodiodes:1 guide:2 walther:1 detailed:1 larger:1 almost:2 thus:2 non:3 coupler:5 itself:1 technology:1 different:8 fibers:3 same:9 any:1 quant:1 split:1 several:1 events:2 pan:1 four:4 used:3 phasematching:2 disagree:1 effect:2 bouwmeester:1 arose:1 fry:1 entanglement:7 changing:1 chromatic:1 qubit:2 interferometers:15 lower:1 schr:2 nevertheless:1 no:11 well:4 davis:1 efficient:1 without:3 does:2 sets:1 swiss:1 plotted:1 parametric:1 ekert:2 subtraction:1 distances:4 less:1 being:2 rosen:2 resp:1 labeled:2 obtain:2 germanium:1 underlying:1 distant:1 thanks:1 predicts:2 world:1 oriented:1 preprint:1 generator:2 application:1 photons:18 conclude:1 passive:3 source:8 setting:1 lett:25 5k:1 input:2 violations:1 mod:1 opt:1 march:1 around:2 metaphysics:1 evaluate:2 possible:1 dark:3 increases:1 zukowski:1 five:1 entangled:5 signals:1 using:7 bit:1 apart:6 necessary:1 like:1 signal:1 manifest:1 discarded:1 either:3 δi:1 output:3 security:1 reduces:1 cooled:1 classical:2 some:1 back:2 supplementary:1 afterpulse:1 meters:1 moreover:1 ribordy:1 undetected:1 provided:2 tmr:1 competitor:1 confirm:1 cavity:1 demonstrates:2 avoid:1 opposite:1 exceeding:1 per:3 fringes:1 connecting:1 assuming:3 transmitted:1 demonstrated:2 refer:1 measuring:1 noise:2 seconds:1 processing:1 analysed:1 rue:1 analyses:1 analyser:4 dictated:1 noisy:1 about:4 would:3 eavesdropper:1 o:1 side:2 practical:2 kwiat:4 ensure:2 shared:1 ou:1 peak:1 equally:1 own:1 beamsplitter:1 significant:2 presence:1 orders:2 communication:2 into:3 within:1 due:3 down:1 pair:2 appropriate:1 determine:5 einstein:2 frames:1 physical:1 rely:1 additional:2 few:1 assumed:1 support:1 there:5 long:3 dispersion:2 physicists:1 way:3 unige:1 was:8 opens:1 function:9 form:2 enough:3 basic:1 analyse:1 but:2 weihs:1 magnitude:2 detect:1 true:2 proposal:1 count:10 made:2 compute:1 whether:1 selects:1 attached:1 up:4 devices:1 crystal:3 note:3 converted:1 limit:1 demonstrate:1 geiger:1 similar:1 called:1 gisin:3 mechanics:6 fractions:1 khz:3 cirac:1 constant:4 defined:1 modules:1 measure:3 denote:1 clauser:4 single:6 downconversion:1 predictions:1 wavelength:4 corresponding:2 quantph:2 defines:1 again:2 functions:7 compared:1 nm:4 locality:4 circulators:3 when:4 ne:1 field:1 prism:1 other:6 detected:3 investigations:1 test:4 really:2 kluwer:1 bellevue:4 accidental:11 separate:1 variation:1 lens:1 meaning:1 allowing:1 variable:2 zbinden:1 correlated:2 fluorescence:1 assume:1 resolution:1 required:1 changed:1 time:5 chsh:3 once:1
|
quant-ph9806044.txt |@word sch:1 illustrates:1 rev:5 lack:1 results:7 leads:4 scalar:1 rebbi:1 research:1 consider:1 whose:1 ıs:1 calculate:1 subjected:1 deterministic:1 under:1 stochastic:33 amplitudes:1 string:25 far:1 wave:4 witten:1 summarized:1 redefinition:1 difference:1 bringing:1 look:1 qni:4 presented:1 issue:1 t0:11 t1:2 marra:3 small:3 markov:1 dealing:1 second:3 canonical:4 index:1 what:1 brackets:3 section:6 current:1 version:1 above:4 new:1 increasing:1 acknowledgments:1 satisfy:1 conf:1 respectively:2 never:1 here:1 objects:1 departamento:1 address:2 path:1 along:1 quark:1 obtained:5 instituto:2 allows:2 poisson:3 stressed:1 action:4 resonance:1 changes:1 formulated:2 useful:1 extra:1 wataghin:1 addressed:1 planck:5 derivatives:2 use:6 proceed:1 would:3 sake:1 next:2 calculation:1 live:1 usp:1 generators:1 themselves:1 type:1 more:1 furthermore:1 started:1 operators:1 odinger:3 validity:1 labelled:1 known:2 iii:3 must:1 quantized:2 equation:22 work:2 salam:1 reproduce:1 mv:2 freedom:2 following:7 making:1 averages:1 example:1 dxi:1 process:5 relativistic:3 choice:1 organized:1 lorentz:6 want:1 allowed:1 νn:7 v0i:1 occur:1 end:1 s1:5 very:3 parameter:2 ensemble:1 simplicity:1 description:2 algebra:2 replacing:1 oscillators:1 different:3 dx0:2 distances:1 law:3 constants:3 natural:1 dynamical:1 imply:1 light:4 correspond:1 element:1 so:1 fundamental:1 correlation:4 definitions:1 order:5 developed:1 pointed:1 thermal:1 paper:2 through:2 existence:1 satisfies:2 its:3 before:4 derive:1 group:1 acknowledge:1 fix:1 gleb:1 coordinates:2 writing:1 degrees:1 choose:1 quant:1 defining:3 correspondence:3 non:5 motivated:1 outlined:1 introduce:2 framework:1 cep:2 inception:1 speculate:1 nor:1 easily:1 term:1 2r:1 always:1 university:3 level:2 identified:1 mode:4 each:1 2m:2 ifi:1 mean:1 established:1 domain:1 square:1 energy:1 related:4 used:1 ey:1 quantum:8 our:9 out:1 shown:2 space:2 defend:1 since:2 lagrangian:2 requires:1 particles:1 reader:1 mν:1 ref:2 math:2 theory:6 interactions:1 ısica:2 governing:2 standard:5 reparametrizations:1 sophistication:1 definition:2 derivation:2 language:1 reinforces:1 transition:1 correctness:1 motion:14 length:1 place:1 δij:1 consequence:1 think:1 first:4 initial:1 probability:3 radical:1 variables:4 xd:2 xim:10 restrict:1 another:1 open:7 given:3 needed:1 introduction:1 system:4 xin:1 their:1 convention:2 variational:5 final:1 gives:2 transverse:1 accords:1 authors:3 x0:9 diffusion:9 princeton:1 require:1 cimento:1 zero:4 succinctly:1 distinguished:1 result:2 exhibit:1 motivation:1 symmetries:1 generality:1 nuovo:1 spectrum:1 generalization:2 already:1 need:1 seen:1 any:1 acceleration:3 forced:1 form:1 depending:1 lim:2 ideas:2 potential:1 xi:8 green:1 δnn:1 davidson:2 sure:1 normal:6 object:1 vni:2 madelung:6 but:1 pair:1 xµ:2 average:3 later:1 typeset:1 traditional:1 points:1 principle:4 exp:7 mechanical:2 velocity:2 physics:4 naively:1 fact:1 slope:2 show:2 escobar:2 nσ:1 nτ:2 infrared:1 gauge:6 cnpq:1 ground:1 based:1 parameters:1 commutators:1 state:3 should:1 only:4 wayne:1 candidates:1 ambiguity:1 ruggiero:1 achieve:1 continuity:4 do:3 his:2 de:5 da:1 cannot:1 dx:5 despite:1 dw:5 dt:3 dq:1 evolution:1 arxiv:1 fixes:1 qc:1 europhys:1 including:1 view:4 requirement:1 set:1 swept:1 achieved:1 guerra:9 notice:2 achieves:1 naturalness:1 decided:1 us:1 close:1 brazil:2 satisfying:1 review:1 functionals:1 propagates:1 written:2 difficulties:1 identification:1 correctly:1 regge:2 invariant:1 neither:1 approach:8 knowing:1 nambu:2 terms:1 nature:2 expanding:2 however:1 council:1 collaborators:1 taking:1 density:4 quantization:1 propagation:1 context:1 comes:1 among:1 point:9 reasons:1 xν:1 harmonic:1 dimensional:4 superstring:1 moreover:1 described:2 been:2 int:1 much:1 treat:1 basic:1 expected:2 ph:1 define:1 divergence:1 remark:1 external:1 fokker:1 spirit:1 case:3 abandoned:1 straight:1 value:1 will:8 euclidean:1 goto:1 mqi:1 mqj:1 thus:1 them:1 surface:3 iv:2 ii:2 im:3 cone:3 dual:1 vanish:1 santos:1 make:3 lett:5 same:4 universidade:2 paulo:4 parts:2 followers:1 arguments:1 coworkers:1 soundness:1 dimensionless:1 several:3 literature:1 estadual:1 i0:5 campinas:2 hand:2 phy:1 moving:1 infinite:1 invariance:5 recent:1 schr:2 modes:4 mention:1 well:2 analysis:1 without:1 consistency:2 position:1 dimension:1 unified:1 newton:2 obtain:3 gravity:1 underlying:1 world:2 alternative:1 now:6 candidate:1 conclusions:1 scales:2 treatment:1 dqm:1 playing:1 real:2 read:1 evaluate:1 possible:2 press:2 using:5 gr:1 modifications:1 like:2 particle:6 follows:7 δs:2 manifest:1 continue:1 steps:1 schwarz:1 δb:3 δa:2 mathematical:1 right:2 methods:2 classical:13 picture:1 phenomena:1 calculated:1 towards:1 specified:3 indistinguishability:1 transport:2 provided:2 scale:6 proceeding:1 lead:1 avoid:2 critical:2 provides:1 proc:1 refer:1 manifesting:1 who:1 rep:2 agreement:2 revtex:1 bq:4 br:2 imaginary:2 between:3 stationary:1 introduces:4 dependence:1 o:1 side:2 obeys:1 xni:2 efforts:1 introduced:1 considerations:1 cambridge:1 intl:1 into:1 functional:3 references:1 proportional:2 bosonic:7 uncertainties:1 criticisms:2 area:1 support:1 there:1 question:1 start:1 describes:1 brazilian:1 forward:2 hooft:1 was:1 naturally:1 function:7 newtonian:1 some:1 smolin:2 m2:1 jun:1 extended:1 encourages:1 promote:1 embedded:1 smooth:1 differentiable:1 fluctuations:4 distribution:1 clear:1 mechanics:5 gone:2 constant:9 computing:1 defined:3 abstract:1 describe:4 ao:4 2mν:1 aq:4 separating:1 examine:1 formulation:6 formalism:3 simplest:1 physical:2 ni:2 susskind:1 cos:1 when:2 field:2 role:1 details:1 theor:1 conclusion:1 polar:1 briefly:1 models:2 unicamp:1 stringy:1 chance:1 important:2 veneziano:2 dτ:3 required:1 speculations:1 dσ:2 together:1 original:1 mass:1 nelson:10 time:2 n2:4 backward:1 starting:2 strings:2
|
quant-ph9806045.txt |@word represent:1 practise:1 partial:3 consider:8 remarkable:1 illustrates:1 lagrangian:12 forbidden:6 particular:4 results:9 leads:6 roy:1 commute:8 obtaining:1 follow:1 expressions:2 research:1 gν1:1 localized:4 row:1 whose:2 certainly:1 dimensionality:1 depend:1 re:2 technique:2 nonlocal:1 shall:3 simplify:1 list:1 finally:3 restriction:4 those:4 th:6 caused:2 include:8 shepherd:1 magnetic:3 ingredient:1 p2:1 labels:1 worse:1 straightforward:5 orthogonal:3 very:3 frequencies:19 desired:4 conditions:12 wave:9 mν:5 electron:2 refractive:6 resonant:17 experimentally:2 emphasized:1 difference:8 exact:1 condition:13 treating:2 differentiated:1 qν2:1 obvious:2 hamiltonian:33 did:1 positions:4 eigenmodes:2 integrating:1 proposals:1 solution:11 occurs:5 discrete:6 vector:7 d3:6 mλ:4 guiding:2 fourier:2 small:1 gauge:15 refer:1 optics:3 noted:1 omit:1 neighborhood:1 carter:3 oscillation:1 foundation:1 renormalized:1 regained:1 consistent:3 fit:1 coefficient:7 direct:1 hillery:3 approximation:2 fold:1 second:3 evaluated:3 further:2 dynamics:2 odd:2 gm:7 summation:8 theory:42 even:8 index:7 oll:1 nonlinear:4 plays:3 appear:2 brackets:2 giving:3 sum:9 near:1 expressed:5 uniform:3 current:1 version:1 poles:6 3n:4 above:13 new:8 increasing:1 waveguide:7 consisting:1 body:1 bi:2 full:4 led:2 lee:1 diagonal:5 exchange:3 integrated:2 component:11 κa:13 here:29 atoms:6 dressed:1 phoenix:1 inverse:3 bj:2 xν:7 represented:1 causality:2 along:1 equations:27 implicit:1 change:1 obtained:13 renormalization:1 property:3 rigorously:1 involved:2 leaves:2 losses:1 exceptionally:1 approaches:4 denominator:1 guide:3 accomplished:1 resulting:7 poisson:2 action:1 resonance:13 narrow:6 makes:1 involves:2 york:2 examining:1 via:1 useful:1 projection:2 ix:1 differentiating:2 problematic:1 semiconductors:1 explained:2 anticipate:1 condensates:1 apply:3 total:2 causal:1 unit:1 readily:2 derivatives:2 use:16 done:3 projector:1 would:4 prove:6 distinct:14 positive:9 contains:1 charge:7 tightly:1 next:11 calculation:2 noting:4 examination:1 therefore:9 lond:1 taken:1 inner:1 themselves:4 simpler:1 type:17 theoretical:1 more:25 separated:1 introducing:1 equivalence:1 winston:1 excluded:1 4c2:2 operators:40 apparent:1 distribution:3 tested:1 baumberg:1 virtue:1 excellent:2 known:10 cases:7 hold:3 iii:13 fν:2 must:32 high:4 account:1 left:1 quantized:7 effectively:2 rν:9 equation:19 work:5 oscillator:8 modified:5 theories:1 ashcroft:1 degrees:1 mv:1 values:3 learn:1 canonically:1 under:2 trans:1 root:3 example:6 proof:1 control:1 leonhardt:1 impose:3 polaritons:7 give:5 process:2 expanding:2 sense:2 ann:1 πj:1 involve:5 really:1 lorentz:12 degenerate:1 allowed:2 unphysical:2 exclude:1 linearized:1 νi:1 occur:1 yang:1 information:3 needs:1 νn:1 requirements:6 advantage:1 turn:2 rather:7 verify:1 eσ:2 breaking:1 feature:3 orthogonality:6 regions:2 how:1 liniger:1 simplifies:1 instead:4 coleman:1 preferable:2 derivations:1 simplicity:5 product:1 express:3 intended:1 may:4 demonstrates:1 oscillators:13 earlier:6 derived:4 treatments:2 substitute:3 constraint:1 applications:1 plane:4 physik:1 waves:2 cambridge:2 verified:1 choice:3 response:1 types:4 goal:1 realized:1 short:1 branches:13 dynamical:1 effective:8 onto:2 explicit:4 correspond:5 provide:2 complexity:1 cannot:3 so:23 fundamental:3 correlation:1 representation:2 lined:1 order:27 restricted:1 typical:3 volume:1 wavelengths:1 excludes:2 over:24 di:3 choose:6 interpreted:2 course:5 r2ν:1 experiments:4 through:2 wolf:1 statistical:1 zµ:11 argued:1 existence:1 satisfies:2 still:3 excitations:5 its:3 roots:18 diagonalized:1 write:3 nonlinearities:1 le:1 group:27 symmetry:1 took:1 termed:2 chosen:4 lai:2 inclusion:2 k3:2 forms:2 absence:3 µa:2 microscopic:5 differently:1 insulator:1 omitted:3 derivative:1 main:4 might:3 ideal:1 non:5 greater:2 combination:5 propose:1 polarizations:1 amenable:1 introduce:7 functional:2 scaling:1 band:20 couples:2 effects:8 they:2 oxford:3 now:19 transparent:7 dielectric:10 suppose:2 easily:2 february:1 clumsy:1 pc2:1 always:7 university:2 level:3 hermitian:5 labeling:1 established:1 realistic:3 lorenz:1 2g:1 mode:48 each:35 found:5 entirely:3 preserve:3 neglects:1 homogeneous:3 domain:1 ei:1 significantly:1 accelerator:1 quadratic:3 t2:4 energy:9 barnett:3 reduce:1 displacement:12 related:4 inhomogeneous:2 frequency:33 expect:1 measurement:1 quantum:21 our:18 operation:1 drude:10 eq:17 description:4 shown:3 evidence:1 matrix:9 machida:1 factors:4 res:4 since:11 interference:1 projected:1 requires:1 replacing:2 europhys:2 dominated:1 rational:3 suggesting:1 formula:1 δrs:1 induced:1 cause:2 correct:10 red:1 shows:3 commutation:15 fiber:2 linear:7 interactions:3 differ:1 free:3 standard:4 remaining:1 completely:4 advantages:1 term:13 eigenvalues:1 indicates:3 generate:2 definition:4 pairs:4 interaction:4 derivation:1 transition:3 lossless:1 times:8 motion:1 appearing:1 explored:1 place:1 isotropic:3 incorporated:2 unknown:3 corrections:9 omits:1 generalizations:1 first:9 origin:4 excitonic:1 justify:1 features:2 probability:1 widely:1 third:1 variables:3 number:10 transform:3 will:15 simplified:1 least:1 directly:1 carry:1 impossible:1 precisely:5 electronic:3 dispersive:15 given:23 necessarily:1 exists:1 needed:5 introduction:2 leading:1 eqs:5 system:3 relations:20 their:6 assumption:4 zeros:1 identity:7 calculations:1 realization:1 normalization:2 consistency:3 structures:3 ranging:1 rinehart:1 gives:4 shifted:1 eigenvectors:6 a31:1 fraction:2 mostly:1 explanation:1 exactly:6 eliminates:1 transverse:26 5µm:1 forward:1 part:8 differentiate:2 somewhat:1 x2:1 natural:1 than:6 coefficients:11 center:2 iωt:5 δµj:1 reason:4 showed:1 sections:2 require:1 summary:2 zero:8 reflectivity:1 loudon:4 annihilation:4 individual:1 a42:3 assumes:3 a40:1 were:1 normally:1 wiley:1 treated:4 damping:1 lowest:1 dielectrics:1 generality:1 correction:5 normal:1 argument:1 summing:5 meyer:1 2aµ:1 variable:6 need:2 requiring:2 seem:1 recover:1 demonstration:2 any:11 relatively:3 iωµ:10 lie:1 hopfield:7 utilizing:1 relationship:1 mermin:1 depending:1 lim:4 self:3 responsible:1 able:3 isolated:1 violates:1 polarization:30 k2:2 k1:2 without:6 generalized:3 analogy:1 finding:2 canonical:13 heisenberg:1 residue:2 begin:1 added:2 multiple:5 allow:5 though:1 gν:30 who:1 gλ:13 systems:1 accurately:1 most:4 involving:8 propagate:1 but:10 significant:1 position:17 device:1 analytically:2 trapping:1 soliton:1 ka:2 takes:1 consequences:1 considered:3 kj:2 clear:4 later:4 kn:1 optical:3 electrons:2 principle:1 mechanical:1 holstein:1 velocity:26 charged:2 physics:4 section:4 fact:8 quantity:1 precise:2 insulators:1 allows:1 show:16 delta:4 dependences:1 dipole:4 scattering:1 purely:1 kδ:1 expressing:1 relation:35 solutions:5 substituting:1 longer:1 trivial:5 find:22 access:1 uiσ:1 based:3 parameters:1 commutators:24 enough:1 elucidated:1 should:5 restating:1 analytic:10 only:20 explicitly:2 study:1 summarizing:1 lower:2 factor:4 integrate:1 hamiltonians:3 local:13 pointed:1 pj:1 dn:10 do:7 dk:14 notation:4 means:1 dependent:6 familiar:3 between:22 overall:1 satisfied:7 define:13 ones:2 pergamon:1 negative:2 words:1 despite:2 lattices:1 polariton:4 becomes:2 processes:1 continuum:12 fields:24 arxiv:1 expansions:4 method:1 reid:1 paper:3 4πa:5 double:2 switzerland:1 including:3 fixed:1 approximations:1 view:1 satisfy:5 requirement:4 set:4 reference:1 physically:1 national:1 gµ:1 hδ:2 hε:1 relative:2 differs:2 depends:2 justification:1 bare:1 result:12 eliminating:2 violet:1 inequivalent:1 limiting:2 theoretic:1 contour:5 quantizing:1 techniques:6 nakano:1 phases:1 interacting:3 supported:1 crystal:2 phonons:2 nuclear:1 complementary:1 sites:1 propagates:1 materials:1 watanabe:3 written:5 closed:1 simplest:3 complications:1 before:6 approach:5 available:2 multiplied:2 notice:4 terms:29 nature:3 spacing:1 focus:1 however:18 science:1 residual:1 council:1 derive:1 huang:3 analyzed:1 longitudinal:18 understanding:1 suppressed:1 valid:3 uσ:4 recall:1 both:6 essentially:3 last:2 sν:1 tractable:1 many:5 taking:4 la:1 equal:18 attributed:1 quantization:4 propagation:2 pµ0:1 transmission:6 contribution:1 expression:9 photons:3 strongly:1 relevant:10 space:1 point:7 simple:11 continuation:1 lagrangians:1 eikx:8 corresponds:1 environments:2 dimensional:38 interface:1 pole:3 grants:1 simply:9 adding:1 bose:1 polynomial:2 constant:1 considering:2 practice:1 combines:1 light:1 described:2 2ak:1 basis:1 addition:4 simplification:1 universal:1 renormalizes:1 due:15 been:6 appears:1 rν2:1 int:1 cauchy:4 complicated:1 treat:4 expected:3 agrees:2 ph:1 unchanged:2 important:6 treatment:1 direction:1 arises:1 corresponding:11 kronig:1 restrictions:1 sufficient:4 undefined:1 photon:8 precision:1 kramers:1 eigenfrequencies:1 vµ:17 systematic:1 δij:10 c2:39 presented:1 present:10 case:36 multi:2 replaces:1 look:1 solid:7 defining:5 straight:1 expanded:3 appearance:1 examine:2 value:9 transformation:2 intimately:1 while:6 replaced:6 viii:1 behavior:4 shift:1 exist:1 revisited:1 ultra:2 region:3 procedure:6 identical:11 studied:1 examines:1 cell:2 coupled:7 phenomenological:2 vi:11 thus:10 them:2 iv:6 ii:15 quantize:2 ik:3 ij:5 dual:2 turns:1 ia:1 mod:1 vanish:1 µk:1 different:15 develop:3 indicate:2 fibers:1 perform:1 media:5 radiation:2 cross:6 same:15 clearly:4 shifts:4 unity:1 complex:12 quant:1 arguments:1 diagonalize:2 louisell:1 units:2 finite:2 eik:13 consequence:2 higher:4 independent:2 used:10 infinity:1 imply:3 see:1 trivially:1 absorb:1 i3:6 effect:1 u0:2 haus:3 inhomogeneities:1 moment:3 levels:1 uses:1 phy94:1 expand:4 recent:3 relies:1 gss:2 specialize:2 off:3 modes:20 primakoff:1 older:1 charges:2 studies:1 shelby:3 well:16 analysis:3 thought:1 solids:1 contact:1 solve:2 components:2 multipolar:11 quantitative:1 model:37 kv:3 dimension:3 usual:17 λs:2 interpret:1 velocities:2 manifold:1 just:8 less:1 being:1 when:14 accurate:1 labeled:1 obtain:7 photonic:1 detail:2 orthonormality:1 identify:1 atomic:12 momenta:5 yamamoto:4 macroscopic:2 previous:7 blow:3 note:7 accepted:1 density:12 absorption:9 regarded:3 qν:7 character:1 except:5 improvement:1 lattice:3 operator:6 potential:4 transformed:1 developments:1 ordering:1 theorem:3 diagonalization:4 apart:2 unprecedented:1 momentum:27 real:4 tests:2 australia:1 aspects:1 around:3 rev:15 eigenvalue:10 rules:4 bands:9 sums:7 possible:2 spanned:1 early:1 test:1 philos:1 lett:7 similarly:6 vacuum:3 press:4 using:10 unique:3 projects:1 prominent:1 loss:1 necessary:8 like:2 particle:10 follows:5 reduces:6 susceptibilities:1 isotropy:2 harmonically:1 separately:1 communications:2 either:4 integrals:3 arbitrary:6 a55:1 anti:1 inter:2 essential:7 permittivity:5 making:1 mathematical:1 because:3 classical:12 picture:1 friberg:1 resonances:10 harwood:1 creation:3 some:3 algebraically:1 b4:1 born:4 b7:1 respect:2 proper:1 pνµ:5 soc:5 diagonalizing:4 transport:3 electric:14 another:1 solving:2 amongst:4 dimensions:3 lead:3 electromagnetic:23 measurements:5 instantaneous:1 does:8 dipoles:1 provides:1 assuming:1 propagating:1 proc:1 rhs:2 minimal:8 2a:4 λi:1 noise:1 power:2 location:1 equivalent:7 unusual:1 expansion:50 infra:1 qnd:1 clarendon:2 step:2 although:5 fused:1 properties:12 stage:2 comparison:2 about:3 central:2 carried:3 algebraic:6 freedom:1 introduces:1 dependence:5 o:1 pν:36 sake:1 range:3 carrier:1 ensure:3 modal:5 calculating:1 ic2:3 introduced:9 slightly:2 bloch:2 automatically:3 hence:12 lieb:1 considerations:2 australian:1 own:2 final:7 presence:2 previously:3 maxwell:11 into:12 within:1 integral:6 bound:2 three:13 queensland:2 appropriate:3 polarizable:3 determine:2 elementary:2 proportional:4 reducing:1 vii:1 behaving:1 additional:5 area:1 assumed:2 there:26 approximate:1 long:5 sides:1 dispersion:80 start:2 accordingly:1 much:1 low:10 way:3 resulted:2 subsequent:1 delocalized:1 was:10 cancel:2 combined:2 function:30 medium:11 complete:9 form:41 gaps:1 opt:4 jun:1 drummond:5 principles:2 changed:1 hk:1 state:2 aµ:19 ho:1 solved:1 atom:6 hc:3 technologies:1 true:3 considerable:2 he:1 directed:1 made:1 slope:3 wish:5 inside:1 meromorphic:3 up:3 us:8 kumar:1 assume:1 implements:1 limit:4 ωn:1 residues:4 demonstrate:8 problem:5 stages:1 similar:6 calculated:1 regimes:1 detailed:1 definitions:1 p2ν:4 defined:10 recognize:1 ki:2 describe:1 am:3 doesn:1 general:9 single:7 proves:1 reservoirs:1 rule:1 wavelength:5 partly:2 huttner:3 identities:3 physical:3 incorrect:1 again:1 functions:4 transitions:9 grs:1 no:15 amounts:1 exciton:18 generally:5 vanishes:2 virtual:2 field:77 other:15 role:3 details:1 branch:11 spatial:5 department:1 out:5 conclusion:1 conclude:1 polar:2 holt:1 intend:2 generates:2 excitation:1 provided:5 models:6 hδij:2 time:8 problems:1 ultimately:1 2n:1 includes:7 commutator:6 a2:1 bounded:1 allowing:1 vectors:2 included:16 replacement:1 n2:5 structure:13 acknowledgment:1 subspace:3 k3n:3 implies:13 coupling:18 coulomb:6 dω:3 complicating:1 typically:6 required:9 curve:1 together:3 having:5 phonon:27 mass:2 wavenumber:1 broad:1 couplings:6 silica:1 starting:2 original:3 fully:1 once:3
|
quant-ph9806046.txt |@word consider:8 equalities:4 results:6 rˆ:1 proposition:1 generalize:1 follow:1 devoted:1 whose:1 inverse:1 const:5 finally:1 tm:1 those:1 under:2 γb:1 γa:2 aut:1 corollary:3 associated:1 difference:1 matrices:1 condition:1 identity:1 intersections:2 presented:2 list:1 t0:213 t1:134 vector:8 small:1 dealing:1 consistent:1 direct:3 hth:3 htv:8 second:1 rigorous:1 further:2 linear:5 plays:1 section:4 expressed:1 sequential:1 above:10 dtγ:5 new:3 method:1 satisfy:2 evolving:1 respectively:12 here:10 address:1 directions:1 path:1 along:27 equations:17 change:2 morphisms:10 obtained:9 remark:1 institute:1 vectors:8 usually:2 suitable:2 uniquely:2 via:4 prefer:1 assertion:1 viz:1 total:1 kind:1 unit:2 derivatives:1 conventional:3 ψy:3 prove:1 remains:1 bundles:3 comparing:1 live:1 bases:8 call:1 therefore:1 taken:1 themselves:1 msc:1 theoretical:1 possible:1 more:2 introducing:1 bulgarian:1 operators:1 quant:3 odinger:19 curvature:1 particular:5 known:3 cases:1 hold:1 iii:21 analogous:1 account:3 valued:3 ma:1 equation:23 work:3 dsγ:3 remain:1 values:2 following:4 conformity:1 example:1 proof:1 f0:4 give:1 calculation:2 december:1 organized:1 purposes:1 states:2 numbers:4 want:1 evidently:3 end:2 provide:1 discussion:1 get:3 feature:2 how:1 pure:2 simplifies:1 instead:1 map:5 description:21 algebra:1 fx:3 fy:1 after:1 derived:8 applications:1 lax:3 representations:2 short:1 natural:2 dynamical:11 third:2 maybe:1 chauss:1 explicit:1 summing:1 cannot:3 so:7 lγ:30 representation:2 order:1 typical:2 fγ:26 interpretation:5 help:2 september:2 developed:1 over:1 produced:1 ended:1 paper:3 through:3 modified:2 mentioned:1 its:10 before:1 sciences:1 derive:1 maps:2 interesting:2 better:1 mail:1 arguments:1 treating:1 them:3 good:1 propose:1 material:1 introduce:1 they:4 front:1 now:11 developments:1 easily:2 february:1 tonian:1 january:1 hamiltonian:15 iff:10 found:2 entirely:2 characterized:1 mean:7 differential:2 directly:2 independent:7 ee:1 series:3 energy:1 revised:2 ea:1 used:3 obtains:1 entering:1 combining:2 quantum:41 our:6 special:4 matrix:16 space:8 restricted:1 since:1 induces:2 research:1 looking:1 may:6 at0:2 print:2 shows:4 theory:4 free:1 admits:1 approaches:1 base:1 besides:4 put:1 definition:4 pairs:2 interaction:5 derivation:3 geometry:1 transition:1 motion:63 separator:1 hence:7 retain:1 footnotes:1 view:9 generalizations:2 first:3 initial:3 bozhidar:17 xb:2 variables:2 timeindependent:1 number:1 thereof:1 approximate:2 another:2 precisely:2 given:11 exists:1 introduction:5 leading:1 system:14 relations:1 their:6 intermediate:1 too:1 convention:1 final:1 realizes:1 observations:1 shifted:1 commutativity:3 academy:1 exactly:2 zeroth:1 measurable:1 assumption:1 part:5 differentiate:2 july:1 representing:1 than:1 updating:1 outline:1 supposes:1 determines:1 sections:4 see:18 determined:1 contrary:1 eγa:7 geometrically:1 tion:1 extracting:1 generality:1 correction:1 modern:1 mixed:1 correspond:1 already:1 say:2 tψ:1 seen:1 any:13 contents:1 paths:19 generalizes:1 zero:1 depending:2 lim:1 self:4 ideas:1 note:2 instance:1 take:1 coincide:2 fxb:2 heisenberg:34 multiple:3 normal:1 most:1 connected:4 ht:4 pair:5 class:1 url:1 coincides:2 nondegenerate:1 points:1 nuclear:2 left:1 physics:1 dot:1 quantity:1 texp:3 ending:1 gauge:1 substituting:3 analogue:4 trivial:2 find:5 fibre:23 based:1 title:1 aψ:2 written:1 only:3 explicitly:7 subsection:6 indeed:1 hamiltonians:1 local:2 oct:1 do:1 notation:3 means:3 dependent:1 expectation:1 da:1 aγ:69 ones:2 words:2 applying:1 dt:6 subscript:1 differentiating:6 evolution:19 bas:2 course:1 approach:2 arxiv:1 investigate:1 vht:1 fixed:1 bulgaria:1 reveals:2 set:2 computed:1 observer:8 hγ:14 notice:2 connections:1 depends:2 sec:4 result:7 subject:1 closes:1 satisfying:1 tensor:1 ways:1 pictures:7 review:1 uγ:30 state:25 classes:1 between:2 invariant:4 geometric:1 conditions:2 commute:2 ends:3 analogues:3 reproduces:1 key:1 modeling:1 holds:3 both:2 last:6 taking:2 according:10 agree:1 april:1 roman:1 finds:1 otherwise:1 ch:5 point:11 simple:4 continuation:1 ca:1 corresponds:2 represented:2 γba:2 simply:1 article:3 respect:12 described:7 transformations:1 basis:4 trajectory:1 locally:2 due:10 been:1 t2:4 basic:2 ph:3 define:1 corresponding:15 observable:10 quantities:6 concerning:2 xxx:2 systematic:1 derivative:2 instant:1 former:2 present:4 case:10 splits:1 pacs:1 value:6 will:2 euclidean:1 while:4 viii:4 unitary:3 almost:3 av:6 thus:4 equal:2 ii:47 itself:1 id:1 different:10 etc:2 φx:3 began:1 geometrization:1 connection:5 same:4 potentially:1 harmony:1 going:1 proved:1 infer:1 transferring:1 evolve:1 arrives:1 http:1 imply:1 hand:2 action:1 moment:1 changing:1 reference:3 avt:5 schr:19 fully:4 nevertheless:1 well:4 concrete:2 without:2 components:2 sets:1 latter:5 usual:5 bellow:1 just:1 being:2 composing:1 sofia:1 obtain:4 reviewed:1 transforms:3 aspect:1 world:5 adding:1 intersection:1 density:1 regarded:1 nonrelativistic:3 character:1 belongs:1 treatment:1 consideration:1 identical:1 march:1 eigenvalue:3 term:1 cf:12 possibly:2 vγ:19 using:5 unique:3 necessary:3 like:3 lost:1 follows:3 reduces:2 server:1 either:1 integrals:11 arbitrary:1 unperturbed:1 page:3 depend:3 mathematical:2 www:1 because:5 ole:1 some:8 ah:45 trends:1 transport:11 lead:1 shall:2 evolu:1 when:3 does:2 idπ:1 linearly:1 inrne:2 bg:2 equivalent:16 bo:1 bx:2 hilbert:16 bz:1 vh:3 discussed:2 dependence:1 essential:1 practical:1 act:1 idf:3 introduced:2 consequently:4 morphism:10 ψv:7 into:7 integral:17 references:4 operator:11 descriptions:3 additional:1 assumed:1 there:4 ψh:2 way:8 was:3 form:15 vanishing:2 but:6 iliev:17 repeated:1 ho:1 hm:6 line:5 true:3 october:3 coefficients:1 evident:2 morf:11 up:3 us:2 until:1 considered:2 below:4 verification:2 problem:2 called:4 eigenvector:4 mechanics:27 ab:4 constant:8 defined:7 certain:1 abstract:1 covers:1 general:7 proves:1 together:1 formulation:3 ay:1 archive:2 physical:1 integrability:1 no:2 commutes:1 generally:6 vanishes:1 rewriting:1 field:6 other:4 details:2 department:1 sufficient:2 conclusion:4 picture:51 briefly:3 elements:1 intend:1 sect:14 problems:6 update:1 bundle:90 transported:2 important:1 variable:10 dψ:2 dτ:3 lanl:2 governed:1 investigated:4 fact:7 time:17 observables:14 transports:1 original:1
|
quant-ph9806047.txt |@word ibid:1 concept:4 consider:2 scratch:1 forbidden:2 focus:1 four:3 eds:2 entropy:24 computation:3 reasoning:1 equiprobable:2 universe:2 deterministic:2 should:1 factoring:1 program:1 present:1 under:1 include:2 ingredient:1 straightforward:1 orthogonal:3 far:1 rise:1 account:1 results:1 worst:1 figs:4 summarized:1 experimentally:2 leads:2 perceived:1 internally:1 quantitatively:1 altering:2 die:1 mirror:2 solution:1 leave:1 unrelated:1 perceives:1 chuang:1 trr:1 inspection:1 consistent:3 direct:2 past:1 second:2 today:1 design:1 equal:1 greenberger:1 copenhagen:1 theories:1 shows:1 belief:1 subscripts:1 what:4 appear:2 apparatus:2 incompatible:1 consistently:2 experiment:6 above:1 reply:1 3a:5 increasing:1 ever:1 acknowledgments:1 developments:1 revealing:1 evolving:1 simultaneously:1 stance:1 proper:2 never:1 component:2 here:3 understanding:1 merwe:1 abandon:1 objects:2 separation:1 grundlagen:1 represented:1 respect:1 appears:5 ensembles:1 cerf:6 substance:1 exemplified:1 institute:1 inspired:1 larger:1 allows:3 completely:4 contradiction:2 ignoring:6 suggests:2 92a:1 involves:3 useful:1 projection:1 bounds:1 marginal:2 outcomes:5 brought:1 thought:3 total:1 use:1 sealed:1 superpositions:1 usa:1 live:1 negative:9 classically:4 depicted:2 going:1 examination:1 therefore:4 type:2 tell:2 diagrams:9 more:4 separated:2 introducing:1 bennett:1 pads:1 definition:2 becomes:2 odinger:8 interacted:1 berlin:2 particular:2 known:3 foundations:1 must:10 none:1 valued:1 locked:1 room:3 science:2 der:3 work:1 ρl:4 cat:19 values:2 three:1 tracing:4 believed:1 purports:1 example:3 unconditional:1 compare:1 computers:1 indicated:1 predict:2 inaccessible:1 share:1 pieces:1 states:6 numbers:1 sense:3 inseparability:1 cushing:1 occur:2 verlag:1 cloning:1 information:39 respective:2 monitoring:1 rather:3 travel:1 holds:1 arrangement:1 very:1 criterion:2 pure:2 mysteries:1 explores:1 description:5 reconciled:1 after:3 detectors:1 diagram:18 summarize:1 elusive:1 imply:2 register:1 ghz:1 element:3 fortunately:1 so:3 allow:3 correlation:3 order:2 horne:1 serving:1 interpretation:5 produces:2 indeed:4 over:5 fall:1 displayed:1 lahti:1 course:1 experiments:4 through:1 statistical:1 still:2 its:6 before:1 perfect:1 monotonicity:3 monitor:1 decay:2 actually:1 lr:3 fig:29 constitutes:1 instruments:1 hidden:3 might:1 macroscopic:1 them:4 incompleteness:1 contention:1 views:1 prevented:1 propose:1 repercussions:1 framework:1 they:4 half:2 inception:1 insisting:1 now:4 hall:1 nor:1 possess:1 represents:1 fully:2 university:4 sufficiently:1 reasonable:1 each:6 found:1 entirely:1 cliffs:1 traces:1 side:1 realism:2 prevailing:1 development:1 mental:1 ed:2 wehrl:1 deterministically:1 owing:1 expect:1 entering:1 measurement:52 quantum:121 laboratory:1 operation:1 beyond:1 eigenstates:3 special:1 assigns:1 living:2 belgian:1 matrix:2 furthermore:1 since:6 rev:7 research:1 particles:7 attracted:1 investigation:1 eprint:2 denoted:1 ref:1 independence:1 common:1 earlier:2 log2:1 theory:30 quite:1 reason:2 truthfully:1 california:2 york:1 imagine:1 intermediate:1 inevitable:1 milburn:1 reflect:4 pairs:1 language:1 created:4 tenets:1 creates:1 doublet:1 transfer:1 consequence:2 repeats:1 first:1 rooted:1 probability:2 variables:7 kafatos:1 reflected:2 peculiarity:1 another:2 carry:1 impossible:3 precisely:1 necessarily:2 exists:2 needed:1 introduction:2 achieved:1 system:40 least:1 their:10 1b:2 postulate:2 perfectly:5 national:1 gives:1 collapse:3 relationship:1 cats:1 tool:1 acquire:1 serve:1 accurately:1 measurable:1 mathematische:1 part:5 representing:1 peculiar:2 observed:2 wootters:1 third:1 princeton:1 namely:1 preparation:1 historical:1 outcome:3 projections:4 epr:31 unchanged:1 conventional:1 say:5 emphasizing:1 disturbing:1 disjoint:2 clearly:1 ray:3 affairs:1 subsystems:1 decorrelated:1 built:2 mermin:4 uncorrelated:2 latter:3 isolated:2 note:3 contact:1 take:1 forces:1 objective:1 new:2 detector:1 unperturbed:1 heisenberg:2 fundamental:4 shall:2 circulated:1 object:2 most:1 demise:1 comparing:1 pair:10 speakable:1 measured:14 why:2 manifested:1 constructed:1 observation:4 consequences:1 considered:3 chicago:2 coincides:1 physica:1 reflecting:1 principle:6 mechanical:4 physics:4 notion:1 fact:5 laws:1 shor:1 show:5 violation:4 supported:1 implying:2 attempts:1 relation:3 find:1 paradoxes:5 q1:9 naturwissenschaften:1 q2:9 based:4 knowledge:1 parameters:1 title:1 situations:2 explain:1 than:2 entities:1 only:5 version:2 essence:2 local:1 interested:1 do:2 his:1 closed:2 quantph:2 king:1 zurek:3 october:1 joint:4 cannot:7 words:4 3b:2 prentice:1 prime:1 reveal:1 evolution:1 podolsky:5 arxiv:1 yield:2 paper:3 predicted:1 weaver:1 wrote:1 view:11 reveals:1 set:1 observer:16 ancillae:6 physically:1 violated:1 correlations:16 maximum:1 relative:3 see:7 result:5 logically:1 discussions:1 terms:2 theoretic:7 aro:1 closer:1 recording:2 inequalities:3 pictures:2 nature:5 yet:2 symmetric:1 halves:1 state:36 correctly:1 between:21 boundary:1 pictured:1 publishers:1 triplet:1 recently:2 creating:1 complementary:1 importance:4 darpa:1 attention:2 however:5 prediction:2 reproduces:1 4a:2 assess:1 wellknown:1 suggested:2 both:7 essentially:1 uncertainty:6 according:2 attributed:1 σz:24 σx:14 experimental:1 unitarily:1 point:4 reasons:1 whatever:1 scientifique:1 moreover:1 venn:1 ferrero:1 speak:1 pp:1 described:4 teaches:1 create:1 due:3 been:1 extraction:2 describes:2 combined:2 quic:1 certain:1 degrees:2 ph:1 prototype:1 systems:3 obtained:3 6b:1 describe:3 corresponding:1 received:1 offered:1 wheeler:1 else:1 assert:2 fund:1 zero:1 confers:1 denote:1 spin:10 those:1 indivisible:1 case:4 unlike:1 undermines:1 quantenmechanik:2 contingencies:1 single:2 value:1 excited:1 will:1 while:14 situation:8 revisited:1 property:1 resolved:1 laflamme:1 von:4 thus:7 non:3 encountered:1 ii:1 need:2 itself:3 partner:2 busch:1 technology:1 monroe:1 formalism:2 grant:2 suggest:2 orthodox:4 radiation:1 lett:3 same:8 any:8 member:2 undecayed:1 unity:1 parts:1 quant:1 split:1 regime:2 infer:3 status:1 independent:2 calculation:1 used:1 effortlessly:1 reinterpretation:1 upon:2 ponder:1 hand:5 phy:2 arrived:1 unpublished:1 entanglement:5 repeatable:1 recent:2 relies:1 schr:8 center:3 records:1 well:5 analysis:3 bohr:7 bohm:3 academic:1 directly:1 without:5 mod:1 landmark:1 position:1 arising:1 drawing:2 left:5 manifold:1 just:3 being:1 when:3 accurate:2 detail:1 underlying:3 atomic:3 predicts:1 immediately:1 illinois:1 ithaca:2 portrayed:1 previous:2 adt:1 kluwer:2 density:2 decayed:2 bell:7 character:1 pasadena:1 treatment:3 versa:1 theorem:3 nos:1 5a:2 remaining:1 momentum:1 5b:1 real:3 spinless:1 increased:1 demands:1 possible:6 kellogg:1 englewood:1 five:2 entangled:7 resolves:1 press:4 using:4 bit:4 projects:1 like:1 counterintuitive:1 necessary:2 incompletely:2 particle:10 exploiting:1 agreement:1 remind:1 either:1 always:1 popular:1 essential:1 adami:6 accessible:3 right:5 neumann:4 classical:28 conditional:6 springer:3 dead:2 learn:2 specified:1 complementarity:4 extended:1 entropic:1 informationtheoretic:1 describing:1 fourth:1 measurements:8 recorded:1 extensively:1 counterfactual:1 does:6 conclusions:1 refer:2 measuring:6 measures:3 scientific:1 dieks:1 wavefunctions:3 confer:1 how:3 inherent:1 relating:1 obscured:1 properties:2 gained:1 comparison:1 about:8 would:6 anything:2 freedom:2 certainty:1 recognized:1 reduced:2 shared:4 consequently:1 gamma:6 mathematical:4 cambridge:2 wineland:1 communication:3 into:8 within:1 integral:1 nsf:1 dissatisfaction:1 down:2 device:10 because:2 references:1 einstein:10 classicality:1 uncertainties:1 van:1 devices:23 conceivably:1 area:1 assumed:1 strictly:1 there:3 cherished:1 long:1 much:1 way:3 subsequent:1 analyze:1 was:6 faulted:1 complete:4 metastable:1 jun:1 gedankenexperiment:1 but:3 cloned:1 construction:1 alive:1 atom:10 radioactive:1 trying:1 true:1 collapses:1 he:3 absent:1 made:1 probabilistic:1 up:4 us:12 entails:1 dordrecht:2 below:2 reflects:1 demonstrate:1 problem:1 piece:1 agree:1 entropies:10 mechanics:15 ab:2 polarizations:3 6a:1 implications:1 abstract:1 measure:5 am:1 general:3 reinstated:1 examine:1 arises:2 our:1 spite:1 physical:21 again:2 mutual:10 paradox:12 no:3 wavefunction:10 rosen:5 vanishes:5 meekhof:1 reality:40 conceptions:1 other:13 shannon:5 you:1 out:2 illusion:1 conclusion:2 conclude:3 picture:4 repeat:1 superposition:5 divincenzo:1 preceding:1 problems:1 a1:16 a2:16 suited:1 variable:1 fundamentally:1 zeilinger:1 independently:1 correlated:5 implies:3 coupling:1 vice:1 assume:2 4b:2 together:2 observe:1 incomplete:4 ternary:1 time:2 observables:1 decoherence:2 quantity:2 requires:1 having:1 unspeakable:1 once:1
|
quant-ph9806048.txt |@word represent:2 logarithms:1 epeau:1 sci:1 consider:2 limited:2 interference:5 magnetic:2 particular:1 focus:1 unchanged:2 four:5 postponing:1 code:1 computation:15 involved:3 contributions:1 particles:1 anticipation:1 leung:2 equivalence:2 factoring:1 program:1 device:1 protocols:1 vandersypen:1 sent:1 supported:1 straightforward:1 shifters:6 implicitly:1 rise:1 wave:4 experimentally:1 difference:1 matrices:2 paz:2 materialize:1 interferometry:2 exits:2 presented:1 issue:1 cascading:1 large:2 discrete:2 convenience:2 vector:2 small:5 optics:6 upper:4 deutsch:1 translating:1 second:7 cost:1 further:1 dynamics:4 implemented:4 port:6 theory:1 even:1 nonlinear:1 stands:3 apparatus:1 dephasing:1 debate:1 experiment:5 new:3 3a:1 method:6 implementable:1 edited:1 full:1 ibid:2 tags:1 respectively:1 realizations:2 component:2 teleportation:11 here:7 objects:1 represented:3 path:11 entire:1 observing:1 cerf:2 incoming:1 institute:1 shift:2 inspired:1 goldwasser:1 allows:1 controversy:1 suggests:2 resulting:2 procedure:1 action:1 resonance:3 implement:1 placing:3 involves:1 king:1 composed:1 technique:6 followed:1 resurrected:1 claim:1 requiring:1 namely:1 explained:1 polarizers:1 logical:3 outcomes:1 turchette:1 nonlocal:1 use:6 reflected:3 superpositions:3 usa:1 commun:1 distinct:1 contains:1 toffoli:1 arms:1 few:1 noting:1 therefore:1 taken:1 goldenberg:1 entails:1 today:1 more:2 introducing:1 formally:1 duality:3 gyroscope:1 tested:2 excellent:1 known:4 foundations:1 iii:1 must:1 none:1 lengths:1 ma:1 science:3 setup:8 work:1 labeled:1 resources:1 following:2 example:4 proof:1 control:3 heart:1 figure:1 process:1 bennett:1 implementations:1 states:4 slit:2 performed:1 sense:3 simulation:5 distinguishable:1 information:4 end:2 kwiat:2 provide:1 acts:3 algorithms:6 far:1 simplifies:1 gate:20 roy:1 brassard:3 product:2 description:3 earlier:1 diagram:1 produce:3 designed:2 society:1 horizontal:4 choice:1 realized:2 branches:1 dynamical:1 effective:2 computations:1 light:5 lines:1 correspond:1 su:2 element:1 rather:3 so:5 fundamental:2 media:1 representation:4 subsequently:1 order:3 operations:1 gershenfeld:2 interpretation:1 produces:1 indeed:1 over:1 fredkin:3 soc:2 interpreted:1 stability:1 experiments:2 through:3 argued:1 existence:1 still:2 ieee:1 its:3 before:2 destructively:1 horizontally:5 supplemented:1 teleporting:1 thumb:1 processed:1 polarizing:5 scully:3 actually:1 forms:1 wineland:1 absence:1 itano:1 fig:29 annual:1 correspondence:2 non:6 photodetection:1 thereby:1 splitter:23 universality:2 polarizations:2 elementary:2 anticipated:1 nsf:1 instead:1 1b:1 now:1 day:1 easily:3 eventualities:3 englert:1 always:3 level:4 kerr:2 mccall:1 fringes:4 transmitted:1 mode:3 each:5 crossing:4 references:1 2n:6 side:1 schemes:1 idea:1 interferometer:13 sands:1 factorization:1 entering:1 measurement:6 quantum:105 laboratory:1 operation:3 out:1 divincenzo:2 shown:6 belgian:1 matrix:2 space:1 furthermore:2 since:4 induces:1 research:1 increase:1 acting:5 eprint:3 performs:1 denoted:1 surprise:1 size:2 ref:1 interchanging:1 shows:1 reck:1 after:4 linear:8 given:2 possibility:2 standard:3 california:2 york:1 jozsa:1 milburn:1 pairs:1 language:4 inspection:1 could:2 phy:2 counterpart:1 circuit:31 unknown:1 first:4 origin:1 initial:7 probability:1 encoding:1 third:1 number:7 reaches:2 engenders:1 simplified:1 leighton:1 array:1 precisely:2 several:3 hood:1 illustrate:1 little:1 errors:1 likely:1 similarly:2 introduction:1 leading:1 1c:1 least:1 1a:3 their:2 returns:1 intermediate:1 too:2 realization:15 scheme:3 bits:9 1l:2 gives:1 implements:1 lange:1 exactly:2 optical:47 shifter:3 manifestation:1 recourse:1 believe:1 than:4 havel:1 observed:1 polarized:7 target:3 wiesner:1 intensity:1 tunable:1 final:7 project:1 whenever:1 symposium:1 pairwise:1 amplitude:1 represents:1 providing:1 cloning:1 bertani:1 correction:3 yielding:1 miquel:2 say:2 manner:1 demonstration:1 any:6 viewed:1 relatively:2 paths:16 generalizes:1 depict:1 genuine:1 depending:2 polarization:28 build:1 performance:2 coincide:1 aro:1 lectures:1 shall:1 probed:1 price:2 correlation:1 reach:2 most:1 involving:4 connected:1 successive:1 pair:1 measured:2 mach:4 constructed:4 observation:2 nonlinearity:1 characterizes:1 considered:1 detectors:2 physica:2 traditional:2 feynman:3 proceedings:1 part:1 principle:4 mechanical:3 usual:1 typically:1 fact:4 decidedly:2 shor:2 simulate:3 show:1 detection:2 random:2 chuang:4 lloyd:2 yurke:1 analogue:1 decoding:1 trivial:3 networks:4 occupation:1 based:1 simulating:2 implementation:7 distributed:1 should:1 technologically:1 only:7 sequential:2 factor:1 bernstein:1 local:1 do:1 erasure:1 quantph:1 means:1 dependent:1 beams:2 zurek:2 simplest:1 straightforwardly:2 addison:1 recombining:1 beam:39 cannot:1 words:2 3b:1 dr:1 lossless:5 prime:1 fields:1 arxiv:1 yield:1 acknowledgments:1 whether:1 contrast:1 london:2 communicated:1 set:1 constructing:1 exists:1 achieved:4 physically:1 national:1 testing:1 flip:1 achieves:1 see:15 computer:7 result:3 discussions:1 terms:1 relabeling:1 arm:7 subject:1 appear:2 phases:1 exploited:2 braunstein:3 interacting:1 channels:1 matter:3 pattern:1 mabuchi:1 opening:1 label:2 symmetric:5 initially:4 state:26 difficulties:1 identification:1 between:12 nuclear:2 reading:1 discovery:1 perfect:1 ends:1 never:1 recently:1 vertical:4 complementary:1 qubits:22 darpa:1 screen:1 analogues:1 however:4 interfere:3 implementing:1 incident:1 key:1 emitter:1 thank:1 both:6 essentially:2 outcome:2 flipping:1 limits:1 many:1 uncertainty:1 flipped:3 etc:2 present:5 logic:11 qubit:30 disappears:1 0l:3 comment:1 splitters:15 adjusted:1 relevant:1 point:3 simple:8 wootters:1 corresponds:6 coincidence:1 dimensional:1 exploit:1 grants:1 simply:6 applicability:1 constructively:1 respect:3 throughout:1 considering:1 pp:1 described:2 transformations:4 puts:1 basis:1 detected:3 been:4 combined:1 quic:1 basic:2 ph:3 abstract:1 lett:9 obtained:4 arises:1 controlled:7 concerning:1 photon:38 bulk:2 fund:1 systematic:1 last:3 spin:1 those:3 instructive:1 applied:1 laser:2 exponential:3 solid:1 kimble:1 value:3 will:3 while:8 walther:1 behavior:1 error:7 rotator:2 property:1 35th:1 leaves:2 characterizing:2 klauder:1 versus:1 unitary:9 laflamme:1 vol:1 drawbacks:1 thus:5 them:1 itself:2 im:1 dual:1 exiting:1 technology:3 monroe:1 different:2 grant:1 perform:3 pay:1 make:1 radiation:1 indistinguishable:1 same:7 clearly:1 shifts:2 drawback:1 quant:3 avoids:1 finite:1 uhl:1 guises:1 used:4 barenco:2 zehnder:4 receiver:1 effect:3 counterparts:1 running:1 entanglement:2 relies:1 interferometers:2 lower:4 task:1 arbitrarily:1 modes:3 largely:1 nevertheless:1 locality:1 well:5 vaidman:1 severe:1 without:2 experimental:4 components:4 simulated:3 paradigm:1 prevention:1 left:1 gates:22 assembling:1 just:5 less:1 being:3 dowling:1 via:4 positions:1 paul:1 yamamoto:1 speed:1 yet:2 note:2 enters:2 density:1 photons:5 bell:1 source:1 operator:1 pasadena:1 location:19 theorem:1 input:12 transformation:4 opt:1 rotators:1 disappearance:1 devised:1 multiport:1 possible:1 regeneration:1 dark:1 kellogg:1 entangled:2 vacuum:1 press:1 using:21 bit:17 scientifique:1 correcting:2 detector:2 mod:1 vertically:1 interestingly:1 performing:2 pol:12 specific:2 yields:1 arbitrary:5 setups:2 output:8 reduced:1 terminology:2 adami:2 accessible:1 parity:1 classical:11 sequence:1 conditional:5 polynomial:2 growth:1 cr:1 scale:1 avoid:1 conditionally:4 exit:3 provides:1 assuming:1 proc:3 collaboration:1 inserting:1 noise:2 substitutes:1 scientific:1 indicated:1 drift:1 equivalent:2 illustration:2 constructive:1 machzehnder:1 wesley:1 substituted:1 reduces:1 although:2 become:1 hadamard:16 prepared:1 cory:2 about:2 central:1 benches:1 constraint:1 tracing:1 discussed:1 o:4 ports:7 remains:1 act:1 mixed:1 eight:1 ou:1 introduced:1 consequently:1 raised:1 rev:18 presence:1 previously:1 into:4 within:1 splitting:3 cascaded:1 phase:18 appropriate:3 promise:1 einstein:1 balanced:3 loc:9 additional:1 support:1 there:2 start:1 accordingly:3 mandel:1 way:1 translate:2 was:4 naturally:1 function:1 eraser:1 form:2 jun:1 delayed:1 but:6 cloned:1 construction:1 atom:1 line:2 grouping:1 irreversible:1 utilizing:1 made:1 improved:1 understood:1 circuits:11 up:4 devices:7 achieving:1 placed:1 below:5 limit:1 reflects:1 spectroscopy:1 demonstrate:1 stages:1 nature:1 mechanics:2 promises:1 associated:1 computing:2 universal:5 am:2 general:4 peres:1 single:11 rule:1 interchanged:1 simulations:1 prasad:1 corresponding:1 physical:6 again:1 us:2 no:3 dashed:1 ekert:1 wavefunction:1 vanishes:1 meekhof:1 preventing:1 other:7 test:2 conclusion:1 optically:3 explaining:1 elements:4 conveys:1 superposition:3 zhou:1 models:2 uniformly:1 interferometric:2 chance:1 variable:1 zeilinger:2 independently:1 correlated:1 algorithm:2 physics:1 proposed:4 required:3 together:1 original:2 teleported:6 time:1 cleve:1 ultrafast:1 decoherence:1 requires:1 having:3
|
quant-ph9806049.txt |@word represent:2 gu:5 partial:1 consider:11 pointing:1 secondly:1 caused:1 lack:1 desirable:1 focus:1 produce:1 existing:3 four:8 jawaharlal:1 quadrature:1 subtle:1 2n2:1 go:2 expressions:3 whose:4 detects:2 depend:1 violate:9 producing:1 concerned:1 tr:20 tp:5 passage:5 finally:3 squeezing:9 present:2 under:8 include:1 overlaps:2 p2:11 belonging:3 straightforward:4 orthogonal:8 very:5 studied:3 wave:4 refractive:1 mixing:2 experimentally:2 difference:1 bringing:3 condition:6 arrange:1 splitter:1 e44:2 level:2 transmission:2 convenience:1 vector:3 destroying:1 recall:1 indices:1 iπ:1 shows:1 optics:2 equation:2 application:1 talked:1 compensated:1 consistent:1 among:1 measurable:2 literature:2 matrices:1 second:6 traveling:1 pass:2 further:6 implemented:2 click:1 canonical:11 even:2 what:5 giving:1 section:3 selected:1 symbolically:2 expressed:1 indian:1 above:15 obvious:1 increasing:1 consisting:1 exercise:1 paradoxical:1 satisfy:1 outgoing:1 full:1 simultaneously:3 chose:1 respectively:4 component:2 here:15 following:9 q2:4 separate:1 directions:6 consideration:2 along:8 observing:1 z1:46 interpret:1 calculate:4 obtained:3 search:1 eij:2 parameters:4 institute:1 involved:2 study:6 vectors:2 allows:1 reason:2 amount:2 simultaneous:1 products:2 action:10 suitable:4 studies:1 eigenvalue:1 involves:1 formulated:1 useful:1 conclusions:1 family:3 kinematically:2 namely:2 outcomes:2 unitary:3 counts:3 total:3 analyses:2 unit:2 plot:1 use:3 figure:10 would:2 nehru:1 probabilities:4 positive:2 give:3 predictions:1 hilbert:2 classically:2 linear:7 therefore:9 hv:13 themselves:1 analysing:1 type:29 theoretical:2 more:11 separated:1 inaccessible:1 composite:1 becomes:3 operators:21 validity:1 warm:1 basically:1 proceed:3 particular:6 known:2 given:18 iii:2 capturing:1 must:2 high:1 keeping:1 r2:5 integrating:1 science:1 setup:5 work:3 det:8 dev:1 theories:2 labeled:1 ij:1 values:23 tracing:3 canonically:2 nonsingular:1 arrive:2 averages:2 example:6 performed:1 point:1 grained:1 indicated:1 mirrors:1 process:2 role:1 arise:1 india:3 define:1 accept:1 dependence:1 states:86 indicates:2 minimum:1 14b:1 numbers:3 allowed:2 counting:1 occur:1 axis:4 information:2 respective:1 end:1 guru:1 provide:1 discussion:1 means:1 range:1 write:1 how:1 nontrivial:5 pure:9 iθ2:3 instead:1 factorise:1 parameter:1 sin:27 inputs:1 product:6 squeezes:2 explores:2 description:10 undergoing:1 singular:3 may:9 after:12 blocks:1 pqm:1 diagram:1 consequence:3 explored:2 multiplication:1 choice:4 unentangled:2 types:2 tranformation:1 pereira:1 dynamical:2 e22:2 light:1 counter:3 su:1 element:1 rather:1 cannot:2 so:10 automatically:1 allow:4 correlation:2 sudarshan:1 definitions:1 looking:2 order:4 typical:1 horne:3 wigner:11 eigen:5 developed:1 over:6 originally:1 encounter:1 ended:1 thermal:3 experiments:2 through:11 statistical:1 omitting:1 mentioned:1 existence:1 still:3 its:3 before:4 derive:5 group:4 chosen:5 exact:1 generalise:2 forms:1 whether:1 detected:2 degrees:1 choose:6 omitted:1 hidden:14 might:1 alter:2 them:3 motivated:1 greater:1 components:1 material:1 i8:4 introduce:1 obeyed:1 yx:1 walls:2 course:1 they:6 half:1 rotation:2 now:8 discuss:1 easily:2 february:1 iθ1:3 stated:1 realist:4 fully:1 university:1 classified:1 hermitian:8 ensemble:1 inequality:20 mode:55 reasonable:1 each:16 accommodated:1 side:4 realism:1 constraints:2 subsystem:1 as1:1 disregarding:1 formulate:1 classifying:1 experiment:1 energy:1 gaussian:13 related:3 investigated:1 connect:1 measurement:4 quantum:49 our:13 beyond:2 eq:2 special:3 out:10 projections:1 emerges:2 shown:2 matrix:18 space:10 quantify:1 since:2 crucial:2 research:1 particles:1 contained:1 coincidences:3 i3:1 common:1 benjamin:1 theory:11 written:2 derived:1 diagonal:8 possibility:4 effect:1 small:1 completely:3 york:1 pramana:1 detecting:4 finite:1 derivation:2 language:1 applications:1 starts:1 could:7 diminished:1 nonnegative:3 turn:2 plane:5 hence:3 undergo:1 onto:1 first:13 initial:4 features:4 probability:8 striking:1 feel:1 relate:1 variables:2 number:8 restrict:2 entanglement:8 obey:6 xy:4 done:2 relations:2 directly:2 carry:1 open:1 several:1 passes:1 differ:1 grangier:1 temperature:3 needed:1 introduction:2 system:7 least:8 their:9 campos:1 assumption:6 rates:23 constants:1 calculations:1 superscript:2 e55:3 scheme:2 final:2 observations:1 originating:2 preserved:1 relationship:1 centered:5 sin2:5 exactly:1 transverse:1 optical:11 too:1 somewhat:1 yurke:1 z4:26 representing:2 than:4 coefficients:1 center:1 distance:4 kind:2 polarized:1 last:2 distinguishes:1 z1n1:1 rate:3 preparation:2 matter:3 determined:1 were:2 outcome:1 distinguished:2 enhancement:2 pre:1 sp:2 ev:1 generality:1 well:7 mind:1 already:2 manner:1 conjugate:2 need:4 seen:4 unaffected:1 saw:1 any:19 elsewhere:2 gives:1 subsystems:4 angle:3 zero:2 depending:2 responsible:1 able:1 polarization:1 instance:1 potential:3 absorbed:1 take:3 objective:3 detector:3 strengths:3 machinery:1 subscripts:2 electric:1 trace:2 centre:1 analyse:3 systems:1 z2:44 most:5 connected:3 locality:7 preliminary:1 pair:1 class:1 constructed:1 observation:1 consequences:1 considered:3 calculated:5 sometimes:1 detectors:6 counted:1 part:1 principle:3 exp:2 mechanical:23 usual:1 physics:5 notion:2 fact:5 quantity:1 emerging:1 axes:2 show:4 violation:37 detection:1 dependences:1 factorize:2 purely:1 registers:2 solutions:1 calculable:1 carefully:2 interpretation:4 d2:15 find:1 substituting:1 d1:8 q1:8 rev:14 q3:7 removed:6 based:4 q4:4 dividing:1 e11:3 situations:3 less:1 outside:1 should:5 lemma:3 only:4 explicitly:2 candidates:1 subsection:1 arvind:4 factor:2 various:8 local:7 interested:1 hope:1 do:5 predict:1 mixture:1 sense:5 get:6 dependent:1 beams:7 express:3 expectation:9 truly:1 ρcs:1 beam:7 ones:3 closely:1 new:1 combinations:3 compute:2 represented:2 disentangling:1 evolution:2 settings:1 fields:3 arxiv:1 remove:1 reid:1 iisc:1 paper:5 roger:1 predicted:1 though:6 fixed:3 qm:55 valid:1 set:9 computed:2 achieved:1 imposing:1 generally:2 violated:5 correlations:9 lett:8 maximum:1 connections:1 opposite:6 intensity:3 individual:6 result:4 w0:19 discussions:1 led:1 violates:2 subject:2 annihilation:1 said:2 capacity:1 inequalities:57 14a:1 ways:2 dutta:3 nature:5 definite:1 label:1 symmetric:1 state:97 future:1 identification:2 between:7 invariant:2 subscript:1 email:1 available:2 undertaking:1 comparable:1 venugopalan:1 terms:3 vertical:1 opening:1 however:6 incident:2 extent:1 distinguish:1 originates:1 both:4 cos:29 prescription:1 always:3 many:1 taking:1 uncertainty:1 equal:6 attributed:1 agree:1 propagation:11 connection:3 hω:1 figures:3 symplectic:2 receives:1 interesting:3 attributes:1 passing:2 expression:3 workers:1 experimental:1 otherwise:2 splitters:1 relevant:2 cn:2 bell:51 simple:4 removal:1 corresponds:3 coincidence:32 dimensional:3 concluding:2 maintained:1 adding:1 cs:44 respect:5 throughout:1 factors:3 entangling:1 considering:2 peng:1 described:3 transformations:16 basis:9 addition:1 equations:4 due:1 been:4 implicit:1 reduction:3 much:1 coarse:1 interest:1 basic:1 expected:2 ph:1 z3:28 fig:4 direction:19 corresponding:11 deeper:1 received:1 quantities:2 sufficient:1 photon:28 zeilinger:1 coherent:26 observe:1 angles:7 demand:1 c2:3 c1:4 spin:2 spirit:1 those:2 case:11 p3:7 multi:1 p1:13 look:2 p4:4 tanh:1 straight:1 expanded:1 examine:1 value:3 choices:2 will:16 while:6 ought:1 observable:1 squeezed:13 situation:3 property:3 leaves:1 stoler:3 klauder:1 a21:1 detailed:1 larger:1 thus:8 discrepancy:1 iv:2 ii:2 itself:1 kt:1 ernet:1 alone:4 different:8 develop:1 multiphoton:5 etc:3 perform:3 make:3 radiation:4 admit:1 same:7 clearly:3 rules:1 complex:3 quant:1 emphasize:2 mixtures:2 undergoes:2 defines:1 ghosh:1 events:1 status:1 independent:7 calculation:3 used:9 context:2 see:8 i1:1 defy:1 i2:5 upon:2 i4:1 hand:14 effectively:1 constraining:1 phy:1 variance:1 infinite:1 identity:1 gauss:10 modes:25 possibly:1 nevertheless:1 makes:1 underlies:1 polarisation:18 epr:1 remain:2 analysis:15 obviously:2 bohm:2 without:3 e66:2 incapable:2 ujk:1 kets:1 ekert:1 left:4 teich:1 construct:1 just:1 generalisation:2 being:6 photo:1 observed:1 rotated:1 obtain:1 actions:1 assigned:1 sources:3 underlying:3 aspect:1 immediately:1 facts:1 followed:1 g0:2 previous:2 oriented:1 signal:1 density:8 absorption:1 photons:16 measure:4 passive:17 lattice:1 disparity:1 setting:1 treatment:2 versa:1 input:3 violations:4 transformation:12 momentum:1 build:1 identical:2 aspects:2 depends:1 represents:2 conclude:2 iβ:1 results:3 possible:9 finding:3 rotate:2 entangled:13 vacuum:7 using:7 advanced:1 ruled:1 loss:1 counterintuitive:1 necessary:1 like:2 lost:1 identifying:2 follows:2 reduces:4 detg:1 specific:5 imposes:1 yields:2 either:6 integrals:1 arbitrary:13 output:2 conclusion:1 variant:1 essential:2 replacement:1 right:3 classical:31 sequence:1 simplicity:2 easy:2 some:11 examples:2 specified:1 proper:1 little:1 2qm:1 neglecting:1 ourselves:1 kimble:1 happens:1 unbounded:1 describing:1 lead:4 electromagnetic:7 measurements:11 recorded:2 extensively:3 overlap:1 squeeze:2 does:7 statements:1 assuming:2 propagating:1 demonstrated:1 refer:2 preassigned:1 noise:1 11a:1 scientific:1 11b:2 equivalent:1 analysed:3 disappeared:1 step:2 yorke:2 nowhere:1 become:1 bangalore:2 refers:1 normalisation:1 properties:3 stage:1 regarded:1 about:5 simplest:1 actual:2 anything:2 cn1:12 freedom:3 prove:1 discussed:1 a3:4 reduced:2 mukunda:4 r1:5 obeys:4 act:1 mixed:6 eight:1 ou:2 introduced:1 block:3 integration:1 conserving:3 contains:1 real:1 presence:1 maxwell:2 into:2 within:3 definitely:2 kk:5 negative:2 phase:4 appropriate:8 because:2 operator:5 capable:2 refined:2 conceptually:1 classicality:1 removes:1 unambiguous:1 weight:1 deal:1 assumed:2 there:2 question:1 transform:1 why:1 start:2 describes:1 mandel:1 way:4 forward:1 was:2 function:15 complete:3 form:8 registered:1 jun:1 but:8 displacement:1 change:1 taken:1 understandable:1 delta:1 line:1 nonclassicality:7 true:2 considerable:1 partially:1 count:24 arranged:1 polariser:26 wish:2 up:6 us:3 placed:5 below:1 converted:1 content:1 distribution:15 quantised:3 similar:5 average:2 clear:1 mechanics:4 bearing:1 required:2 defined:8 certain:2 ak:1 describe:1 general:22 dξ:8 clauser:2 single:12 exist:1 dλ:13 saleh:1 formulation:2 journal:1 formalism:3 distributions:5 check:1 physical:2 again:1 functions:4 compared:2 e33:3 know:1 no:8 amounts:7 whereas:3 wavefunction:1 when:12 detail:3 field:22 other:22 remarks:2 gξ:1 department:2 polarisations:6 optically:4 a46:1 draw:1 elements:4 superposition:2 a12:5 hindrance:1 nonclassical:26 a1:54 meaning:2 a2:47 a4:4 observables:2 variable:18 simon:3 implies:2 vice:1 assume:2 typically:1 interval:2 having:2 equivalently:1 time:2 n1:25 n2:29 starting:3 original:4
|
quant-ph9806050.txt |@word consider:4 leads:1 grateful:1 nwo:1 localized:3 sch:1 aug:1 permanently:1 applied:2 very:3 electron:14 figs:1 stays:2 experimentally:2 difference:1 condition:1 entire:6 level:1 transmission:3 t2:2 t0:9 t1:2 large:1 small:1 attracting:1 elegant:1 second:2 index:1 dephasing:1 current:13 experiment:1 new:1 coefficient:3 respectively:2 here:3 understanding:1 behaviour:1 relaxation:1 equations:2 obtained:2 institute:1 study:3 allows:2 fourier:1 wetenschappelijk:1 via:1 useful:1 scales:1 modulated:1 wis:1 total:2 heiblum:1 would:4 probabilities:1 weizmann:1 visit:2 therefore:2 onderzoek:1 type:3 introducing:1 israel:1 rehovot:1 becomes:4 odinger:6 particular:1 science:1 equation:3 work:1 ρl:3 macroscopically:1 my:2 example:1 give:1 process:3 states:4 slows:1 monitoring:2 provide:1 chemical:1 numerous:1 description:2 realized:2 short:1 whenever:2 explicit:1 interrupted:1 element:1 so:4 talk:1 reservoir:1 experiments:1 through:1 looks:1 statistical:4 its:1 blocked:1 acknowledge:1 solving:3 actually:2 detected:1 lr:2 systems:1 ωlr:5 effects:1 now:1 yu:1 2t:1 term:1 university:1 traced:1 possibilities:1 accommodated:1 el:3 financial:1 mesoscopic:1 expect:1 measurement:9 quantum:8 our:1 damped:1 collector:4 special:1 out:3 shown:4 matrix:9 umansky:1 since:3 rev:4 denotes:1 evaluation:1 integrated:1 linear:3 barrier:3 diagonal:1 possibility:1 e1:5 e2:5 interaction:1 transition:1 voor:1 motion:1 first:3 there:1 probability:3 number:2 done:1 given:1 iω0:5 eqs:6 behaves:1 system:12 their:1 ballistic:1 collapse:8 continuous:6 part:1 manifestation:1 schr:6 determines:1 double:4 rate:3 a44:2 determined:2 nederlandse:1 treated:1 occupies:2 occupied:7 any:1 eq:4 zero:1 latter:3 instance:3 contact:8 finding:2 detector:20 connected:1 measured:2 average:3 electrons:4 exp:1 mechanical:2 physics:2 fact:1 show:2 mahalu:1 relation:1 organisatie:1 schenzle:1 find:3 d1:10 based:1 b116:1 should:1 going:1 hamiltonians:1 mixture:5 means:3 cannot:2 nonequilibrium:1 during:1 evolution:5 continuum:1 dpp:1 approach:1 arxiv:1 investigate:1 including:1 body:1 observed:2 electrostatic:1 result:3 discussions:2 mechanically:2 µr:5 µl:5 between:5 conditions:2 nature:1 initially:3 attention:1 however:4 rostock:1 both:1 last:1 many:1 hint:3 april:1 whole:1 finds:2 point:8 cf:1 height:1 fruitful:1 described:4 observing:1 due:1 been:1 workshop:1 expected:1 microscopic:1 ph:2 fig:4 dots:4 arises:1 corresponding:2 influence:1 coherent:2 c2:3 c1:2 case:4 solid:1 value:2 near:2 hdd:3 behavior:3 situation:1 coupled:2 technology:1 different:3 lett:1 same:2 quant:2 development:1 i1:9 i2:2 effect:2 flows:1 hand:1 harris:1 potentials:1 recent:2 off:1 nevertheless:1 well:3 without:2 left:7 buks:3 obtain:1 thanks:1 yet:3 density:10 shuster:1 iρ:1 nazarov:1 b56:1 possible:1 corresponds:1 increases:2 using:2 particle:1 follows:1 either:2 reduced:3 right:7 sight:1 oscillations:1 transport:2 generates:1 describing:1 affects:1 gurvitz:3 assuming:2 noise:1 σij:4 jumps:2 oscillating:1 tracing:1 repulsion:1 bloch:2 block:1 numerically:1 down:1 references:1 determine:1 penetrability:1 support:1 initial:3 transform:1 long:1 way:1 ed:1 was:2 function:1 hp:3 but:1 2d1:1 line:2 made:1 whether:1 inside:3 us:1 placed:1 shtrikman:1 problem:3 similar:1 display:2 b57:1 detailed:1 penetrating:1 zeno:2 abstract:1 am:1 general:1 single:1 ar:3 reservoirs:5 hamiltonian:1 again:1 mutual:1 dashed:1 when:4 other:1 department:1 er:3 superposition:3 berman:1 june:1 generated:2 important:1 stodolsky:1 implies:1 coupling:4 assume:1 shnirman:1 dot:12 time:6 delft:1 decoherence:1 starting:1
|
quant-ph9806051.txt |@word limited:4 squared:1 magnetic:13 desirable:1 four:2 consists:1 localized:3 whose:3 calculate:4 paris:4 under:3 spec:1 connects:1 experimentally:2 4n2:1 solution:5 vector:7 guiding:1 indices:1 degeneracy:3 lagrangian:1 direct:1 unpolarized:1 approximation:22 likely:1 even:11 christ:1 incompatible:1 cimmino:1 above:10 new:4 increasing:2 agreement:5 evanescent:68 equals:2 here:2 atoms:27 reported:6 κz:3 represented:1 path:9 blinov:1 interpret:4 obtained:10 suitably:3 study:3 robin:1 symmetrical:1 fourier:5 changes:3 numerical:8 golden:5 reflectivity:1 mobility:1 explained:2 replace:1 modulated:15 total:2 circumvent:1 unit:1 would:6 noting:1 kinematics:3 therefore:1 lennard:1 type:1 separated:5 populations:3 successful:1 odinger:10 wark:1 must:3 me:3 ma:1 setup:2 work:4 theories:1 ere:1 concepts:2 root:3 example:4 sinusoidal:2 indicated:1 give:3 involve:2 indicates:2 degenerate:2 end:4 provide:4 feature:3 far:11 ens:1 widespread:1 description:4 modulation:20 after:7 summarize:1 parallel:4 types:1 effective:3 deutsche:1 decreasing:1 acknowledges:1 order:40 interpretation:5 diagonalizes:1 over:3 satisfied:1 xi:1 london:3 thesis:2 linewidth:1 before:1 fit:1 fiz:1 pritchard:2 fig:29 overcome:1 eventually:1 them:2 combination:1 steane:3 detunings:4 effects:3 they:9 represents:2 bonn:10 each:4 acoustic:3 lorent:2 lifted:2 series:3 principles:1 taught:1 substantially:1 network:1 gradient:2 crucial:1 re:1 scopes:1 trajectories:1 turning:8 linear:1 barrier:2 assures:1 estimate:3 condon:2 enormous:1 r9:1 creates:1 corrections:2 onto:1 already:1 features:1 channels:16 another:5 thick:1 trost:1 eqs:2 needed:1 too:1 sengstock:1 zeroth:1 took:1 distance:5 showed:3 second:13 tunable:1 preparation:1 matter:4 iωl:1 tion:1 perturbative:5 spectrum:1 manner:1 seen:3 seem:2 ray:1 szriftgiser:1 thoroughly:1 latter:2 circles:1 acquire:1 though:2 twolevel:1 simplify:1 optimized:6 germany:7 phase:28 calculated:2 points:8 principle:5 section:2 probe:2 subtle:1 d2:4 eliminated:2 proposed:5 explain:3 integrate:1 do:5 di:2 dg:1 de:8 wallis:6 dz:2 despite:1 fields:5 acknowledgments:1 twice:7 bad:1 analytical:9 traverse:2 reference:1 observes:2 sensitivity:1 condensed:1 richer:1 observed:9 depends:5 result:9 w0:2 discussions:1 optimum:5 subject:4 draws:1 manson:2 propagates:2 modulate:1 µm:1 conceptual:1 approach:14 glasgow:1 terms:4 weak:6 however:9 extent:1 bose:1 faced:1 received:1 cos:4 exceeds:1 uni:1 contribution:1 argue:1 had:2 height:4 active:1 2nq:2 grazing:33 strong:4 basis:2 union:1 kzn:11 three:1 been:24 much:12 interest:1 basic:4 expected:1 θi:5 θn:2 quantities:1 concerning:1 coherent:4 spin:2 applied:3 excited:15 near:1 suppose:1 applies:1 property:1 leaves:1 schumacher:1 ii:3 suggest:1 make:4 complex:1 quant:1 split:4 accumulating:2 dimensionless:2 several:4 european:1 independent:2 peaks:7 laboratoire:1 pick:1 hand:4 potentials:28 hans:1 weakly:4 shortly:1 scenario:2 academic:2 contact:1 simulated:1 quantitative:2 jean:2 unified:1 just:1 2δd:1 bandwidth:1 transforms:2 scattering:7 yet:2 enters:2 infinitely:1 cornell:1 character:2 friedrich:1 board:1 easy:1 gave:1 opt:17 possible:6 possibly:1 interferometer:2 sublevel:6 arbitrary:2 right:3 begin:1 deflection:2 born:10 escape:1 bord:2 golub:1 normal:36 witte:1 scholz:1 linearly:1 caustics:1 oscillating:3 stenholm:2 emits:4 proceed:1 waveguides:2 asimov:1 o:1 plus:1 efforts:1 slightly:1 soc:6 beamsplitter:8 formerly:1 presence:2 down:2 wν:1 reducing:1 orsay:7 support:1 initial:6 transform:1 width:7 anderson:1 conservation:5 editor:1 way:5 call:1 was:9 lowest:3 form:8 simplifications:1 denoting:1 failure:1 cedex:1 true:2 iqx:3 beamsplitters:5 resonator:2 inside:6 maximum:9 fermi:4 gould:1 ψe:2 abstract:1 conserved:2 exist:1 distributions:1 interferences:1 physical:5 no:9 whereas:1 wavefunction:13 generally:1 vanishes:1 interested:1 role:3 investigations:2 nq:1 picture:15 models:8 preceding:3 interferometric:1 fabry:1 transfers:4 jones:1 assume:1 interval:1 governed:2 time:10 n2:1 focus:2 leads:8 roy:3 garching:1 inverse:1 zone:1 passage:2 finally:4 circumstances:1 advantage:1 frequencies:1 choice:1 sidebands:5 stays:1 cook:2 exact:3 notations:1 kazantsev:2 solves:1 level:37 did:1 solved:2 der:5 oscillation:1 dealing:1 prediction:1 slowed:1 schiffer:1 adds:1 current:1 hajnal:3 haberland:1 westbrook:9 understanding:4 groups:1 along:11 appears:2 change:2 incoming:5 shift:30 studied:3 zener:10 accomplished:1 usually:1 resonance:7 conveniently:1 studies:1 plotted:1 tasks:1 spatially:6 convolution:1 marked:1 modifying:1 planck:2 franck:2 prove:1 positive:1 predictions:7 france:9 theoretical:7 introducing:1 apparent:2 envelope:4 validity:2 diffracted:9 vmax:4 cases:1 spinpolarized:1 yves:1 modified:1 labeled:2 values:1 theresienstraße:1 following:8 kyi:2 kyn:1 figure:2 mirrors:3 expanding:1 performed:3 sakaki:1 allowed:1 unphysical:1 kyr:1 occur:1 rays:3 divided:1 pure:5 parameter:1 product:2 explores:1 may:24 max:1 applications:1 levi:1 explored:2 hannover:3 natural:1 outline:3 so:10 representation:4 typical:6 wavelengths:1 canberra:6 indeed:5 pointed:2 years:1 course:2 raman:13 experiments:23 kopfermann:1 cold:1 still:5 equalling:1 group:18 how:1 interesting:1 vicinity:2 decreases:5 mail:1 main:2 non:3 thereby:1 matches:1 mølmer:2 processes:1 introduce:2 equidistant:2 now:10 discuss:4 term:9 name:1 domain:3 square:3 significantly:1 populated:3 ee:1 gaussian:1 inhomogeneous:1 wavelength:9 approximated:2 avoided:21 eq:16 shown:7 jackson:1 space:2 interference:2 formula:3 squares:1 shows:5 theory:34 mechanisms:3 quite:8 complicated:1 training:1 arnaud:1 transition:7 motion:6 place:2 gordon:4 first:22 hκ:2 simplifies:1 xz:1 long:1 impossible:3 array:2 open:1 angular:1 size:1 given:12 necessarily:1 checked:2 crossings:14 structured:1 speaking:2 gives:2 fraction:2 continuous:1 eliminates:1 transverse:1 segev:1 absorbs:4 sublevels:14 than:18 coefficients:4 population:9 accordance:1 were:3 questionable:1 eliminating:1 remained:1 correction:2 turned:1 argument:4 generalization:3 renn:1 distorted:7 invalidates:1 recover:3 any:1 efficient:11 ideas:1 note:10 goodman:1 potential:80 take:5 performance:1 coincide:2 channel:11 surf:3 cnrs:1 multiple:2 opposite:1 incidence:52 analytically:1 inserted:1 breakthroughs:1 average:1 feron:2 typically:7 quantity:1 show:3 german:1 recipe:1 obtains:5 nakata:1 ground:28 specifically:1 ratio:3 only:20 explicitly:2 extremum:1 kxi:4 closed:1 kxn:3 get:1 expectation:1 cannot:5 nearly:4 secondary:1 adiabatically:6 yield:1 summary:1 predicted:3 discussing:1 physically:1 ends:1 namely:2 ignores:1 surfaces:12 fails:1 review:4 outside:1 between:25 justified:1 multiplied:1 concentrate:1 analyzed:1 article:1 jg:9 dates:1 many:1 region:7 according:3 contract:1 propagation:1 expression:1 nearby:1 among:1 period:3 exploit:1 je:4 moreover:1 fruitful:1 jetp:1 mark:1 combined:1 reflective:1 direction:13 formed:3 photon:12 andrew:1 observe:1 wavevectors:3 diffuse:1 those:1 case:3 klaus:2 brouri:2 promising:1 situation:2 tunneling:1 coupled:11 couples:2 coupler:1 different:18 develop:2 multiphoton:1 circularly:2 pay:1 same:8 shifts:3 regime:13 extended:2 siegel:1 driven:1 running:7 delicate:2 asympotic:1 invariance:1 largely:1 roughly:2 without:6 solve:2 components:1 coordinate:1 repulsive:11 model:28 researchers:1 manifold:1 being:7 when:13 relevant:3 aspect:7 baldwin:2 heuristic:1 photons:3 seems:1 lhs:1 wavevector:13 lett:9 grating:44 momentum:16 real:2 around:2 read:1 neuen:1 early:1 raizen:1 vacuum:3 using:8 accepted:1 adams:1 particle:1 velocities:3 either:2 output:1 stationary:14 reduced:3 ezi:1 specified:1 nonzero:2 provided:3 vzi:2 kaiser:5 confirm:1 extensively:1 critical:1 exit:1 provides:6 bessel:2 power:1 equivalent:1 wavefunctions:7 found:2 2n:3 comparison:7 ol:1 discussed:11 wolf:2 greatly:1 mixed:1 ot:2 vi:1 perturbed:1 follows:4 communication:1 numerically:4 references:2 einstein:1 operator:2 theoretically:1 landragin:5 formulate:1 strictly:1 there:7 stark:1 start:3 low:8 donley:1 complete:1 vanishing:6 alain:1 jul:1 recoil:8 elimination:1 applying:1 ponderomotive:1 ωl:3 ωa:2 semiclass:1 agree:1 regimes:1 detailed:4 ac:1 af:6 certain:1 describe:3 am:4 deep:1 general:3 au:1 controlled:1 gradients:1 moves:1 spends:1 again:2 field:23 prism:1 valid:2 spatial:2 deviation:1 condens:1 includes:2 important:4 peak:2 chris:1 building:2 calls:1 curve:2 mass:1 firstorder:1 appl:4 starting:1 scl:3 sci:3 consider:6 caused:1 forbidden:1 splitting:6 scalar:6 commute:1 follow:1 reasoning:1 nord:2 r16:1 amplitudes:10 straightforward:1 returning:1 very:9 difference:10 condition:11 splitter:2 washing:1 hamiltonian:3 large:15 small:17 zero:3 enhancement:1 pass:1 further:1 sud:1 deeply:1 sum:1 version:1 waals:4 method:6 contrast:14 edited:2 outgoing:1 full:1 component:10 answers:1 behaviour:2 kzi:18 equations:6 tilman:1 nth:1 losses:1 allows:8 experience:1 prior:1 periodic:4 published:2 action:5 narrow:1 rors:1 palais:1 via:1 followed:1 analyzing:1 establish:1 λdb:1 takes:3 probabilities:5 contains:2 ψi:4 ψm:1 taken:5 ψf:2 ψg:2 more:8 flat:6 coating:1 corrected:1 emission:3 particular:4 known:2 recall:6 equation:9 paragraph:3 could:3 evolved:1 spontaneous:3 dee:1 compare:2 νq:3 stated:1 neglected:1 states:14 minimum:1 sharp:2 axis:2 respective:1 minist:1 ct96:1 simplicity:1 fx:1 derived:1 reflect:1 pfau:1 plane:4 waves:21 horizontal:1 unchen:2 associ:1 fascinating:1 negligibly:1 secs:1 negligible:6 playing:1 ito:1 developed:4 soon:1 thermal:2 paper:2 through:9 kinetic:7 its:15 rapidly:2 termed:2 energies:3 solving:1 actually:3 recombined:2 travelling:1 huang:1 good:2 schematic:1 number:11 framework:1 walls:1 accumulate:2 jhe:1 inelastic:1 easily:1 gets:2 2q:4 presented:2 2l:4 2m:6 universit:6 characterized:2 tilted:2 weight:1 generation:1 fisk:2 energy:25 hard:6 reduce:2 idea:3 vansteenkiste:2 expect:2 quantum:3 operation:2 beyond:2 dominates:1 discrete:1 since:14 induces:2 research:1 schematical:1 hill:2 occurs:2 doppler:23 circumstance:2 reason:2 positiondependent:1 specular:3 exponentially:8 consequence:3 integrand:2 corrugated:3 substate:3 probability:5 reflected:10 linking:1 done:4 neglects:1 passes:1 differ:2 perturbation:3 introduction:1 leading:1 least:2 calculations:3 scheme:2 observations:1 shifted:1 passed:2 trapped:1 optical:45 schr:10 translation:1 reflection:31 polarized:9 determines:2 bachor:2 konstanz:1 aims:1 determined:1 intensities:5 nathalie:1 treated:4 motivation:1 substantial:1 confirms:1 orders:15 paths:5 depending:1 internal:4 generalized:1 analogy:3 play:2 added:1 electric:2 mlynek:1 serve:1 rhs:1 most:5 measured:1 counterpropagating:5 coincides:3 part:4 exp:10 velocity:11 kx:1 physics:3 relation:1 find:1 impact:1 parameters:2 iet:1 convoluted:1 factor:4 circle:1 dominant:1 notation:1 dependent:3 beams:2 combinations:1 during:4 hartmut:1 arxiv:1 common:2 vincent:1 set:1 ser:3 achieved:2 undergoes:1 unpublished:1 see:14 sec:5 close:9 resonantly:1 dipole:2 eksp:1 contrary:2 conditions:4 rosa:1 available:1 recently:2 creating:1 attention:1 incident:17 interface:4 endows:1 both:13 recherche:2 last:1 quantization:1 sensitive:2 vopt:3 context:2 finds:3 experimental:8 sinh:1 point:5 simple:8 asymptotically:5 steele:1 corresponds:3 coincidence:1 semiclassical:4 throughout:1 complication:1 described:2 perspectives:1 px:1 due:13 whom:1 detuning:17 combine:1 ph:3 meeting:1 gas:2 understand:2 exponential:3 pacs:1 solid:6 straight:1 expanded:3 suhl:1 evaluated:2 while:8 couplings:5 stueckelberg:3 angewandte:1 vectors:1 vol:2 encountered:1 reads:2 itself:1 mott:1 vanish:1 fibers:1 lengths:1 stimulated:2 widely:2 wilkens:1 neutron:1 higher:2 used:13 levels:4 moving:2 horvath:3 focal:1 recent:1 task:1 analysis:1 obviously:1 convenient:2 distances:2 construct:2 mol:2 reviewed:1 atomic:77 useful:4 alternative:5 erbfmrx:1 sektion:1 cut:1 transformation:1 build:1 march:1 showing:1 integer:1 microfabricated:1 excluding:1 shaped:1 confront:1 adiabatic:16 translates:1 continue:1 yields:2 translated:1 methods:1 spring:1 some:4 back:1 understood:1 towards:4 sight:1 mirror:2 oscillations:3 courtois:4 savage:4 scale:2 resonances:6 integration:2 efficiencies:1 tends:1 copropagating:2 proc:3 perpendicular:5 gratings:3 recalling:1 range:1 cutoff:6 into:18 integral:7 suppl:2 appropriate:1 proportional:1 hollenberg:1 institut:7 classically:1 question:1 fast:2 u2:2 analyze:1 elsewhere:1 murphy:3 multilevel:4 atom:49 line:5 intuitive:1 up:11 us:8 ur:4 similar:10 called:7 constant:3 defined:3 single:7 formalism:1 amounts:1 dashed:1 application:1 potsdam:3 elements:8 calculating:1 meaning:1 kz:10 structure:4 tailored:1 implies:1 practically:1 diffraction:179 depth:3 weights:1 berman:2 meystre:1 having:2 once:1 discards:1 partial:1 enseignement:1 results:9 illustrated:1 softer:1 go:1 contours:1 excluded:1 include:1 indicating:1 letokhov:1 2re:1 straße:1 wave:98 resonant:6 transmission:8 notes:1 eigenvalues:1 optics:7 smaller:7 zh:1 zi:2 sin2:1 zc:7 imply:2 compensates:1 dynamics:2 odd:7 welfengarten:1 index:9 experiment:10 led:3 lee:1 degree:1 exchange:1 respectively:1 erieur:1 rausch:1 objects:2 separation:3 others:1 extreme:1 remark:1 involved:3 larger:14 contradiction:2 suggests:3 resulting:1 makes:2 sup:1 involves:2 scales:1 decrease:1 apply:2 standing:10 use:8 asymptotic:5 commun:10 remains:1 next:1 process:15 jonathan:1 historically:2 subsection:1 becomes:7 benchmark:1 account:6 balls:1 gabriel:1 challenge:1 averaged:1 reproduce:2 obvious:1 thin:12 meet:1 sligthly:1 calculation:6 high:4 hit:3 tan:2 mix:1 varies:1 sin:1 modulations:1 profile:1 physik:4 efficiently:2 realized:3 light:22 lines:1 correspond:1 element:7 realizes:1 subsequently:1 discussion:3 interpreted:1 mentioned:1 perfect:2 lg:1 outer:1 decay:3 chosen:1 rabi:4 lz:1 jn2:1 wolfgang:1 outlined:3 innermost:1 landau:9 mention:1 quantenoptik:2 realize:1 dielectric:12 university:3 magnitude:1 transmitted:2 mode:1 crossing:20 accompanied:1 few:2 related:3 society:1 frequency:10 static:2 interplay:1 our:1 transitions:10 out:6 specularly:1 matrix:13 rep:2 rev:19 mediated:1 maximized:2 ref:5 interactions:3 diagonal:4 approaches:3 york:2 interaction:14 elastic:1 geometry:2 route:2 times:1 ahler:1 length:2 produce:1 hence:13 quadratically:1 teor:1 corrugation:1 manuscript:1 reaches:1 improvements:1 precisely:1 quality:1 michelson:2 fair:1 πn:2 their:10 intermediate:5 perfectly:1 final:4 exactly:1 forschungsgemeinschaft:1 reverses:1 dynamical:1 colleagues:1 clebsch:1 limiting:1 roberts:1 amplitude:7 cohen:4 curves:1 need:1 angle:4 able:2 gravity:1 mechanism:11 polarization:9 instance:2 schematically:2 techniques:1 unless:1 who:1 courtesy:3 propagate:1 overlapping:1 why:5 laurent:1 repeated:1 mechanical:2 fact:11 galton:1 charles:1 connect:4 decade:1 optique:3 q2:1 based:4 should:1 dalibard:5 achieve:4 exchanged:1 means:2 familiar:3 impinging:1 overall:1 beam:16 villetaneuse:4 lossless:1 evolution:1 densities:1 qx:1 dpg:1 europhys:1 contain:3 fixed:2 carsten:9 view:2 monochromatic:1 omission:1 computed:1 acquired:1 frame:3 hδ:4 intensity:8 enhanced:1 acquires:1 phases:1 pattern:10 ralph:1 state:37 difficulties:2 correctly:2 boundary:1 reinhardt:1 comparable:9 efficiency:11 job:1 key:1 limits:1 taking:1 la:1 equal:5 zeeman:13 refraction:3 passing:1 estimation:1 marte:1 otherwise:2 splitters:1 ch:1 co:1 nonadiabatic:6 cm:1 conclude:1 wall:8 cf:2 distinguish:1 respect:5 crystalline:3 trajectory:5 treat:1 proposal:2 arises:1 corresponding:4 sufficient:2 essentially:1 angles:6 present:6 labeyrie:2 multi:1 laser:12 value:8 will:6 henkel:18 molecular:1 refs:1 wkb:1 thus:12 surface:18 vs:1 properties:1 cross:3 unity:2 parts:1 diagonalize:1 units:6 finite:3 polarizations:2 difficult:2 infinity:2 subbotin:1 upon:3 effect:5 v0:3 compared:7 infinite:2 frequently:1 expand:1 off:6 center:1 nevertheless:2 well:5 patterns:1 position:10 usual:2 spherical:1 restore:1 less:1 accurate:4 wagner:1 obtain:3 storey:1 cˆ:2 predicts:6 momenta:1 elaborating:1 adv:2 density:1 smith:2 transparent:1 nath:2 extends:1 attractive:7 identical:3 saturation:4 increased:1 bichromatic:1 increases:1 press:3 hollow:1 dimensional:1 necessary:2 like:6 lost:2 qualitative:2 martin:4 become:6 δd:7 works:1 armand:2 exceed:1 because:23 classical:11 sequence:1 2qx:3 ertmer:4 balykin:2 nondiagonal:2 qex:2 neglecting:1 happens:3 lead:3 broad:1 avoid:2 overlap:1 does:8 assuming:4 ralf:1 demonstrated:1 2q2:1 reaching:1 expansion:3 although:3 imaginary:1 stage:1 about:1 actual:1 carrier:2 introduced:2 equally:1 own:1 pergamon:1 probabilites:1 functional:1 mrad:1 van:4 additional:1 vˆ:5 transfer:12 noticed:1 tannoudji:4 quadratic:2 crucially:1 interferometry:4 function:10 yakovlev:1 but:3 neutral:4 gain:1 partially:2 compute:10 instructive:1 wieman:1 smooth:1 exerts:1 limit:2 problem:6 mechanics:1 geometrical:1 contribute:1 unmodulated:1 periods:1 pis:1 functions:3 gordan:1 dressed:8 percent:1 detail:2 other:10 details:2 dwba:13 conclusion:2 june:1 ultimately:1 variation:2 coupling:17 resolution:1 factors:1 rule:5 inset:3
|
quant-ph9806052.txt |@word represent:2 concept:1 gr:1 ceases:1 switched:2 crucial:1 forbidden:1 jones:1 results:4 four:2 eds:1 grib:1 follow:1 expressions:2 denotes:1 causes:1 consider:6 increase:1 volovik:1 depend:1 calculate:1 concerned:1 ts:10 vef:1 charge:11 critical:1 present:2 th:1 under:2 slowest:2 must:9 overlaps:1 p2:3 jensen:4 outside:2 very:4 rise:2 seemingly:4 wave:20 bjorken:1 electron:14 putting:1 should:7 refractive:3 experimentally:2 matrices:1 condition:3 generalised:1 unlike:1 immediately:1 transmission:15 solution:3 large:15 discrete:1 vector:1 waxman:1 small:4 originally:1 zh:1 specially:1 sin2:3 prediction:1 sign:3 approximation:1 zero:11 resultant:1 enhancement:1 pass:1 further:3 dynamics:3 estimated:1 odd:4 situated:1 scientific:1 even:5 index:1 section:4 current:19 en:2 above:2 flowing:1 international:1 increasing:1 method:1 filled:2 coefficient:7 barton:1 full:1 2ma2:1 fiz:2 respectively:2 component:1 here:3 b31:1 asymmetry:3 γx:1 others:1 laughlin:1 strong:6 equations:5 appears:1 interpret:1 box:1 tunneling:2 burstein:1 clarify:1 averages:1 changed:1 ravndal:4 amount:1 published:1 usually:1 resonance:4 narrow:2 changes:1 pathological:2 york:3 followed:1 ratios:1 4a2:5 scales:1 semiconductors:1 manage:1 plenum:1 iet:2 apply:1 total:3 causal:1 use:4 takes:1 would:10 positive:7 contains:1 negative:12 properties:4 anticommutation:3 nucl:1 call:1 therefore:7 m2:14 taken:2 theoretical:1 subcritical:4 more:6 hermitean:1 becomes:7 operators:1 factor:1 emission:21 berlin:1 appendix:4 particular:2 known:2 hole:1 iv:1 iii:1 analogous:2 fermionic:3 involve:1 springer:1 crosses:2 ma:8 tunnel:1 equation:9 work:2 det:1 crossed:2 following:1 hansen:4 spontaneous:3 example:2 history:1 give:3 process:4 relativistic:10 states:15 effectively:2 o:4 arise:1 unphysical:1 tan:2 occur:3 calculated:1 charged:1 end:1 viewpoint:1 rather:3 hol:1 get:2 write:3 how:1 nontrivial:1 pair:4 fourth:1 instead:2 verlag:1 gordon:1 de:5 petersburg:1 singular:1 may:3 advice:1 earlier:1 br:1 barriers:2 wrong:1 waves:1 destructive:1 concentrating:1 attempt:1 effective:3 bind:3 correspond:2 st:1 deepest:1 so:18 discussion:1 looking:1 order:3 talk:1 wine:1 wavelengths:1 acts:1 words:1 essence:1 over:5 years:2 produced:5 course:1 paper:3 through:4 still:3 its:2 before:1 derive:1 group:2 thank:1 gershtein:1 energies:7 interesting:4 expectations:1 decreases:3 d31:1 better:1 absence:4 production:9 systems:1 travelling:1 puzzle:1 versus:1 eventually:1 non:6 return:1 pauli:6 qp:9 ya:2 material:1 processes:2 number:11 repulsive:2 effects:1 they:4 oxford:1 now:9 dede:1 transparent:6 nor:1 easily:3 2v:1 dirac:9 always:1 normand:1 2ev:1 sufficiently:3 transmitted:2 2a:5 2el:1 2m:12 side:1 2k:3 heavy:5 square:14 directly:1 ed:1 energy:29 kane:1 idea:1 used:1 conventions:1 frequency:1 static:3 measure:2 quantum:2 our:7 beyond:1 eq:10 out:2 shown:4 rw:1 rs:8 furthermore:2 since:3 interference:1 research:1 particles:6 attracted:1 nauk:1 asymmetries:1 hill:2 rc:1 denoted:1 etalon:1 occurs:1 shows:1 after:1 turning:2 theory:6 barrier:29 correspondingly:2 1s:1 free:1 nth:2 completely:2 supercritical:18 term:4 ask:1 seventy:1 definition:2 pairs:1 derivation:1 could:3 times:2 lundqvist:1 place:1 exponentially:4 tempting:1 hence:8 teor:1 first:8 origin:5 already:3 conform:1 third:1 coming:1 timeindependent:1 reflected:4 reaches:2 linking:1 restrict:2 clear:4 approximately:2 another:1 carry:2 indices:1 illustrate:1 passes:2 given:17 necessarily:1 exists:2 needed:1 eqs:3 behaves:1 system:1 relations:3 their:2 fermions:3 calculations:3 ordered:1 final:2 gives:4 relationship:5 asymmetric:1 estimates:1 explanation:1 continuous:1 interband:2 part:1 simulate:1 authors:1 nca:1 zc:4 than:7 coefficients:4 modes:1 wide:5 colleagues:1 unfortunately:1 require:2 second:1 annihilation:1 represents:1 were:3 wiley:1 sees:1 electrodynamics:1 modern:1 turned:2 argument:1 say:3 conjugate:1 need:1 seem:1 seek:1 any:6 lie:2 angle:1 vanishes:2 partly:1 convenient:1 note:6 high:1 potential:30 build:2 finding:1 leftand:1 coincide:1 begin:1 exactly:1 vnc:1 electric:1 centre:1 measures:1 reach:1 most:2 involving:1 connected:1 plus:2 phase:2 measured:1 class:1 exact:1 operate:1 surprising:2 considered:2 average:2 physica:1 reflecting:1 electrons:9 principle:4 inaccuracies:1 αx:1 velocity:2 usual:1 physics:4 lying:1 quantity:1 spaced:1 phenomenon:3 show:9 nπ:2 timedependent:2 cdi:2 least:1 discovered:1 bring:1 attempts:1 relation:2 solutions:4 calculable:1 threshold:1 substituting:1 positrons:24 find:2 ground:2 q0:3 finally:2 ratio:3 quoted:1 parameters:1 escaped:1 explain:2 state:21 zα:4 being:1 only:2 going:2 positively:1 indeed:2 pointed:1 hope:1 do:1 his:4 2mv:2 zeldovich:2 klein:41 means:3 simplest:2 overall:1 expectation:3 preferred:1 cannot:1 eiet:2 closely:2 new:5 v1c:2 entity:1 subscript:2 dp:1 adiabatically:2 qs:8 continuum:5 textbooks:1 fields:2 hinges:1 arxiv:1 investigate:2 experiments:1 though:1 fixed:2 satisfy:2 set:1 observer:8 relative:1 see:8 result:5 enhanced:1 greece:1 terms:9 theoretic:1 performed:1 ways:1 nuclear:1 review:1 written:2 various:1 between:9 neither:1 approach:1 p2n:1 recently:1 positron:26 initially:3 emitted:10 weak:1 jr:2 2pa:4 incident:8 pieper:1 distinguish:1 distribution:1 exclusion:1 suggested:1 both:3 cos:2 last:1 region:3 according:2 emit:1 σz:1 connection:4 σx:1 context:2 reassessed:1 stratton:1 disappears:1 experimental:1 eksp:1 point:3 perot:1 corresponds:2 height:2 dimensional:1 simply:1 respect:3 considering:1 sensible:1 described:4 tuning:1 kinematic:1 basis:1 quantisation:1 help:1 due:3 been:1 quickly:1 int:5 pa:5 damping:1 expected:2 ph:1 pn:1 po:1 important:1 attractive:2 obtained:2 arises:1 corresponding:10 quantities:2 sufficient:1 longitudinally:1 spectrum:3 popov:1 understand:1 angles:1 evidence:1 those:2 case:7 p1:2 look:3 exponential:1 value:6 spontaneously:1 will:13 while:6 bakke:1 shall:2 situation:1 revisited:1 property:1 guide:1 maximal:1 studied:1 electronpositron:2 almost:1 vi:1 thus:8 them:1 equal:1 ii:1 vr:3 conserve:1 currents:1 around:1 different:2 bottles:1 blount:1 propagation:1 perhaps:1 media:1 slab:1 seeking:1 cross:2 same:5 clearly:1 unity:2 complex:1 quant:1 arguments:1 unfortunate:1 avoids:1 finite:7 difficult:2 independent:10 calculation:3 investigated:3 singapore:1 σy:10 differing:2 noticing:1 necessity:1 potentials:6 describe:3 greiner:2 expand:1 electromagnetism:1 off:8 reflection:9 scenario:1 nevertheless:2 mz:1 vacant:1 well:39 telegdi:3 analysis:1 accumulation:1 solids:1 without:1 inability:1 claims:1 model:1 left:8 just:7 linked:1 increasingly:1 accurate:1 obtain:2 reviewed:1 underlying:2 atomic:1 integer:1 momenta:1 scattering:22 yet:1 previous:1 onset:1 dropped:1 conclusions:1 mostepanenko:1 rose:2 conclude:1 seems:1 except:1 discuss:1 internal:1 treatment:1 easy:3 momentum:7 rafelski:1 vii:1 increased:1 rev:3 alternatively:1 evaluate:1 sussex:2 possible:2 cf:2 tunnelling:22 increases:3 vacuum:16 using:6 v2c:1 necessary:3 like:3 particle:15 follows:3 velocities:1 noted:1 continue:1 yields:1 either:2 ikx:4 arbitrary:2 become:5 dets:1 university:1 right:15 old:2 classical:1 resonances:2 creation:1 phenomena:2 play:2 friedmann:1 consultants:1 choosing:2 specified:1 enormous:1 ourselves:2 scripta:2 provided:5 describing:3 electromagnetic:2 normal:3 integration:2 overlap:1 does:3 tends:1 demonstrated:1 refer:1 measuring:1 who:1 obey:1 kleingordon:1 bl:1 journal:1 wavefunctions:6 jl:2 expansion:1 step:24 although:3 found:3 emits:2 anselm:1 stone:1 world:1 mcgraw:1 instantaneously:1 discussed:3 supercriticality:5 range:4 misleading:2 nothing:2 propagate:1 introduced:1 gamma:1 okun:1 seeing:1 muller:2 own:1 presence:8 pergamon:1 into:1 bound:13 down:1 lies:1 appropriate:1 because:4 references:1 blankenbecler:1 determine:1 next:3 nowadays:1 theoretically:1 schrodinger:1 classically:1 normalised:1 there:7 long:2 width:1 bosons:1 way:3 kinematics:1 was:4 function:4 lindstrom:1 form:1 enough:7 some:2 jun:1 but:21 change:1 properly:2 larger:1 vl:3 true:1 considerable:1 he:2 count:1 absent:1 ke:1 understood:2 characteristic:2 inside:1 up:3 us:1 ur:10 ul:8 below:4 limit:4 uk:2 demonstrate:2 problem:6 similar:5 called:2 polarised:3 distance:1 detailed:1 ac:1 constant:6 uspekhi:1 defined:4 year:1 deep:2 general:2 conserved:1 ar:5 initial:1 lifetime:5 fizika:1 physical:6 again:3 functions:5 compared:3 paradox:9 no:9 whereas:4 when:9 detail:1 schwinger:1 field:3 other:1 role:2 really:1 belong:1 conclusion:1 picture:1 repeat:1 topic:1 models:1 problems:1 a2:2 nucleus:6 fabry:1 boyanovsky:1 sides:1 careful:1 ago:1 implies:1 longer:2 coulomb:10 assume:2 values:1 dosch:1 together:2 transient:5 fact:2 time:17 nuclei:2 having:2
|
quant-ph9806053.txt |@word represent:1 schwendimann:1 managed:1 consider:3 langevin:4 results:1 elisabeth:1 sonderforschungsbereich:1 go:1 expressions:1 contributions:1 gh:1 iin:1 recurrence:4 squeezing:1 under:2 γb:14 γa:14 p2:8 amplitudes:2 very:1 2γa:1 2γb:1 ωz0:1 ωz2:1 resonant:2 encounter:1 2κb:2 2κa:2 level:7 bonifacio:1 t2:4 solution:21 damped:5 large:2 solved:3 settle:2 small:6 warszawa:1 der:1 neighborhood:1 zi:4 zj:2 foundation:1 sin2:1 prediction:1 pulse:4 approximation:2 second:4 evaluated:2 further:1 estimated:1 haake:5 even:2 deeply:1 section:2 expressed:1 reminiscent:1 τmin:3 above:2 order:7 acknowledged:1 contrast:1 full:1 christian:2 respectively:1 κa:11 here:2 atoms:31 l21:3 ansatz:1 address:1 represented:1 strong:1 z0:8 z1:14 z2:6 sending:1 involved:1 studied:2 eberly:1 periodic:3 resulting:1 harmonics:2 hospitality:1 narrow:2 s00:3 s01:2 s02:1 explained:1 integrations:1 rρ:1 use:2 would:3 linear:1 taken:1 resonator:1 entails:1 more:1 separated:3 populations:1 operators:4 stable:3 corrected:1 transient:1 normalized:1 eλ:2 iil:1 cases:1 given:3 iii:1 high:1 account:1 valued:1 science:1 equation:5 averaged:1 ρl:7 values:1 following:1 performed:1 indicated:2 give:2 process:1 haroche:1 states:2 assumptions:2 numbers:3 occur:1 needs:1 end:1 s2:1 discussion:2 dependent:1 sij:3 parameter:2 sin:12 description:1 may:5 broad:1 after:3 derived:1 physik:2 centrum:1 constants:3 short:1 effective:1 light:1 spectra:2 explicit:1 correspond:1 switch:1 so:7 g12:10 serge:1 pulsed:2 saturated:2 over:2 expects:1 produced:1 course:1 paper:2 pulses:5 linewidth:1 before:1 perfect:1 lc:1 decay:2 sγ:1 temporal:1 fig:9 rabi:1 into:2 eventually:2 non:6 good:1 propose:1 break:1 they:1 now:4 2t:1 easily:1 term:2 2p:3 fizyki:1 fully:1 hamiltonian:1 mode:7 2l:5 2m:2 universit:1 constraints:1 financial:1 series:1 gaussian:1 recapitulate:1 frequency:1 expect:1 quantum:8 our:3 transitions:1 es:1 out:4 shown:2 driving:2 rep:1 since:4 rev:6 rz:1 fx:1 pan:1 ref:1 correct:1 occurs:1 theory:1 discontinuity:4 pumping:5 quite:1 mikhail:1 proportionality:1 intermediate:1 could:1 transition:7 filter:2 große:1 δij:1 corrections:3 first:7 indebted:1 already:1 humboldt:1 variables:1 number:5 preservation:1 done:1 electronic:1 between:1 illustrate:2 ewski:1 perturbation:2 periodicity:1 introduction:1 2ωt:3 system:2 their:2 assumption:2 rates:1 calculations:3 master:2 dt1:3 scheme:1 1m:4 final:1 dt2:2 kept:1 eliminated:1 than:1 population:1 colleagues:1 zero:3 limiting:2 annihilation:2 amplitude:2 perturbative:1 entail:1 fluctuation:1 spectrum:1 need:1 seen:1 clearly:2 kolobov:4 strength:2 bz1:2 lim:2 latter:1 s21:1 take:3 forces:3 heisenberg:2 towards:1 shall:3 germany:1 phase:4 acknowledgements:1 inserted:1 manifested:1 observation:1 radiating:1 considered:3 clear:1 later:1 typeset:1 points:1 ku:1 mechanical:4 thank:1 sum:1 show:2 odkiewicz:1 relation:4 solutions:1 find:7 ground:5 teoretycznej:1 parameters:5 claude:1 commutators:1 state:7 analytic:1 only:2 subsection:1 g01:10 coherences:1 dominant:1 notation:1 get:3 occupation:2 de:1 cannot:1 nearly:1 dt:1 adiabatically:3 introduced:1 arxiv:1 l02:5 bad:1 analytical:1 through:1 set:1 physically:1 ωt:6 collectively:1 intensity:2 college:1 result:1 enhanced:1 closer:1 project:1 2πp:1 ways:1 irr:2 superradiant:7 symmetric:1 pump:4 various:1 simplest:1 notice:1 terms:3 extend:1 initially:1 however:1 gratefully:1 κb:9 bose:1 improve:1 cos:5 hω:1 und:1 uni:1 whole:1 cos2:1 point:1 simple:1 period:1 height:1 semiclassical:16 kazimierz:1 moreover:2 described:2 equations:3 due:2 been:3 dropping:1 damping:4 ph:1 pn:4 define:2 corresponding:1 relaxing:1 photon:2 fritz:1 external:1 present:1 case:2 p3:3 laser:9 look:3 pacs:1 expanded:1 value:1 will:6 behavior:5 opt:1 coupled:1 t1:7 thus:1 them:1 iv:1 ii:1 reads:2 il:1 vanish:2 different:3 develop:1 anymore:1 make:2 same:1 beside:1 quant:1 figures:1 dimensionless:2 finite:1 conflict:1 higher:2 independent:2 used:2 see:1 hand:1 levels:3 expand:2 shortly:1 modes:6 expression:1 poland:1 well:4 roughly:1 s22:5 s20:1 without:1 solve:2 model:3 atomic:1 previous:1 death:1 density:3 photons:1 seems:1 dicke:1 add:1 lett:1 excited:1 identical:1 using:1 like:1 necessary:1 2r:1 δx:2 collective:2 adiabatic:2 temporally:2 output:2 stationary:15 signal:1 therein:1 classical:3 creation:2 some:6 examples:1 respect:1 giacobino:3 gross:1 scale:1 cavity:5 fachbereich:2 investigations:1 l10:3 integration:1 does:1 eliminate:2 τmax:4 moderate:2 bessel:1 s12:2 s11:2 s10:1 expansion:5 revtex:1 references:2 invaluable:1 eiω:1 2n:4 plug:1 discussed:1 o:3 range:4 ensure:1 transients:1 ow:1 mean:3 soc:1 ηb:4 ηa:5 h0:2 numerically:2 three:2 down:1 accounts:2 operator:4 proportional:2 essen:4 additional:1 prepare:1 reynaud:3 assumed:1 support:2 initial:1 fast:1 width:5 low:2 az2:2 was:1 lowest:1 lotnik:1 complete:1 jun:1 but:1 change:1 atom:1 elimination:1 irreversible:1 inside:1 up:3 us:1 placed:1 limit:3 fluctuations:3 display:1 strongly:4 smeared:3 int:3 certain:1 abstract:1 am:1 eu:1 az:1 check:1 regime:11 again:1 functions:1 polarisation:1 nc:1 imax:2 field:5 interested:1 np:1 seeger:2 semiclassically:1 fabre:3 allowing:1 additionally:1 max:1 implies:1 coupling:2 assume:3 dτ:3 coherent:1 time:7 observables:4 starting:2 having:1 once:1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.