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quant-ph9912023.txt |@word represent:1 consider:9 remarkable:1 limited:1 directions:2 results:7 illustrated:2 commute:1 generalize:1 grateful:1 aiello:3 contributions:1 ˆb2:5 row:1 whose:1 certainly:1 inverse:2 depend:4 calculate:10 zone:1 graph:2 tr:2 presents:1 finally:5 infinitesimally:2 ti:2 kλ:2 stochastic:1 analogous:1 bracket:1 norm:1 applied:1 amplitudes:4 straightforward:3 orthogonal:2 very:1 frequencies:1 desired:1 differently:1 wave:5 putting:1 axes:1 mixing:3 elena:1 difference:1 exact:1 condition:3 splitter:4 cianci:1 dij:1 presented:2 transmission:4 knight:1 eiω2:7 t2:5 solution:1 t1:5 discrete:10 convenience:1 vector:5 angelis:1 small:1 relation:3 ueda:1 optics:2 noted:1 passante:1 correct:1 sapienza:1 illustrating:2 oscillation:2 10b:1 dutra:1 consistent:2 10a:1 direct:1 10d:1 sign:1 past:1 zero:11 exter:1 spontaneously:1 expressive:1 canonical:8 bilinear:6 will:8 ˆr:3 g22:1 appear:1 rate:1 cˆi:8 giving:1 section:8 associate:1 cˆb:1 near:3 rome:1 ˆa:2 ˆb:24 ˆc:3 above:1 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quant-ph9912024.txt |@word neighbors:2 limited:1 consider:4 magnetic:1 results:7 four:2 consists:1 anggi:3 denotes:2 localized:4 sch:1 aug:1 eigenbasis:1 segments:1 tu:3 corrections:1 tn:1 finally:2 those:2 th:1 ti:1 perature:1 p2:2 choice:1 resonant:6 exact:1 condition:1 squids:1 λβi:1 exponential:3 vibrational:7 level:6 issue:1 applicable:1 t0:23 t1:1 large:2 discrete:4 subway:1 science:1 small:1 eigenvalues:2 markov:1 lines:2 grifoni:1 averaged:4 tem:1 findings:2 consistent:2 prediction:1 cosh:2 approximation:6 rate:12 enhancement:1 dynamics:21 acid:1 linear:1 even:3 index:1 assisted:1 graduiertenkolleg:1 expressed:2 switch:1 sequential:2 increasing:2 method:3 contrast:2 splittings:1 full:4 respectively:1 qµν:2 here:5 pumping:1 objects:1 sinh:1 relaxation:7 path:15 strong:3 equations:5 obtained:2 solid:1 chaotic:1 involved:3 vectors:2 prior:1 egger:1 rdm:6 frictional:1 gwinn:1 via:1 fµ:1 scales:1 problematic:1 ls:1 scaled:1 sgn:1 apply:1 predicted:1 use:3 charge:1 reactive:1 λαi:1 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quant-ph9912025.txt |@word scl:13 consider:6 represent:1 rev:5 magnetic:9 global:1 results:6 leads:2 eds:1 generalize:1 computation:1 depend:1 calculate:3 aug:1 irrelevant:1 finally:1 p2:1 rise:1 splitting:6 electron:1 difference:2 exact:1 condition:4 northwestern:1 level:11 anisotropy:3 large:3 small:1 eigenvalues:4 barbara:1 degeneracy:15 eiϑ:1 dilute:2 cosh:1 approximation:6 fold:33 zero:2 value:2 further:1 odd:4 even:3 plays:1 stands:1 giving:1 section:3 expressed:3 experiment:1 above:6 values:2 contributes:2 ˆn:1 condensed:1 simultaneously:1 degree:1 respectively:4 here:1 sinn:2 cos2:2 address:1 directions:2 consideration:1 along:7 equations:1 obtained:4 tunneling:58 shift:1 study:1 changed:1 periodic:11 action:6 makes:1 eiφ:2 increased:1 replace:1 translational:1 summation:2 apply:1 quenching:10 use:1 negative:2 comparing:2 call:1 eϑ:4 more:6 introducing:2 becomes:5 varying:2 known:2 cases:3 hold:1 rotational:3 integrating:1 tunnel:5 science:1 equation:1 mn:3 reproduce:1 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quant-ph9912026.txt |@word represent:2 since:3 consider:2 ceases:1 limited:1 comparatively:1 results:3 extensively:2 leads:1 grateful:1 consists:1 3a2:1 contributions:1 scr:1 supposedly:1 dimensionality:1 depend:1 fokker:1 white:3 supported:1 critical:1 shenoy:1 under:8 stochastic:4 norm:1 global:2 amplitudes:4 frequencies:2 springer:1 atoms:1 choice:1 figs:1 stays:3 resonant:1 difference:1 exact:3 feeble:1 condition:4 level:3 turns:1 notes:1 solution:5 t0:2 try:1 solved:1 adjust:1 small:10 optics:2 degeneracy:1 work:2 zh:3 ten:1 lecture:1 estimates:2 direct:1 b21:1 approximation:9 go:1 second:5 arnold:1 dynamics:3 estimated:1 odd:3 linear:4 even:5 what:1 nonlinear:9 trapping:2 rate:3 brackets:1 section:4 shares:1 consequent:1 version:1 above:4 replaced:1 coefficient:4 agreement:1 degree:2 fiz:1 respectively:1 diagonal:3 behaviour:3 asymmetry:1 inverse:1 address:2 concluding:1 ignore:1 quite:1 equations:14 change:2 obtained:2 solid:2 almost:1 spite:1 technical:1 shift:4 study:1 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quant-ph9912028.txt |@word partial:1 consider:6 illustrates:2 roc:1 desirable:1 results:5 gy:3 gx:3 leads:1 scalar:1 commute:1 consists:2 follow:1 expressions:1 contributions:8 cases:1 gi:6 whose:3 amplification:1 depend:1 uβ:1 rayleigh:1 nonlocal:1 tn:1 matrix:7 finally:2 program:1 those:2 th:4 under:2 breach:1 analogous:1 include:1 ionizing:4 supported:1 straightforward:1 very:1 frequencies:1 springer:2 wave:18 photoabsorption:1 electron:14 photodissociated:1 mixing:2 experimentally:1 difference:3 four:3 annihilated:1 hamiltonian:10 positions:1 t4:19 t2:33 t3:32 t1:42 large:2 discrete:1 indices:3 eigenvalues:1 optics:8 correct:1 dilute:1 illustrating:1 dealing:1 direct:2 approximation:2 located:1 second:3 evaluated:1 colciencias:1 further:1 dynamics:2 linear:1 established:1 what:1 nonlinear:1 plays:1 rate:5 diag:2 section:5 selected:1 expressed:1 current:4 experiment:1 establishes:1 new:4 contributes:2 consisting:1 contrast:2 satisfy:1 edited:1 full:1 κi:2 exchange:14 d1:2 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quant-ph9912031.txt |@word homomorphism:27 four:1 entropy:1 consists:4 relationships:1 whose:8 const:3 paris:4 unanswered:1 whatsoever:3 under:8 ontological:5 characterised:2 risk:1 impinges:1 rise:2 every:10 summarized:1 affect:1 solution:3 concise:1 miller:1 consistent:12 direct:1 surrounding:1 second:12 even:13 established:1 incompatible:20 specification:3 selected:1 above:18 new:8 ever:1 consisting:3 evolving:1 simultaneously:2 never:3 equals:2 here:5 hundreds:1 represented:1 interpret:4 obtained:1 elaborate:1 changed:3 completely:2 procedure:1 stressed:6 adopting:1 changes:2 criticism:1 appropriately:5 projection:20 spooky:1 plenum:1 highly:1 circumvent:3 kobayashi:1 would:14 chooses:3 tm:6 call:5 therefore:3 survive:1 25th:1 type:5 tell:1 supporters:6 odinger:6 aware:3 correspondingly:1 hold:5 must:34 obeying:1 join:4 characterize:5 work:7 entertained:1 theories:6 macroscopically:1 concepts:1 appraisal:1 example:25 indicated:3 give:10 preserving:1 want:3 keep:1 cushing:1 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quant-ph9912035.txt |@word passively:1 limited:1 caused:1 lack:1 results:1 leads:3 avalanche:1 computation:1 causes:1 looking:3 repetition:1 calculate:1 advantage:2 send:1 finally:1 does:2 device:1 preserved:1 under:1 tb:4 tc:4 case:10 collaborate:1 confidential:1 orthogonal:1 shifters:1 desired:1 noncommuting:1 choice:1 every:1 stays:1 experimentally:1 difference:8 condition:1 common:1 splitter:2 transmission:4 dif:1 brendel:3 accidentally:1 t0:5 large:1 coincidences:4 indices:1 smaller:1 force:1 hillery:2 second:2 noise:1 pass:1 greenberger:2 distance:1 port:4 even:2 what:1 errors:6 adds:1 rate:3 sum:1 bo3:1 brief:1 swiss:1 access:1 experiment:2 above:5 new:2 method:1 counters:2 quenched:1 full:1 chose:1 channeled:1 respectively:4 never:1 here:2 sexp:2 following:1 amplification:1 mermin:1 kilometers:2 alone:1 path:3 respect:1 obtained:1 sender:1 technical:1 shift:1 losses:1 contradiction:1 lo:1 usually:2 bob:22 sinusoidal:1 klyshko:1 emerge:1 via:5 stabilization:1 secure:2 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quant-ph9912036.txt |@word secondly:1 switched:3 gupta:1 magnetic:4 fabricated:2 existing:3 four:1 per:2 computation:9 consists:6 hase:1 disk:1 issues:1 etching:2 technique:1 finally:3 th:7 under:3 sound:2 acoustic:2 very:1 frequencies:3 rise:1 floated:1 results:6 electron:25 manipulated:3 resonant:11 difference:6 hamiltonian:2 large:3 vector:2 succession:1 small:1 der:1 configurations:1 upper:5 smaller:2 oscillation:1 deutsch:1 pulse:5 rate:3 design:2 dynamics:3 estimated:4 even:1 established:1 xor:2 nano:3 giving:1 section:3 switch:1 localized:4 above:3 pashkin:1 method:6 nakamura:1 satisfy:2 kamada:1 respectively:16 here:2 ranges:1 deposition:2 mev:5 operating:4 groups:1 address:1 layout:1 along:6 change:2 box:3 shift:1 study:2 larger:3 resonance:6 studies:1 via:1 vij:3 explained:1 highly:1 separation:3 addressed:1 9s:1 establish:1 estimate:1 manipulate:1 gaas:1 use:6 sake:1 contains:1 charge:2 occupying:3 nanoelectronics:1 therefore:3 m3:1 films:2 becomes:1 spoils:1 emission:4 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quant-ph9912037.txt |@word secondly:2 dewitt:1 sci:1 consider:4 chain:3 limited:1 interference:4 alternatives:1 results:1 eds:1 commute:2 notationally:1 grateful:1 consists:2 follow:1 contributions:1 gr:2 whose:2 certainly:1 depend:1 deterministic:1 tr:4 tp:1 passage:1 environment:5 charge:1 behave:1 preserved:1 under:14 indicating:1 p2:4 string:1 orthogonal:1 very:7 brownian:2 wave:1 difference:1 exact:8 condition:1 entire:1 level:3 ref:9 t2:2 t1:3 large:11 annihilates:1 small:7 entropy:1 programme:1 benjamin:1 dilute:4 coordinate:1 rivers:1 approximation:1 surrounding:1 zero:12 go:2 further:1 calzetta:3 quite:1 even:2 established:1 what:2 appear:1 sum:2 localization:2 brief:1 d3:1 version:1 above:6 suppose:3 consisting:2 contrast:1 satisfy:2 edited:4 evolving:1 full:1 degree:3 respectively:1 never:2 preserves:1 here:3 desired:1 asymmetry:1 q2:19 smearing:3 separation:1 directions:1 d51:1 strong:1 equations:13 deduced:1 obtained:3 trans:1 numerator:3 suitably:1 involved:1 larger:1 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quant-ph9912047.txt |@word represent:1 sci:1 consider:1 rev:1 magnetic:4 results:2 existing:1 four:5 computation:6 managed:1 expressions:1 whose:2 inverse:1 const:2 acting:2 under:3 forbidden:2 applied:1 ermakov:2 very:3 frequencies:7 kcn:1 wave:1 resonant:2 affect:1 difference:1 matrices:1 condition:1 entire:1 large:2 discrete:3 indices:3 specially:1 direct:4 pulse:5 sign:1 approximation:1 zero:2 pmm:4 pmn:6 4x4:1 linear:1 appear:1 multiqubit:2 sum:1 expressed:3 3k:1 axial:1 above:3 satisfy:1 exchange:3 respectively:2 component:1 here:3 diagonal:1 desired:1 asymmetry:1 represented:1 along:2 change:1 obtained:1 institute:1 leaves:1 larger:1 allows:1 periodic:1 products:1 resonance:5 fourier:3 projection:2 logical:1 assertion:2 p32:2 iz:1 apply:1 p44:4 p43:2 propagators:1 unit:2 use:3 p31:2 takes:2 would:2 contains:1 next:1 m1:1 therefore:2 a57:1 m2:1 populations:1 operators:6 iiy:2 particular:1 known:1 states:8 room:1 vladimir:1 permits:1 mm:1 science:1 work:1 temperatures:1 following:1 dec:1 averages:1 example:1 calculation:3 sample:1 r22:1 axis:3 information:4 needs:1 end:1 itω:2 negation:2 instead:1 parameter:1 sin:7 ρeq:8 product:4 after:2 variant:1 collection:1 produce:1 designed:1 parallel:1 sy:1 sx:2 effective:2 computations:1 sp:2 negligible:1 representation:3 order:2 operations:3 pulsed:2 indeed:2 paper:2 during:1 before:1 complicate:2 rapidly:1 energies:1 writing:2 forms:1 systems:1 schrödinger:1 mail:1 correspondence:1 measurement:1 them:1 greater:1 combination:1 propose:1 p11:1 p12:1 p13:2 rotation:6 easily:1 term:1 obviates:1 ensemble:1 possibilities:2 filling:1 magnitude:1 each:1 em:4 el:1 en:2 directly:1 ek:1 populated:1 energy:8 idea:1 frequency:6 static:2 measure:1 quantum:14 our:1 operation:2 transitions:2 special:1 out:3 ru:2 matrix:14 space:9 gradient:1 rx:1 rf:8 performs:3 theory:1 interactions:1 b34:5 1s:4 free:1 clarify:1 complicated:1 besides:1 e4:2 e1:3 e3:3 e2:4 interaction:5 determining:1 transition:1 so:2 place:1 hence:1 symmetry:1 timeindependent:1 number:1 done:1 specifically:1 quadrupole:3 reached:1 size:1 given:2 1r:2 temperature:2 similarly:1 system:2 adopted:2 1a:1 their:1 cooling:1 calculations:1 scheme:1 bits:2 final:2 speaking:2 gives:1 academy:1 transverse:1 optical:1 pnm:3 pnn:2 than:1 relative:1 polarized:2 preparation:1 amplitude:1 identical:1 similar:1 russia:1 spectra:1 unchanged:2 spectrum:2 substantial:1 need:1 any:2 ρout:2 angle:5 convenient:2 note:1 sciences:1 high:1 ur1:1 ur2:2 algorithms:3 divers:1 eff:2 electric:5 shall:4 object:1 simplify:1 boltzmann:1 letter:1 pair:1 coil:1 measured:1 considered:2 average:1 principle:1 exp:10 kt:1 χm:2 p34:1 show:1 detection:1 notations:1 spaces:4 radio:1 pkk:2 find:2 pkl:1 µm:1 slow:1 implementation:2 written:1 only:2 equilibrium:2 subspaces:1 notation:1 ϕz:1 ϕk:1 ϕe:1 ϕd:1 ϕf:6 ϕa:5 ϕc:1 alexander:1 evolution:6 precession:3 fields:2 uz:2 constructing:2 exists:1 observed:1 p24:1 see:1 computer:3 p21:2 result:7 p23:1 rmm:1 recording:1 eigenfunctions:2 nuclear:6 currently:1 symmetric:1 initially:1 state:17 difficulties:1 between:2 invariant:1 reading:2 conditions:1 speed:1 terms:4 rotating:1 nature:1 qubits:3 implementing:1 configuration:2 distribution:1 suggested:1 cos:7 ωb:1 last:1 ωe:2 equal:4 zeeman:1 logic:1 ρinit:6 simple:1 corresponds:1 dimensional:5 crystalline:2 described:2 transformations:4 leads:1 basis:6 addition:1 three:2 goes:1 ph:1 define:1 carriers:1 controlled:2 quantities:1 sufficient:1 angles:2 spin:26 present:2 case:2 kazan:2 single:1 remaining:1 will:5 while:1 situation:1 procedure:2 iy:3 ix:2 unitary:3 coupled:1 according:1 containing:1 verified:1 perform:3 make:1 same:2 quant:1 split:2 used:2 moment:1 levels:8 purpose:1 entanglement:1 cycle:2 suitable:1 center:1 s22:1 materials:1 components:4 model:1 possesses:1 gates:1 proposed:2 less:1 generally:2 obtain:2 intervals:1 voltage:1 aspect:1 macroscopic:1 eigenstates:1 λm:2 density:10 except:1 5r:1 dqg:1 easy:1 technological:1 b12:5 transformation:6 real:4 read:2 sums:1 possible:1 using:1 bit:1 accepted:1 necessary:2 particle:1 follows:1 signal:2 performing:1 smm:1 arbitrary:2 become:1 spins:7 accessible:1 because:1 methods:2 back:1 choosing:1 small:1 nonzero:2 esr:1 p42:1 does:2 provides:1 demonstrated:1 nmr:2 equivalent:3 processing:1 oscillating:1 illustration:1 ratios:1 standpoint:1 p33:1 pll:2 properties:1 cnot:1 rare:1 most:1 discussed:1 carrier:1 stand:1 act:1 computational:3 isomorphic:1 down:1 schemes:1 operator:6 additional:1 initial:3 u1:2 u3:1 u2:2 low:1 subsequent:1 propagator:6 form:2 but:2 russian:1 ha:1 hf:1 made:2 consist:1 kessel:1 us:1 placed:1 below:1 uk:1 ωa:4 ud:2 ωc:1 uf:13 ua:3 ωd:2 ub:3 mechanics:1 constant:1 defined:2 certain:3 abstract:3 contribute:1 2ha:1 examine:1 proves:2 tomography:1 corresponding:4 formalism:1 check:1 physical:1 functions:1 when:2 virtual:3 field:10 role:1 suppress:1 elements:5 generates:2 mechanical:1 important:1 nucleus:2 assume:3 required:3 changed:1 time:2 nuclei:2 requires:1
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quant-ph9912048.txt |@word dewitt:1 gr:2 similarity:1 alg:1 global:1 results:13 invent:1 leads:13 roy:1 commute:5 generalize:2 grateful:2 foundations:1 go:1 gl:4 rom:1 compact:5 preserves:1 duistermaat:1 factoring:1 ıa:1 finally:1 critical:1 present:7 under:4 analogous:1 include:2 ingredient:2 applied:3 conjecture:1 straightforward:1 orthogonal:1 implicitly:1 relatively:1 polarization:13 splitting:1 mour:1 interpreting:1 decide:1 noncontractible:1 lerman:1 difference:2 bringing:1 condition:13 splits:2 annihilated:1 riemann:2 hamiltonian:7 suffices:1 large:2 discrete:5 vector:5 phase:55 esi:1 dealt:4 aachen:3 eigenvalues:3 o0:4 employing:1 ga:2 dealing:2 direct:2 literature:1 translating:1 zero:8 further:6 goes:1 spectral:2 established:1 plays:1 appear:1 brackets:1 section:7 experiment:1 en:1 above:14 new:1 method:8 satisfy:1 edited:1 guillemin:4 simultaneously:2 chose:1 realizations:2 abstractly:1 here:6 desired:1 fairly:1 les:1 groups:3 address:2 represented:4 along:2 quite:1 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quant-ph9912049.txt |@word consider:1 rev:3 results:2 four:2 roy:1 generalize:1 broader:3 inverse:1 longstanding:1 equivalence:1 ts:2 under:1 norm:1 orthogonal:3 springer:1 wave:14 figs:2 summarized:1 kazuo:1 matrices:1 condition:16 ladders:2 presented:2 transmission:3 solution:6 large:1 discrete:1 vector:1 small:3 eigenvalues:2 unexpected:1 2k0:2 periodicity:1 renormalized:1 direct:1 cosh:3 jump:1 second:1 rigorous:1 reine:1 eik0:2 even:3 giving:1 section:2 current:5 goes:2 new:1 consisting:1 satisfy:1 full:1 respectively:3 realizations:1 component:1 here:3 understanding:1 possibility:1 sinh:3 eikx:3 quite:2 appears:3 deduced:1 hamiltonian:1 parameters:1 rigorously:1 vectors:1 tial:1 periodic:18 krohn:1 shaded:1 changes:1 examining:2 yamada:1 useful:1 family:8 scales:1 apr:1 inducing:1 would:1 commun:1 distinct:1 positive:1 century:1 negative:4 m2:1 eϕ:1 historically:1 more:2 separated:3 jpn:1 duality:3 becomes:8 operators:4 odinger:5 dirichlet:1 particular:1 known:2 cases:14 iii:1 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quant-ph9912052.txt |@word limited:2 partial:1 consider:4 remarkable:1 represent:1 rev:14 resist:1 varying:1 results:1 leads:1 per:1 inverse:1 ver:1 etching:1 rayleigh:7 passage:1 under:2 lord:1 vrijen:3 applied:1 amplitudes:1 advantage:1 orthogonal:1 shifters:1 seemingly:1 choice:1 manipulated:1 ultraviolet:1 matrices:1 illustrated:1 transmission:1 turns:1 trench:3 bangor:1 phase:18 small:1 optics:1 still:1 upper:7 smaller:1 ten:1 deutsch:1 pulse:1 approximation:6 colin:1 pass:1 recalculate:1 port:3 linear:3 even:1 will:6 what:1 nonlinear:1 sub:2 rate:6 clock:1 giving:1 section:2 3p:1 optoelectronics:1 expressed:1 current:1 experiment:2 above:5 new:2 ever:1 method:2 respectively:3 spacing:3 here:4 reported:1 deposition:8 ramsey:1 operating:1 separation:1 address:1 represented:1 path:7 calculate:1 daughter:1 accomplishes:1 institute:1 shift:7 yablonovitch:3 allows:3 reason:1 leaving:1 slb:1 fourier:1 makes:1 york:1 eˆ:8 followed:1 scales:5 namely:1 bs:6 highly:1 scaled:2 controlled:1 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quant-ph9912059.txt |@word partial:10 consider:3 dynamic:2 results:2 four:5 scalar:2 gn:5 expressions:4 bremsstrahlung:4 calculate:1 zd2:2 γk:7 charge:2 under:1 cm2:2 eikonal:6 kρ:1 kπ:16 amplitudes:1 far:3 connects:1 wave:39 electron:12 formula:2 matrices:1 condition:1 presented:3 turns:1 applicable:3 leave:1 vector:5 aρa:1 sin2:1 za:4 approximation:13 zero:1 follow:1 further:2 correspond:5 odd:1 linear:5 blue:2 index:1 sun:1 section:14 expressed:2 above:1 lifshitz:1 3c:1 3b:2 3a:2 acknowledgments:1 outgoing:1 simultaneously:2 exchange:1 respectively:5 even:1 equals:1 here:3 making:3 path:1 along:1 strong:4 obtained:7 dividing:1 reason:1 periodic:1 products:2 action:2 fourier:3 makes:1 plotted:2 via:1 total:5 unit:2 recurrence:1 eω:1 takes:1 would:1 comparing:2 taken:3 scope:1 introducing:1 becomes:1 carrying:1 normalized:1 varying:1 known:3 cases:1 iii:2 high:1 account:5 integrating:1 unessential:1 equation:2 averaged:1 infinitesimal:1 following:6 ρx:2 dec:1 f1:2 figure:4 process:12 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quant-ph9912060.txt |@word consider:2 rev:3 blanchard:10 results:11 commute:2 computation:1 consists:1 gl:2 gk:2 gj:13 inverse:2 depend:3 calculate:1 deterministic:2 under:1 x02:1 x01:1 x00:6 g1:1 very:3 wave:5 electron:7 matrices:1 condition:3 trm:2 solution:3 solved:1 vector:1 small:7 shows:4 zl:1 smaller:3 zi:2 zj:2 past:1 go:1 imply:1 dynamics:6 ct0:2 invertible:1 section:1 above:3 new:1 increasing:4 connected:2 method:1 component:4 equals:2 free:1 represented:1 respect:1 change:4 deduced:1 changed:1 reports:1 resulting:1 changes:2 uniquely:2 formulated:1 projection:1 9c:1 plenum:1 total:6 use:5 andreas:1 takes:1 would:1 prove:1 probabilities:2 positive:1 negative:6 noting:1 call:1 therefore:3 ψb:3 ψa:2 until:1 separated:2 flat:1 becomes:2 operators:3 normalized:2 impulse:1 stochastic:1 cases:1 detects:3 iii:2 eγ:1 must:3 high:7 mc:8 equation:6 modified:1 theories:2 infinitesimal:3 values:9 mechanic:3 following:9 dec:1 example:5 compare:1 figure:7 process:1 relativistic:39 states:5 lorentz:1 want:2 sense:1 get:9 how:3 pure:1 ωref:2 acta:2 allowable:1 parameter:2 singular:1 after:1 plane:3 physik:1 faculty:1 short:2 light:4 so:7 allow:3 representation:1 playing:2 nearly:4 helv:2 ith:2 indeed:1 over:3 paper:4 looks:1 y0:2 belavkin:1 its:7 discretizing:1 τj:1 thank:1 τi:6 solving:1 decreases:2 choose:3 versus:1 non:13 good:4 greater:1 horwitz:2 propose:3 fig:7 introduce:5 walls:1 they:2 rotation:1 now:10 discuss:1 densities:3 2w:1 dirac:6 university:1 2d:1 2e:4 each:1 2m:1 universit:1 characterized:4 mean:1 square:4 directly:1 formulate:3 doing:2 energy:1 operator:10 measurement:12 quantum:32 our:1 happen:4 eq:8 event:14 out:1 shown:2 matrix:1 space:14 induces:1 particles:4 jadczyk:9 ra:4 rm:2 forth:2 math:1 zj0:1 earlier:1 theory:9 barrier:1 possibility:2 standard:2 reason:1 york:1 put:1 r4:4 definition:1 r3:8 starts:1 area:1 times:11 int:1 place:3 errorbars:1 first:6 initial:6 probability:25 number:5 xd:14 another:3 open:1 aharonov:4 given:9 width:6 introduction:2 adjoint:1 system:12 1a:4 assumption:1 calculations:1 postulate:6 sensitivity:5 petruccione:3 wessels:2 way:1 continuous:3 albert:4 part:10 simulate:1 x2:7 x0:36 x1:3 than:5 diffusion:1 wide:8 kind:1 breuer:3 second:3 hypersurfaces:1 preparation:3 ann:1 atsstr:1 zero:1 lim:1 note:2 ideal:4 take:2 ex0:2 xi:1 detector:44 circles:1 systems:2 propagate:1 pair:1 intrinsic:2 calculated:2 later:2 detectors:8 order:1 points:1 exp:20 mechanical:1 velocity:1 physics:1 notion:1 show:2 text:1 random:1 find:6 paradoxes:1 based:1 parameters:6 aω:1 outside:1 should:11 only:10 summarizing:1 factor:2 adequate:1 do:6 distance:1 de:1 2mc:1 preparing:1 dx:8 momentums:7 dt:4 dp:8 evolution:1 continuum:1 textbooks:1 arxiv:1 acknowledgments:1 europhys:1 fixed:3 remains:1 arrival:25 set:5 computed:1 reference:7 frame:3 detection:8 see:7 result:3 enhanced:7 discussions:1 detect:2 review:2 definite:1 state:24 difficulties:2 between:6 invariant:3 boundary:3 conditions:3 email:1 preserve:1 weak:2 2pc:3 both:1 last:1 many:1 taking:1 density:11 equal:1 pdp:2 0c:5 uni:1 point:18 coincidence:3 dimensional:1 anti:3 wider:1 moreover:6 mc2:24 ct:2 described:1 transformations:3 piecewise:2 trajectory:1 invert:2 defined:2 reduction:6 expected:16 pk:1 ph:9 define:4 direction:2 observable:2 traversal:1 external:2 c2:12 those:4 case:3 p0:29 look:2 approximated:3 solid:4 value:4 will:2 5c:1 error:2 situation:1 characterizing:1 discretize:1 unitary:2 formulation:1 iv:2 ii:6 cone:4 different:6 formalism:1 perhaps:1 make:1 formulations:1 same:5 poincar:4 quant:1 φi:9 finite:3 events:7 development:2 independent:4 used:1 trajectories:2 v2:11 normalization:1 eigenvectors:1 lower:1 reflection:2 well:1 p12:1 solve:1 simulated:2 position:1 dimension:1 usual:1 being:4 λx:1 rest:6 λi:4 previous:2 application:4 interested:1 lett:4 easy:1 ruschhaupt:2 transformation:2 momentum:10 caspers:2 around:1 depends:1 big:2 possible:1 press:1 using:4 bit:3 height:8 helpful:1 like:11 particle:25 follows:1 reduces:1 velocities:1 zoom:1 detections:5 δj:1 arbitrary:2 because:1 classical:9 some:1 supplementary:1 mirror:2 proper:17 happens:2 undisturbed:1 electromagnetic:2 avoid:1 measurements:8 integration:1 cτ:10 assuming:1 steps:1 ωin:3 columbus:1 2c:8 agreement:1 illustration:1 step:1 found:4 cγ:4 properties:1 extension:1 dependence:3 o:4 simulation:1 covariant:5 range:3 germany:1 sensitively:1 considerations:1 communication:1 numerically:2 lies:1 bielefeld:3 references:1 frames:4 ea0:2 additional:1 pc:16 there:5 question:1 start:1 ψi:1 editor:1 lot:1 forward:1 function:14 form:2 piron:2 but:4 aµ:2 line:13 trying:1 compute:1 minkowski:2 inside:1 ωt:4 differentiable:1 discretized:1 below:1 limit:11 continuously:1 problem:2 mechanics:12 ai:2 abstract:1 describe:3 examine:7 right:1 simulations:3 moves:1 operation:1 again:1 dotted:7 no:4 dashed:4 nc:2 field:3 other:2 role:2 papers:1 theor:1 conclusion:1 uniformly:1 prepared:4 generated:2 coupling:2 algorithm:21 assume:5 dτ:7 time:54 observables:2 backward:4
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quant-ph9912061.txt |@word consider:2 desirable:1 results:6 quadrature:2 knill:1 send:1 squeezing:10 resources:2 case:5 orthogonal:3 very:1 wave:3 wishes:3 mixing:1 erp:1 difference:3 condition:1 swapping:2 presented:3 positions:3 solution:1 discrete:2 eigenvalues:3 optics:1 cosh:3 second:2 greenberger:1 canonical:1 even:1 multiqubit:1 experiment:1 shared:2 contrast:2 satisfy:1 full:1 lee:2 teleportation:17 here:1 bj:3 sinh:3 others:3 obtained:2 property:2 sender:1 involved:1 accomplished:1 resulting:1 bob:7 via:2 spatially:1 outcomes:1 hardy:1 apply:1 total:7 establish:1 use:2 would:1 hilbert:1 more:1 separated:1 operators:15 particular:1 known:1 must:2 account:2 join:1 science:1 equation:1 work:2 oscillator:3 modified:1 following:1 unconditional:1 boschi:1 bennett:1 share:1 states:4 dxn:1 arise:1 dxa:1 teleport:5 needs:5 feature:1 write:2 how:2 pure:2 instead:1 parameter:1 sin:3 map:1 information:2 after:2 dx1:1 bourennane:1 beam:1 revzen:1 light:14 ghz:15 claire:3 so:2 representation:1 martini:1 operations:1 horne:2 words:1 produces:1 indeed:1 over:1 satisfied:1 produced:1 experiments:1 its:3 perfect:4 writing:1 main:3 them:3 they:1 yq:3 now:2 discuss:1 eigenvalue:1 2p:1 2q:1 mode:2 found:1 polzik:1 series:2 frequency:1 expect:1 measurement:13 quantum:5 ep:1 shown:1 matrix:1 space:1 rev:6 projected:2 bennet:1 particles:15 acting:2 eprint:1 performs:2 print:6 mattle:1 rj:4 foundation:1 retrieved:1 standard:1 jozsa:1 r4:2 pairs:5 r2:2 r3:4 aj0:2 similarly:1 first:2 xj:1 there:1 xn:2 variables:10 another:1 xq:5 given:4 their:2 introduction:1 unknown:9 system:1 needed:2 πp:3 realization:4 scheme:2 bits:4 recovered:1 continuous:14 optical:6 x2:17 x3:11 x1:18 x4:4 x5:4 detection:1 wootters:1 fuchs:1 tree:1 zero:2 annihilation:1 crepeau:1 vaidman:1 enables:1 epr:15 recover:2 any:1 convenient:1 gorbachev:2 note:1 instance:1 take:1 transmit:1 channel:3 heisenberg:3 connected:4 jul:1 pair:13 measured:2 considered:5 braunstein:7 part:1 exp:6 supported:1 loock:3 find:8 based:2 popescu:1 state:40 only:5 version:2 developed:1 local:1 do:1 beams:2 de:1 db:1 joint:7 cannot:2 dx:8 dp:2 dq:3 resource:1 arxiv:1 she:2 set:4 fair:1 achieved:2 j0:2 relative:8 result:1 exploited:1 eigenfunctions:3 nature:1 ralph:1 written:1 2pp:1 triplet:9 reproduced:2 receivers:6 qubits:1 however:3 suppressed:1 both:3 cos:2 outcome:5 many:1 taking:2 equal:2 receiver:2 qubit:2 finds:2 mann:1 bell:7 simple:1 werner:2 expensive:1 photocurrents:1 considering:1 pp:4 described:3 basis:15 three:7 been:3 describes:3 combined:2 pj:1 ph:8 lett:4 arises:1 observable:1 sorensen:1 xxx:1 photon:1 2ip:3 zeilinger:2 maximally:4 spin:1 present:1 p2:11 p3:10 p1:13 p4:6 p5:6 kimble:2 eigenstate:3 squeezed:9 balance:1 unitary:11 laflamme:1 averaging:1 thus:1 site:1 weinfurter:1 same:1 quant:8 pan:1 used:1 moment:1 kim:1 entanglement:15 task:1 modes:9 modeled:1 well:1 obviously:1 position:14 model:1 parametric:2 protocol:5 proposed:3 less:1 being:2 eigenstates:2 mix:1 photons:1 quadratures:2 source:2 transformed:2 attractive:1 input:4 transformation:5 momentum:17 iθ:1 nielsen:1 possible:1 entangled:19 using:8 opo:4 mod:1 like:2 particle:31 follows:3 signal:1 alice:7 output:5 because:2 classical:2 creation:1 some:1 b4:3 b5:2 b2:2 b3:5 broadband:1 electromagnetic:1 per:2 does:1 2xq:1 demonstrated:2 noise:1 bc:3 aj:1 expansion:2 properties:5 noisy:1 discussed:1 range:1 furusawa:1 mixed:2 introduced:1 beamsplitter:5 into:4 splitting:1 karlsson:2 references:1 operator:12 bosonic:1 uncertainties:1 van:3 prepare:1 initial:2 way:1 was:1 function:1 complete:3 form:15 but:1 beamsplitters:1 transmits:1 up:2 2πp:2 problem:1 uc:8 ub:9 mechanics:1 defined:2 abstract:1 describe:1 linearity:2 denote:1 peres:1 single:2 formalism:1 identities:2 functions:4 bouwmeester:1 when:4 field:2 other:2 branca:1 deviation:1 picture:3 superposition:1 prepared:2 a0:2 a3:2 a2:1 a5:1 a4:1 ubc:4 correlated:2 factorized:1 assume:1 required:2 together:1 teleported:7
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quant-ph9912062.txt |@word gt:12 consider:2 ceases:1 maximum:9 rev:10 magnetic:4 suggests:1 results:5 leads:3 grateful:1 pershan:1 increase:1 amplification:1 transferred:2 technique:2 environment:1 finally:1 those:1 elliptic:5 under:4 γc:1 4x10:1 cm2:7 ingredient:1 applied:4 random:1 amplitudes:5 g2:1 advantage:1 without:2 very:14 frequencies:9 multi:1 wave:12 ultraviolet:1 figs:1 refractive:1 mixing:4 ui:1 difference:6 exact:2 condition:9 metrologia:2 treating:1 four:4 level:3 turns:1 gasphase:1 solution:5 integrated:1 large:5 discrete:2 progress:1 section:1 small:7 relation:2 optics:5 configurations:1 smaller:2 compensated:1 10b:1 10c:1 seventies:1 pulse:1 approximation:3 imply:1 doppler:5 enhancement:1 concludes:1 ζmax:4 qualitatively:2 dynamics:2 substitute:1 blue:2 established:1 what:1 nonlinear:12 wavenumbers:1 appear:2 rate:11 opaque:1 assisted:2 selected:2 near:1 current:2 3m:1 nm:2 3c:1 3b:1 3a:1 increasing:2 method:1 3d:1 coefficient:1 χns:2 full:1 degree:1 respectively:2 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quant-ph9912063.txt |@word katz:1 gt:1 consider:5 rev:11 magnetic:2 particular:2 splitting:1 gy:1 four:1 broader:1 op:1 gn:2 gm:46 collisions:1 hemmer:6 amplification:1 depend:1 transferred:1 technique:1 supported:1 finally:1 stable:1 include:1 cm2:2 applied:5 probe:1 amplitudes:3 g2:35 dϕn:1 g0:14 very:8 frequencies:6 induce:1 wave:14 refractive:1 mixing:1 specific:1 exact:1 condition:5 eit:17 treating:1 leads:1 obvious:1 level:4 turns:1 nagel:1 solution:6 integrated:1 large:9 solved:2 small:7 optics:2 application:1 work:4 grateful:1 sin2:10 direct:1 approximation:1 rate:11 traveling:1 ζmax:3 further:1 dynamics:1 blue:2 established:1 nonlinear:2 g22:19 trapping:3 section:1 zhao:1 expressed:3 cell:1 matsko:1 experiment:2 3n:2 above:4 3b:1 3a:1 d1:1 acknowledgments:1 agreement:2 σ3n:5 degree:1 respectively:2 here:9 atoms:9 ranges:2 δωm:1 cos2:4 address:1 active:1 path:2 along:3 strong:6 equations:7 change:5 19b:1 obtained:1 arrive:1 arimondo:1 shift:1 study:2 studied:2 allows:2 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quant-ph9912064.txt |@word limited:1 partial:1 ciao:1 rev:18 results:2 switches:1 eds:1 go:1 follow:1 remarkably:1 research:2 discern:1 whose:2 depend:2 violate:3 alamos:2 tl:3 program:2 device:1 those:3 under:1 td:15 te:9 supported:1 choice:6 figs:1 affect:2 difference:1 condition:2 arrange:1 applicable:2 correct:1 postselection:1 prediction:1 second:1 subtle:1 further:1 port:1 even:10 aim:1 what:1 apparatus:1 uniform:1 current:1 version:2 above:3 net:1 full:2 simultaneously:1 ibid:2 respectively:1 realizations:1 here:2 reported:2 objects:2 address:4 path:8 along:1 appears:1 change:1 obtained:5 arrive:1 institute:1 shift:1 popescu:1 allows:1 symp:1 shaded:1 changes:2 ake:2 pearle:1 followed:1 namely:1 ug:1 hardy:1 counts:1 should:4 establish:1 select:1 wang:1 fed:1 takes:3 would:5 prove:2 probabilities:3 predictions:2 hong:1 call:1 therefore:1 taken:2 survive:1 type:6 more:2 treated:2 formally:1 knows:2 emission:3 visibility:1 particular:1 foundations:1 hold:1 must:2 me:1 high:1 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quant-ph9912065.txt |@word homomorphism:1 four:1 reasoning:2 excludes:1 depend:2 ts:2 excluded:1 under:4 rise:1 electron:1 every:3 positions:1 deals:1 consistent:3 direct:1 likely:1 specker:2 even:1 employ:1 what:1 appear:1 incompatible:1 giving:1 sun:3 consistently:1 above:1 international:1 whose:1 here:4 along:1 change:3 study:3 contradiction:1 prior:1 published:1 opinion:1 projection:1 family:24 problematic:1 logical:2 assertion:1 boolean:5 should:2 angelo:1 takes:1 would:3 remains:1 hilbert:1 criteria:1 taken:2 type:1 theoretical:3 more:2 whatsoever:1 operators:1 ignorant:1 objections:1 must:3 account:2 pretend:1 salam:1 obvious:1 following:3 dec:1 example:1 history:11 claim:2 indicated:1 accept:1 assumptions:1 want:1 times:1 rather:1 indirectly:1 ghirardi:4 feature:1 trieste:3 answer:1 description:2 algebra:1 may:6 derived:2 objectively:3 summarize:2 meaningful:2 short:1 remember:1 assign:2 their:1 ones:1 so:3 order:2 se:1 belong:6 interpretation:1 constituents:1 move:4 unacceptable:1 negation:1 paper:2 including:1 statistical:1 argued:1 its:5 actually:2 resorting:1 systems:1 inconsistencies:2 mail:2 hidden:2 main:1 might:1 them:3 greater:1 framework:1 they:8 now:3 discuss:2 nor:1 possess:1 easily:1 university:2 truth:19 each:1 realism:1 directly:1 journ:1 measurement:1 quantum:5 our:12 happen:1 out:1 shown:1 space:2 since:1 rev:1 reader:1 correct:1 decoherent:32 theory:1 free:1 standard:2 admits:1 advantages:1 put:1 bassi:4 turn:1 consequence:3 think:2 first:3 already:2 features:1 probability:3 variables:2 reflected:1 proposing:1 given:6 checked:1 rejects:2 system:9 least:1 anyone:1 attach:2 assumption:8 postulate:1 perfectly:1 gives:1 rejected:1 part:1 believe:1 than:1 accordance:1 false:3 giancarlo:1 argument:1 recover:1 any:11 affairs:1 gleason:1 centre:1 most:1 letter:1 position:1 phase:1 accepting:1 probabilistic:3 consequences:1 considered:8 clear:1 possesses:1 mechanical:1 physics:3 notion:1 fact:2 precise:4 earth:3 analogue:1 debate:1 knowledge:2 spite:1 situations:1 histories:17 peculiar:1 only:3 going:1 do:3 goes:1 dh:8 means:3 accomodated:1 cannot:4 new:2 conjunction:1 arxiv:1 implication:1 kochen:2 view:1 requirement:2 set:2 reference:2 clarified:1 mentioned:3 violates:1 acquires:1 said:2 functionals:2 rejecting:1 state:2 closed:1 between:3 limit:1 neither:1 previous:1 approach:8 preserve:1 terms:1 legitimacy:1 article:1 come:1 suggested:1 many:2 according:3 reply:2 whole:1 detailed:1 relevant:1 bell:1 reasons:1 corresponds:1 simply:2 table:3 speak:3 considering:1 sensible:1 been:1 abdus:1 basic:2 ph:2 formalized:1 define:3 direction:1 families:8 reasonings:1 assert:1 understand:1 despite:1 spin:1 subsets:1 value:8 will:1 while:3 endowed:2 thus:2 ready:1 different:2 italy:1 things:1 make:2 formulations:1 member:1 quant:2 arguments:1 development:1 independent:1 extended:1 hand:1 devoid:1 moving:3 necessity:1 changing:1 possessed:4 well:1 analysis:2 thought:1 claims:3 dimension:1 quoted:1 among:1 when:2 physically:2 assigned:1 momenta:1 griffiths:14 preprint:1 infinitely:1 point:4 seems:2 mathematically:1 belongs:3 lett:2 around:3 rules:2 disagreement:1 possible:8 matters:1 know:1 using:1 unique:3 moreover:2 formal:1 like:4 specific:1 become:1 mathematical:1 satisfactory:1 because:2 classical:5 some:4 respect:1 curious:1 lead:3 avoid:1 measurements:1 per:1 everything:1 does:1 refer:2 nowhere:2 properties:10 about:5 theorems:1 accepts:1 obeys:1 act:1 other:4 considerations:1 raised:1 statements:2 previously:1 into:3 within:3 spoiling:1 references:1 indispensable:1 there:2 question:1 accordingly:1 way:1 forward:1 analyze:2 was:2 naturally:1 form:1 but:3 promote:1 true:3 he:8 infn:2 made:1 evident:1 up:1 us:4 nicest:1 distribution:1 attaches:1 agree:2 mechanics:3 associated:1 defined:1 abstract:2 doesn:1 general:3 single:7 formulation:1 formalism:3 denying:2 physical:10 no:1 generally:1 reality:1 valid:1 papers:2 department:2 acceptable:1 conclusion:1 stat:1 felt:1 meaning:3 important:2 allowing:1 disjunction:1 structure:5 independently:3 implies:2 values:8 rule:9 having:1 implied:1 time:1 original:1
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quant-ph9912066.txt |@word consider:2 remarkable:1 magnetic:1 focus:1 leads:1 roy:1 ge:1 go:1 factorizing:1 terms:2 irrelevant:1 concerned:1 presents:2 present:4 stable:2 te:2 interacting:1 straightforward:1 outside:1 very:2 could:2 results:3 every:2 nieto:3 condition:2 evi:1 annihilated:1 hussin:1 hamiltonian:3 solution:3 small:2 eigenvalues:2 c02:1 force:5 2k1:2 sukhatme:1 dealing:1 consistent:1 prediction:1 approximation:3 zero:2 further:1 displacement:2 laha:1 plays:2 letts:1 selected:1 near:3 shares:1 find:2 experiment:2 above:5 new:6 increasing:1 method:4 edited:1 exchange:1 modify:2 here:3 nodeless:1 behaviour:2 reported:1 mev:7 quite:2 equations:2 remark:3 accomplishes:1 involved:4 study:3 larger:1 allows:1 completely:1 commonly:1 superpotential:3 domains:1 hospitality:1 conveniently:1 makes:2 exited:1 involves:1 plotted:2 varshni:1 useful:1 hulthen:1 ipn:1 patience:1 claredon:1 total:1 establish:1 would:3 stated:1 negative:1 almost:2 ψh:8 ψn:7 therefore:10 scope:1 means:2 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quant-ph9912068.txt |@word results:5 eds:1 zinc:2 expressions:2 reineker:2 contributions:1 reasoning:2 synthetic:1 looking:1 terms:1 calculate:1 tu:1 company:1 charge:5 does:1 present:4 presentation:1 applied:2 2rm:2 methyl:1 r12:1 r13:1 advantage:2 very:3 springer:1 wave:1 electron:5 mixing:1 difference:1 condition:1 vibrational:20 hamiltonian:3 issue:1 solved:2 small:8 biological:1 markov:1 vµν:1 barbara:1 originally:1 htm:1 direct:1 approximation:2 second:5 further:1 dynamics:3 estimated:3 rappaport:1 spectral:5 index:1 ˆs:1 plays:1 sub:1 g21:5 blum:1 assisted:1 ˆb:1 sequential:1 3m:1 values:2 increasing:3 method:1 condensed:1 full:1 exchange:1 even:1 component:1 here:4 atoms:1 mev:2 possibility:2 separation:3 relaxation:8 along:2 equations:1 change:1 acceptor:18 obtained:4 trans:1 studied:2 excitonic:1 resonance:2 mujica:1 changes:2 plotted:1 vib:2 spatially:1 extra:2 tennant:1 plenum:1 scaled:2 kilin:3 names:1 linearly:1 franck:4 haken:1 takes:4 would:2 remains:1 beginning:1 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