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is the best-studied and most famous example. These are typically discrete systems, with particles fixed at different points of a lattice, but limits of results obtained by the QISM can give predictions even for
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of the Lax representation and reproduces the results of the Bethe ansatz. In fact, it allows the Bethe ansatz to be written in a new form: the
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Takhtadzhan, L A; Faddeev, Lyudvig D (31 October 1979). "The
Quantum Method of the Inverse Problem and the Heisenberg Xyz Model".
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448:. Asymptotics of correlation functions which include space, time and temperature dependence were evaluated in 1991.
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While the classical inverse scattering method is used to solve integrable partial differential equations which model
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was developed, relating determinant representations, descriptions by differential equations and the
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462:: the bulk free energy of the six vertex model depends on boundary conditions even in the
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659:"Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States"
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334:(for example, the KdV equation models shallow water waves), the QISM is used to solve
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Faddeev, L. (1995), "Instructive history of the quantum inverse scattering method",
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Sklyanin, E. K. (1992). "Quantum
Inverse Scattering Method. Selected Topics".
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The quantum inverse scattering method relates two different approaches:
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727:"RTT relations, a modified braid equation and noncommutative planes"
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The steps can be summarized as follows (Evgeny Sklyanin
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413:. This led to further progress in the understanding of quantum
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Quantum inverse scattering method and correlation functions
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Korepin, V. E.; Bogoliubov, N. M.; Izergin, A. G. (1993),
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It can be viewed as a quantized version of the classical
16:
Method used to solve integrable many-body quantum systems
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is used to construct solutions to the original system.
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405:. The quantum inverse scattering method starts by the
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Integrable PDEs/Classical integrable field theories
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179:. Unsourced material may be challenged and removed.
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823:, Cambridge Monographs on Mathematical Physics,
657:Zabusky, N. J.; Kruskal, M. D. (9 August 1965).
455:of the integrable models were obtained in 1989.
1232:Six-dimensional holomorphic Chern–Simons theory
864:
8:
458:Essential progress was achieved in study of
351:defined on a continuum, such as the quantum
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53:Learn how and when to remove these messages
1459:Classical and quantum statistical lattices
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390:. The center of the Yangian, given by the
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697:See for example lectures by N.A. Slavnov
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257:Learn how and when to remove this message
239:Learn how and when to remove this message
75:needs attention from an expert in Physics
475:
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277:(QISM), similar to the closely related
394:plays a prominent role in the method.
382:This method led to the formulation of
85:may be able to help recruit an expert.
7:
1285:Exactly solvable quantum spin chains
1220:Four-dimensional Chern–Simons theory
451:Explicit expressions for the higher
338:quantum systems, sometimes known as
177:adding citations to reliable sources
1149:Anti-self-dual Yang–Mills equations
188:"Quantum inverse scattering method"
1004:Superintegrable Hamiltonian system
594:{\displaystyle {\mathcal {T}}_{R}}
524:{\displaystyle {\mathcal {T}}_{R}}
14:
1326:Quantum inverse scattering method
1172:Integrable Quantum Field theories
285:in 1+1 dimensions, introduced by
275:quantum inverse scattering method
119:to comply with Knowledge (XXG)'s
34:This article has multiple issues.
1351:Classical mechanics and geometry
153:
106:
64:
23:
1089:Kadomtsev–Petviashvili equation
731:Journal of Mathematical Physics
644:10.1070/RM1979v034n05ABEH003909
164:needs additional citations for
42:or discuss these issues on the
1074:Nonlinear Schrödinger equation
553:
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423:nonlinear Schrödinger equation
317:partial differential equations
1:
1245:Exactly solvable statistical
785:Acta Applicandae Mathematicae
531:satisfying the RTT relations.
1133:Inverse scattering transform
624:Russian Mathematical Surveys
399:inverse scattering transform
397:An important concept in the
376:inverse scattering transform
1024:Quantum harmonic oscillator
77:. The specific problem is:
1527:
1257:in one- and two-dimensions
825:Cambridge University Press
684:10.1103/PhysRevLett.15.240
310:Korteweg–de Vries equation
281:, is a method for solving
1368:Ferdinand Georg Frobenius
973:Garnier integrable system
534:Find the spectrum of the
298:inverse scattering method
1299:Quantum Heisenberg model
1142:ASDYM as a master theory
994:Liouville–Arnold theorem
725:Chakrabarti, A. (2001).
419:quantum Heisenberg model
308:used to investigate the
132:may contain suggestions.
117:may need to be rewritten
1506:Exactly solvable models
1445:Alexander Zamolodchikov
1105:Bäcklund transformation
1034:Pöschl–Teller potential
906:Liouville integrability
894:Frobenius integrability
887:Geometric integrability
663:Physical Review Letters
446:Riemann–Hilbert problem
1204:Principal chiral model
1154:Twistor correspondence
999:Action-angle variables
915:In classical mechanics
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411:algebraic Bethe ansatz
279:algebraic Bethe ansatz
79:copyedit, create lede.
1383:Joseph-Louis Lagrange
934:Central force systems
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561:
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442:correlation functions
344:Heisenberg spin chain
323:features heavily and
1450:Alexei Zamolodchikov
1419:Martin David Kruskal
1393:Siméon Denis Poisson
1331:Yang–Baxter equation
1226:Affine Gaudin models
1069:Sine-Gordon equation
1017:In quantum mechanics
574:
559:{\displaystyle t(u)}
541:
504:
491:Yang–Baxter equation
386:, in particular the
173:improve this article
1409:Clifford S. Gardner
1179:Quantum Sine-Gordon
1126:Topological soliton
1116:integrals of motion
929:Harmonic oscillator
753:2001JMP....42.2653C
675:1965PhRvL..15..240Z
636:1979RuMaS..34...11T
536:generating function
464:thermodynamic limit
431:Tonks–Girardeau gas
425:(also known as the
392:quantum determinant
83:WikiProject Physics
1378:Sofia Kovalevskaya
1276:Chiral Potts model
1271:Hard hexagon model
1266:Eight-vertex model
880:Integrable systems
797:10.1007/BF00994626
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427:Lieb–Liniger model
415:integrable systems
403:Lax representation
1511:Quantum mechanics
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1189:Quantum Liouville
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1079:Gross–Neveu model
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834:978-0-521-37320-3
761:10.1063/1.1365952
604:Find correlators.
489:which solves the
453:conservation laws
353:sine-Gordon model
283:integrable models
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121:quality standards
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1261:Square ice model
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1114:Infinitely many
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440:The theory of
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349:field theories
306:Martin Kruskal
302:Norman Zabusky
287:Leon Takhtajan
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1062:KdV hierarchy
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319:. In both, a
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300:pioneered by
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291:L. D. Faddeev
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190: –
189:
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184:Find sources:
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162:This article
160:
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127:
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118:
115:This article
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73:This article
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47:
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41:
40:
35:
30:
21:
20:
1429:Robert Miura
1344:Contributors
1325:
1321:Bethe ansatz
1304:Gaudin model
1222:(Lagrangian)
1057:KdV equation
961:Kovalevskaya
820:
791:(1): 69–84,
788:
784:
744:math/0009178
734:
730:
709:
693:
666:
662:
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630:(5): 11–68.
627:
623:
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484:
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410:
407:quantization
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369:Bethe ansatz
362:
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183:
171:Please help
166:verification
163:
135:
126:You can help
116:
88:
78:
74:
50:
43:
37:
36:Please help
33:
1255:Ising model
1184:Quantum KdV
340:spin chains
1500:Categories
1319:Algebraic
703:1804.07350
609:References
433:) and the
359:Discussion
321:Lax matrix
314:integrable
199:newspapers
39:improve it
1424:Peter Lax
1110:Lax pairs
899:Foliation
813:120648929
470:Procedure
336:many-body
293:in 1979.
130:talk page
45:talk page
1292:Examples
1050:Examples
966:Lagrange
922:Examples
482:Take an
91:May 2019
843:1245942
805:1329554
749:Bibcode
671:Bibcode
632:Bibcode
566:of the
496:Take a
487:-matrix
429:or the
401:is the
388:Yangian
213:scholar
1313:Theory
1098:Theory
987:Theory
841:
831:
811:
803:
568:centre
273:, the
215:
208:
201:
194:
186:
128:. The
1438:IQFTs
956:Euler
809:S2CID
770:arXiv
739:arXiv
699:arXiv
220:JSTOR
206:books
1402:PDEs
829:ISBN
476:1992
374:the
367:the
304:and
289:and
192:news
793:doi
757:doi
679:doi
640:doi
570:of
478:):
269:In
175:by
1502::
839:MR
837:,
827:,
807:,
801:MR
799:,
789:39
787:,
755:.
747:.
735:42
733:.
729:.
677:.
667:15
665:.
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