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quant-ph9709040.txt |@word beckers:1 sci:1 consider:2 chain:2 results:1 p02:1 scalar:2 spiridonov:3 gl:1 gj:1 gi:9 inverse:3 depend:1 paris:1 intensive:1 th:1 under:2 anharmonic:1 vladislav:1 zaved:1 belonging:1 straightforward:1 far:1 dokl:1 wave:2 witten:3 every:3 difference:6 feeble:1 condition:7 generalised:1 annihilated:2 hamiltonian:4 stimulus:1 irreducible:1 t2:7 solution:1 t0:3 discrete:6 eigenvalues:3 noted:1 wronskian:4 sturm:1 miller:1 direct:1 literature:1 sign:2 fold:3 second:5 further:1 odd:1 situated:1 even:2 nonlinear:2 stands:1 expressed:1 current:1 poles:1 sur:1 above:2 q2i:1 new:2 sukumar:1 method:1 full:1 degree:2 respectively:1 component:2 here:1 nodeless:6 l21:4 l20:13 superhamiltonian:1 separation:2 marchenko:1 equations:5 spbu:2 obtained:3 ref:2 institute:1 completely:1 generale:1 action:3 suitable:3 appropriately:1 via:1 hermite:1 cons:1 establish:1 lσ:1 conventional:5 takes:1 intensively:1 remains:1 agranovich:1 properties:1 nucl:1 call:1 therefore:1 usp:1 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quant-ph9709048.txt |@word represent:1 consider:4 magnetic:3 particular:1 results:2 roy:2 entropy:3 per:1 grateful:1 follow:2 expressions:1 inverse:2 calculate:2 weightings:1 stochastic:1 analogous:1 characterised:3 case:12 rαβ:1 provides:1 straightforward:1 orthogonal:1 implicitly:1 rise:1 percival:1 geometrical:1 electron:1 lynch:1 difference:1 strand:1 hamiltonian:8 tanh:1 joined:1 vector:5 subscript:1 indices:2 eigenvalues:5 path:1 configurations:1 slower:1 periodicity:1 consistent:1 sin2:1 measurable:1 ωac:1 ωab:2 generalisations:1 second:1 street:2 further:1 dynamics:5 implemented:1 canonical:15 what:1 nonlinear:2 specification:1 foregoing:1 expressed:1 uniform:4 poles:4 above:2 international:1 change:1 exercise:1 edited:2 led:1 dcb:1 component:2 here:10 behaviour:2 dimensionality:1 tangent:1 cos2:1 sinh:1 address:2 represented:1 ratio:1 appears:1 interpret:2 deduced:1 magnetisation:1 study:4 vectors:1 helv:1 resulting:2 suitable:2 york:1 churchill:1 projection:4 family:1 iz:1 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quant-ph9709049.txt |@word replacing:2 code:51 consider:2 caused:1 gf:10 entropy:1 computation:1 research:1 duplicated:1 simon:1 alamos:2 tr:4 factoring:2 th:1 under:1 dramatically:1 alexei:2 worse:1 straightforward:1 orthogonal:6 print:8 every:1 entries:1 matrices:4 condition:1 dim:2 evj:1 presented:3 transmission:1 positions:2 large:1 discrete:2 small:1 gc:4 upper:7 tel:2 2k1:7 l2k:1 coefficient:1 mceliece:1 10z:2 zero:1 append:1 linear:25 even:1 what:1 errors:2 rate:1 section:6 expressed:1 3t:1 3i:2 version:3 3n:4 dieks:1 values:6 seemed:1 consisting:2 exercise:1 satisfy:1 degree:2 equals:1 here:3 growing:1 protection:1 bj:8 represented:1 strong:1 ωa1:1 ωa2:1 obtained:1 vectors:2 allows:2 8x:1 reports:1 eigenspace:1 supplements:1 survey:1 knill:3 devices:1 formulated:2 useful:1 bounds:21 sloane:4 welch:1 apply:1 total:2 linearly:1 use:1 asymptotic:3 would:2 prove:2 contains:1 single:1 hilbert:1 call:1 memory:1 associated:1 type:15 israel:1 becomes:1 operators:1 particular:2 known:1 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quant-ph9709053.txt |@word logarithms:1 code:4 partial:1 consider:8 pointing:1 induces:1 forbidden:1 ours:1 focus:1 existing:1 leads:1 executing:1 scalar:2 computation:8 go:1 follow:3 remarkably:2 objections:1 shattered:1 maximally:1 depend:1 eigenbasis:1 alamos:6 factoring:3 violation:1 finally:4 those:1 under:1 kwong:1 include:1 applied:2 supported:1 rescue:1 orthogonal:1 very:6 implicitly:1 rise:1 hughes:1 choice:8 electron:2 every:1 should:2 hewlett:1 fall:2 telling:1 winning:1 trouble:1 eqs:2 matrices:6 arrange:1 entire:1 disturb:1 encodes:1 immediately:2 level:1 transmission:2 turns:3 notes:4 trb:3 large:2 discrete:1 insights:1 phase:14 progress:1 dealt:1 small:1 goldenberg:1 challenge:1 20th:1 prevent:2 foundation:2 till:1 dealing:1 maximization:1 suffices:1 breakers:1 zero:6 pass:1 initialized:1 implemented:1 odd:3 makers:1 machines:2 belief:3 even:11 what:6 essence:1 appear:1 rate:1 cryptographers:2 version:2 fortschritte:1 above:10 utkenhaus:1 new:8 ever:1 method:1 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quant-ph9709058.txt |@word limited:1 code:4 both:1 entropy:7 certainly:1 depend:1 send:5 environment:12 presumed:1 string:1 choice:3 difference:2 securely:1 entire:2 michael:1 eve:6 large:1 trq:1 eigenvalues:1 upper:2 deutsch:2 consistent:1 zero:1 infimum:1 dynamics:2 peredachi:1 approached:1 will:6 apparatus:1 decoding:5 access:2 above:1 sup:1 shared:1 net:1 revealing:1 full:1 exchange:4 never:1 here:3 desired:1 address:1 sending:2 great:3 sender:3 barnum:1 larger:2 published:1 amount:3 schumacher:7 bob:23 suitable:2 makes:1 composed:1 via:1 regardless:1 private:3 establish:2 use:5 usa:2 probabilities:1 positive:1 properties:3 ψk:2 therefore:1 taken:2 possession:1 suggestions:1 operators:1 about:2 known:3 kenyon:1 must:4 states:7 orner:1 ρe:7 recall:1 ρk:2 ρq:25 westmoreland:4 strategies:2 trans:1 example:1 control:1 allowed:1 share:1 high:1 performed:2 want:1 sense:1 information:28 goal:1 interacts:1 holds:1 how:2 pure:11 granville:1 optimal:2 ordinary:1 inputs:5 communicating:1 may:7 after:2 data:1 efficiently:1 short:1 third:2 purification:1 so:3 se:4 closely:1 indeed:1 pointed:1 including:2 fidelity:1 ieee:3 its:3 perfect:1 derive:1 thank:1 chosen:2 interesting:1 better:1 choose:1 might:1 conveying:2 non:1 conversations:1 effects:1 they:5 instead:1 represents:1 always:1 university:1 theory:3 each:1 entirely:1 macchiavello:1 subsystem:2 schemes:1 tre:2 related:1 measure:1 quantum:27 out:1 since:2 rev:7 holevo:1 contained:1 benjamin:1 maurer:1 linear:1 activity:1 imagine:2 put:1 jozsa:2 definition:1 interaction:3 could:1 times:2 length:1 assumed:1 first:1 channels:2 another:1 message:1 given:6 privacy:7 interact:1 system:11 least:2 their:1 statement:1 wootters:3 bits:2 final:2 exactly:1 part:1 superoperator:8 than:1 depends:1 determined:1 kth:1 supposed:1 were:1 result:2 generality:1 correction:1 any:6 viewed:1 csisz:1 note:1 sciences:1 channel:32 begin:1 transactions:2 trρ:1 measures:1 significant:1 intrinsic:1 χq:11 considered:1 average:2 gather:1 stronger:1 typeset:1 χe:9 χd:2 physics:1 fact:1 quantity:2 probl:2 attempts:1 relation:1 lloyd:1 find:1 popescu:1 only:3 local:1 oct:1 exchanged:1 do:1 over:4 his:2 cryptography:4 means:1 overall:1 joint:1 cannot:1 words:4 report:1 during:1 evolution:3 arxiv:1 qe:6 contain:1 through:1 set:1 reference:2 see:1 college:1 usefulness:1 close:2 theoretic:1 ability:2 exploited:1 capacity:2 ways:1 importance:1 state:19 between:6 available:3 creating:1 initially:4 however:3 key:3 received:2 acquiring:1 many:3 receives:1 receiver:4 arbitrarily:2 conclude:1 simple:1 guaranteed:4 simply:1 maximize:1 considering:1 described:2 basis:1 create:1 secret:3 describes:1 pg:5 pk:7 ph:2 define:1 arises:1 observable:4 coherence:1 coherent:7 tapping:1 denote:1 case:1 employ:2 near:1 suppose:1 reliably:3 error:1 aid:1 property:1 unitary:1 von:1 thus:4 examined:1 supremum:1 ie:3 nielsen:3 φq:2 perform:2 suggest:1 make:4 same:1 quant:2 party:2 used:7 0e:5 hand:1 entanglement:4 lower:1 variety:1 thought:1 without:2 gambier:1 greatest:1 unitarily:1 protocol:1 just:3 being:1 actions:1 tasks:3 identify:1 density:3 seems:1 signals:1 other:4 lett:2 denison:1 increased:1 big:1 showing:1 measurement:1 possible:6 entangled:2 sanpera:1 using:2 helpful:1 loss:1 necessary:1 like:1 lost:1 signal:4 alice:25 continue:1 output:3 security:1 mathematical:1 because:2 neumann:1 classical:5 some:5 convey:2 proper:1 provided:1 describing:1 does:1 measuring:1 noise:3 processing:1 conveyed:3 revtex:1 although:1 prepared:1 optimize:1 noisy:3 limitation:1 central:1 would:1 oh:2 eavesdropper:8 discussed:2 mixed:2 efforts:1 introduced:1 automatically:1 presence:1 communication:3 bound:3 ussr:1 references:1 parties:1 operator:3 log:1 her:2 measured:1 initial:3 question:1 decode:1 way:1 was:1 link:1 line:1 trying:2 made:3 whether:1 wish:1 up:1 distribution:1 called:1 later:1 defined:1 abstract:1 describe:1 general:2 transm:1 ar:1 inf:4 no:4 ekert:1 generally:1 priori:1 department:2 picture:1 conveys:1 includes:2 prepares:2 cryptographic:4 assume:3 governed:1
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quant-ph9710001.txt |@word represent:2 partial:24 consider:25 diagonalizes:1 control:1 global:2 results:22 leads:2 commute:1 entropy:19 grateful:1 follow:1 reasoning:2 whose:1 certainly:1 inverse:10 terms:3 calculate:4 pb2:2 irrelevant:2 concerned:4 tr:24 contained:2 shall:1 tn:8 finally:3 program:1 preserved:1 under:14 include:1 tb:1 worth:2 t11:1 case:24 belonging:2 supported:1 ρtb:1 straightforward:5 ρta:2 very:5 rise:2 emphasizes:4 subject:1 focus:1 corollary:6 isomorphism:7 ma:1 matrices:12 condition:62 illustrated:2 magic:9 tra:16 suffices:1 t4:2 trb:6 t2:2 t3:2 cascading:1 t1:2 large:2 vector:19 phase:4 small:1 eigenvalues:17 darpa:1 antiunitary:7 der:1 concluded:1 tetrahedron:6 illustrating:1 disordered:1 dealing:4 sign:10 second:3 further:1 linear:9 spectral:1 subadditivity:1 3x:1 plays:1 stands:2 ferrero:1 section:8 axes:1 expressed:3 above:3 ρu:1 3a:4 acknowledgments:1 contrast:1 satisfy:2 edited:2 give:1 ρaa:13 reverses:1 ρab:151 respectively:4 component:7 here:6 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quant-ph9710013.txt |@word consider:2 depends:1 rev:4 varying:1 results:7 four:5 assembled:1 looking:1 certainly:1 violate:1 nonlocal:3 tl:2 efficiencies:1 under:2 γb:8 analogous:1 rb:1 orthogonal:1 rise:1 wave:10 massar:1 hewlett:1 telling:1 pbs:1 vector:4 dip:1 align:1 vincenzo:1 upper:1 sapienza:2 incremented:1 consistent:1 second:2 pass:2 further:1 click:3 theory:1 even:1 what:2 nonlinear:1 apparatus:3 uniform:1 experiment:6 reconstruction:1 overcomplete:1 new:2 method:3 told:1 satisfy:1 degree:3 never:1 teleportation:15 here:3 reported:1 alone:2 path:7 obtained:1 sending:1 instituto:2 sender:1 institute:1 vectors:1 accomplished:1 professor:1 bob:19 narrow:1 makes:2 honor:1 klyshko:1 appropriately:3 via:1 followed:2 projection:3 explained:2 outcomes:7 hardy:1 total:1 linearly:2 use:1 graphs:1 would:4 roma:2 positive:3 next:1 classically:2 tele:1 taken:1 type:2 tell:1 more:4 setup:1 becomes:4 operators:2 visibility:1 appendix:3 normalized:2 particular:3 mounted:1 1µm:1 must:4 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quant-ph9710014.txt |@word restriction:2 guang:1 show:1 indeed:1 supported:1 mainly:1 satisfied:1 rotating:1 lanl:2 gl:4 eliminated:1 multiples:1 previous:1 copy:1 knowledge:2 parameters:8 re:1 implementation:1 true:1 technique:4 should:1 source:1 detected:1 lu:1 transformed:1 choose:1 easy:1 under:2 republic:1 oct:1 do:1 advantage:2 was:3 far:1 vary:1 practice:2 introduce:1 wave:1 test:1 walls:1 know:1 they:2 dv:1 condition:1 four:2 evolution:1 hamiltonian:10 fhe:8 university:1 arxiv:1 guo:3 deals:1 each:1 done:1 works:1 reduces:1 homogeneous:1 measuring:1 adiabatic:1 poyatos:1 exists:1 people:1 national:1 still:1 some:1 related:1 prevents:1 approximation:2 collectively:1 intensity:1 violet:1 quantum:3 our:2 operation:5 eq:5 special:1 subject:1 project:1 fails:1 nonlinear:1 describing:2 acknowledgment:1 driving:1 since:1 rev:3 dephasing:1 qubits:8 eprint:2 reply:1 construction:1 ref:4 consisting:1 contrast:1 bz:1 foundation:1 noise:7 detuned:1 circumstance:1 bl:3 respectively:1 equivalent:1 however:1 hefei:1 china:3 here:2 cnot:3 thank:1 advance:1 interaction:1 zoller:2 σl:2 many:1 feasible:1 practical:1 ωopt:3 usually:1 qubit:1 argue:1 changes:1 other:1 comment:5 therein:1 acceptance:1 decohered:1 simple:2 into:1 coefficient:1 bath:1 dissipation:3 independently:1 references:2 another:1 operator:1 moreover:1 open:1 use:2 described:1 classical:1 needed:1 unknown:1 there:5 system:1 belongs:1 describes:2 damping:9 encode:1 free:3 ph:3 scheme:2 type:1 lett:3 questionable:1 only:1 controlled:1 collective:1 form:2 influence:1 operators:2 accurately:1 but:2 environmental:1 assumption:1 hi:1 elimination:1 encoded:4 optical:3 general:3 iii:2 present:1 coupling:1 case:1 springer:1 gardiner:1 holland:1 pacs:1 science:3 work:1 zero:1 value:1 heidelberg:1 annihilation:1 remain:1 determined:1 amplitude:5 following:1 im:1 similar:1 procedure:1 zanardi:5 cirac:1 process:1 nature:1 universal:4 thus:1 ming:1 ii:2 duan:3 numbers:1 technology:1 their:1 constructed:2 nl:1 no:1 perform:1 whereas:1 acts:1 when:1 verlag:1 same:2 note:1 field:3 points:1 quant:3 pure:1 frequencies:1 department:1 gate:4 several:1 parameter:1 adjusting:1 rasetti:5 kinds:1 irrational:1 see:2 though:1 may:1 after:1 satisfy:2 shown:1 less:1 most:2 detect:1 designed:2 letter:4 observables:1 phase:4 class:1 recent:1 realized:1 suitable:1 center:1 required:1 well:2 berlin:1 vl2:1 efficient:1 without:3 so:1 time:2 claims:2 decoherence:2 physics:1 having:1 fact:1
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quant-ph9710015.txt |@word footing:1 partial:3 consider:3 rev:6 hands:2 brownian:4 lincei:1 eds:3 horsthemke:1 follow:1 albeverio:2 whose:4 certainly:4 inverse:1 depend:1 referring:1 exploited:1 disposal:1 deterministic:7 including:1 uniqueness:1 pathological:1 present:4 under:7 stochastic:25 must:2 applied:2 supported:1 worse:1 virtue:1 evolves:1 far:1 mikami:1 rise:7 seemingly:1 choice:7 formula:2 telling:1 variance:1 condition:2 bρ:1 generalised:2 induced:1 obvious:1 divorced:1 solves:2 presented:1 issue:4 having:1 t2:23 solution:20 prototypes:1 large:1 discrete:1 interpolating:4 markov:10 specified:2 hasegawa:1 still:1 effective:1 force:3 lecture:1 consistent:2 za:1 literature:1 sign:1 likely:3 displays:1 further:1 dynamics:28 implemented:2 jamison:2 incompatible:1 quite:2 linear:2 even:4 nonlinear:10 plays:1 stands:1 ct2:1 affected:1 section:3 exclude:1 fulfilled:1 access:1 consistently:3 version:4 above:8 international:1 principal:1 shandarin:1 seeks:1 evolving:1 proliferation:1 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quant-ph9710016.txt |@word beckers:1 fleury:1 villeurbanne:2 consider:1 exponentiation:1 results:2 leads:2 eds:1 scalar:2 generalize:1 spiridonov:1 grateful:1 intricate:1 follow:2 reasoning:1 devoted:2 looking:1 inverse:1 superspace:1 eα:1 concerned:2 equivalence:1 passage:1 tn:7 finally:3 tm:9 monteiro:1 th:4 under:2 generating:1 worth:1 presently:1 straightforward:1 far:1 zachos:3 chaichian:1 every:1 summarized:1 nieto:1 matrices:1 deformations:2 hussin:1 presented:1 irreducible:1 deals:1 vector:2 interpolating:3 recall:1 rk:9 optics:1 still:1 zn:3 employing:1 occurrence:1 periodicity:1 zk:2 matheus:1 ghosh:1 progress:1 theo:1 further:1 linear:1 64a:1 64b:1 plays:1 giving:1 section:6 goes:1 fractional:7 new:1 acknowledgments:1 satisfy:3 chose:1 ibid:4 arik:1 respectively:9 realizations:3 here:3 diagonal:1 rausch:1 objects:4 groups:2 consideration:3 sine:1 19a:1 transformation:2 19b:1 obtained:3 remark:1 institute:1 involved:1 study:1 vectors:1 periodic:3 products:2 published:1 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quant-ph9710019.txt |@word ibid:3 similarity:6 results:1 grateful:1 equivalence:2 those:2 analogous:1 include:1 worth:2 g1:1 orthogonal:1 wave:5 normalizability:1 jack:2 matrices:1 partitions:1 generalised:1 school:1 hamiltonian:4 solution:3 eigenvalues:1 noted:1 degeneracy:1 zg:1 integrability:1 odd:1 theory:1 even:3 tewari:1 sum:1 en:1 above:3 new:2 increasing:1 equivalent:2 multivariate:1 lee:1 degree:2 exchange:1 respectively:1 diagonalises:1 here:6 cappelli:1 diagonalised:1 obtained:1 azuma:1 accomplishes:1 studied:1 muirhead:1 action:3 suitable:1 makes:1 relation:1 schur:1 eˆ:1 useful:2 altshuler:1 brought:1 translational:1 viz:1 establish:1 linearly:1 levine:1 use:2 would:2 prove:1 sake:1 jpn:1 generate:2 nucl:3 noting:1 ψn:1 therefore:1 zemba:1 associated:1 type:13 operators:3 known:1 iii:1 must:1 characterised:1 equation:1 oscillator:2 theories:1 following:3 making:1 dec:1 decoupled:7 proof:1 india:2 degenerate:1 csm:6 motion:4 needs:1 provide:1 verify:1 acts:1 srinivasan:1 maps:3 product:1 description:1 algebra:5 oscillators:11 after:1 mapping:1 applications:1 choice:1 constants:5 sectors:1 explicit:2 su:4 sn:3 g12:2 xj:8 jevicki:2 xk:1 paper:1 through:2 statistical:1 mentioned:1 existence:2 its:1 acknowledge:1 interesting:1 coordinates:1 systems:3 mail:1 main:1 defining:1 yi:1 non:1 combination:1 noticing:1 elementary:1 they:2 das:1 oxford:1 hall:2 wiley:1 easily:2 gets:1 james:1 university:1 establishing:1 found:2 entirely:1 homogeneous:5 differential:1 financial:1 mesoscopic:1 energy:3 related:1 moser:5 conductance:1 literature:1 quantum:3 special:2 out:4 shown:1 furthermore:1 since:3 rev:8 particles:1 contained:1 math:6 earlier:1 linear:5 panigrahi:3 interactions:2 free:2 reason:1 khare:2 york:2 e0:11 degeneracies:1 hψ0:1 creates:1 iso:1 symmetrised:3 δij:1 hence:2 first:1 origin:1 hyderabad:2 xi:22 variables:1 set:7 relations:1 wadia:1 sutherland:7 given:5 law:1 checked:1 forrester:2 sivakumar:2 system:5 construct:2 scheme:1 gives:2 exactly:1 minahan:1 authors:2 x2:1 sˆ:4 john:1 showed:1 annihilation:2 fermionic:1 fˆ:15 manner:1 sen:1 any:4 calogero:7 gravity:1 note:1 caselle:1 transparent:1 olshanetsky:2 ordinates:2 letter:2 shastry:1 pair:1 why:1 commutation:2 constructed:3 kj:2 clear:1 partition:1 typeset:1 hi:9 exp:14 mechanical:1 physics:1 sector:2 show:2 random:1 gauge:1 trivial:1 ground:4 explain:2 written:1 should:1 monomial:1 only:1 explicitly:1 generators:3 various:1 hamiltonians:1 harikumar:1 define:2 ones:2 words:1 dr:1 arxiv:1 method:1 mapped:2 including:1 2δij:1 achieved:1 lnl:2 result:1 discussions:2 terms:1 murthy:1 eigenfunctions:9 symmetric:9 state:6 identification:1 between:2 invariant:1 available:1 notice:1 recently:1 nature:1 however:1 trugenberger:1 solv:1 ket:3 askey:1 both:1 diejen:1 x2i:8 x2j:1 many:1 connection:4 profs:1 relevant:1 co:2 point:2 harmonic:8 dimensional:2 cs:6 respect:2 aˆ:1 copies:1 been:2 int:2 polychronakos:1 interest:1 basic:1 ph:1 algebras:2 abstract:1 pl:1 choose:1 quantities:2 spin:1 present:2 unlike:1 bhaduri:1 procedure:1 vectors:3 simons:1 ii:1 cond:1 ernet:1 different:3 make:2 same:1 quant:1 units:1 several:2 higher:1 independent:3 used:1 i1:1 i3:1 i2:4 effect:1 totally:1 recent:2 academic:1 kawakami:1 sets:2 model:16 dimension:2 being:1 obtain:1 identify:1 thanks:1 yamamoto:1 eigenstates:3 adv:2 haldane:1 manybody:1 macdonald:1 dhar:1 lett:7 easy:1 mandal:1 solvable:1 transformation:7 beenakker:1 aspects:1 eigenfunction:1 press:2 using:2 mod:1 like:2 particle:4 interestingly:1 yields:1 arbitrary:1 become:1 works:1 reduces:1 therein:1 creation:2 algebraically:1 polynomial:3 normalisation:2 comments:1 bra:3 provides:1 prof:1 chains:1 power:1 rep:1 bn:10 illustration:1 clarendon:1 revtex:1 properties:1 stage:1 carried:1 basis:6 range:1 act:1 illuminating:1 perelomov:2 soc:1 h2:1 h1:1 compos:1 appropriate:1 square:2 references:2 operator:5 bosonic:1 van:1 support:1 there:3 long:1 bosons:1 inner:1 ed:1 notices:1 function:5 complete:5 form:3 hj:3 hk:2 construction:1 hn:1 made:2 wise:1 mat:1 up:1 fluctuations:1 quantised:1 ki:4 later:1 constant:1 ai:2 sxi:1 universal:2 general:1 tˆ:3 conserved:2 proves:1 exist:1 commuting:4 check:1 physical:1 functions:11 when:1 application:1 other:2 conclusion:1 models:4 polynomials:5 jastrow:1 structure:1 correlated:1 coupling:1 baker:2 cherednik:1 starting:1 having:1 chaturvedi:1
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quant-ph9710020.txt |@word represent:1 cosines:2 sci:1 consider:18 pointing:1 gupta:1 rev:4 magnetic:2 results:4 leads:2 eǫ:1 consists:1 issues:6 compact:1 simon:1 advantage:1 equivalence:4 including:1 easiest:1 presents:1 finally:2 does:1 those:7 mod2π:6 analogous:3 include:1 applied:1 delhi:1 chennai:1 amplitudes:1 eilθ:2 very:3 observables:2 differently:1 wave:63 implicit:1 sons:1 lynch:1 emphasized:1 rn:1 condition:11 entire:3 hamiltonian:4 diverging:1 suffices:1 large:14 discrete:4 minimizing:1 small:12 gauge:36 optics:2 configurations:1 antinodes:2 sin2:1 measurable:1 approximation:1 limǫ:1 second:5 pass:1 further:5 oneto:1 acid:1 odd:1 quite:1 canonical:2 even:9 will:1 ˆu:1 apparatus:1 2cos:2 trivial:1 section:9 adhoc:1 uniform:5 henceforth:1 consistently:1 axial:1 localized:1 above:1 new:9 falling:1 ground:1 consisting:1 contrast:1 satisfy:1 edited:1 bi:1 measurements:1 respectively:1 here:4 understanding:1 address:1 represented:3 cosec:1 extrema:3 appears:1 z2:5 box:23 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quant-ph9710021.txt |@word limited:2 dynamic:1 entropy:1 localized:1 whose:1 const:1 γk:2 γn:1 under:1 worth:1 conjecture:1 unrenormalized:2 rise:2 every:3 summarized:1 school:2 cause:3 solution:4 convenience:1 succession:1 indices:2 markov:2 excited:11 consistent:26 direct:1 approximation:12 second:4 even:8 zinn:1 incompatible:5 selected:1 ˆa:3 ˆb:31 ˆe:7 above:4 new:1 ˆj:1 ˆm:4 evolving:2 never:2 here:3 atoms:23 met:1 plenio:2 represented:5 interpret:1 study:2 changed:1 approaches:2 orthogonalization:1 california:1 suitable:1 appropriately:1 projection:18 plenum:1 highly:6 total:5 propagators:1 would:10 dnm:5 dnn:1 therefore:5 type:5 until:4 separated:4 remark:1 δhh:2 odinger:4 berlin:2 excellent:1 unraveled:1 hold:2 must:12 springer:2 ih:13 setup:2 work:7 dn1:1 iheff:19 dn3:1 concepts:1 example:2 renormalization:1 give:4 preserving:3 generically:1 involve:1 indicates:1 want:2 end:1 provide:1 describes:2 feature:1 far:4 env:2 significance:1 symposium:1 ordinary:1 iiid:2 ψin:1 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quant-ph9710022.txt |@word represent:1 partial:1 funct:1 eds:1 scalar:1 scr:1 looking:1 inverse:5 depend:2 tn:1 δhn:1 finally:2 under:1 analogous:1 characterised:1 worth:3 eikonal:1 p2:5 belonging:1 miele:1 comm:1 siena:1 translations:1 dell:1 dokl:1 geometrical:3 milani:1 wishes:1 nijenhuis:4 generalised:1 dubrovin:1 hamiltonian:19 turns:3 notes:2 solution:1 δh1:3 δh0:4 deals:1 discrete:1 vector:11 eigenvalues:4 div:1 sapienza:1 occurrence:1 dealing:1 approximation:1 second:1 value:2 further:1 dynamics:7 eigenspaces:3 canonical:11 bilinear:1 what:1 nonlinear:17 brackets:3 section:2 shares:1 current:1 new:4 method:5 satisfy:2 degree:1 whose:3 respectively:2 sins:1 les:1 concluding:1 marchenko:2 equations:5 implicit:1 δλi:3 bibliopolis:1 remarks:2 technical:1 national:1 allows:2 survey:1 poisson:10 action:1 studies:1 jackiw:1 italiana:1 via:2 useful:1 societa:1 addressed:1 apply:1 tools:1 use:2 takes:2 working:1 commun:2 hilbert:3 tecnologica:1 ψh:1 criteria:1 type:2 ψd:1 more:5 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quant-ph9710024.txt |@word consider:2 similarity:5 rev:4 berry:1 results:4 leads:3 eds:1 scalar:1 commute:2 parameterization:1 consists:1 remarkably:1 gl:1 reasoning:1 compact:1 inverse:3 calculate:2 iii:2 tr:8 acting:1 finally:1 does:6 under:3 stochastic:1 alternatively:1 must:4 case:4 straightforward:2 orthogonal:1 emphasizes:1 sons:1 every:1 entries:1 matrices:21 illustrated:1 immediately:1 hamiltonian:1 irreducible:2 notes:1 solution:1 large:1 vector:7 indices:2 eigenvalues:8 rk:1 equation:4 dis:1 upper:1 mn:13 deutsch:1 oscillator:1 zero:7 chem:1 expressions:3 spectral:14 established:3 voros:1 invertible:2 brackets:2 giving:1 trivial:1 sum:2 expressed:5 version:3 en:4 establishes:1 expresses:1 contributes:1 method:4 coefficient:2 full:2 simultaneously:1 respectively:4 equals:1 here:2 courtens:1 behaviour:1 illustration:1 groups:9 exponent:1 along:3 equations:3 mod:1 referring:1 obtained:2 antisymmetric:3 involved:6 study:1 vectors:3 allows:1 round:1 twamley:1 products:4 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