Quantum integrable systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2004
|
| Series: | Chapman & Hall/CRC research notes in mathematics series
435 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 399-409) and index |
| Physical Description: | 412 S. Ill., graph. Darst. 23 cm |
| ISBN: | 1584883804 |
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| 245 | 1 | 0 | |a Quantum integrable systems |c Asesh Roy Chowdhury and Anindya Ghose Choudhury |
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| 490 | 1 | |a Chapman & Hall/CRC research notes in mathematics series |v 435 | |
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| 650 | 7 | |a Hamiltonianen |2 gtt | |
| 650 | 7 | |a Mathematische fysica |2 gtt | |
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Record in the Search Index
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| adam_text | IMAGE 1
ASESH ROY CHOWDHURY
AND ANINDYA GHOSE CHOUDHURY
QUANTUM INTEGRABLE
SYSTEMS
CHAPMAN & HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK
WASHINGTON, D.C.
IMAGE 2
CONTENTS
PREFACE XI
1 NONLINEAR SYSTEMS AND CLASSICAL 1ST 1
1.1 INTRODUCTION 1
1.2 DEFINITION OF INTEGRABILITY 2
1.3 LAX PAIR TECHNIQUE 4
1.4 INVERSE SCATTERING TRANSFORM 5
1.5 HAMILTONIAN STRUCTURE 10
2 COORDINATE BETHE ANSATZ 15
2.1 INTRODUCTION 15
2.2 NONLINEAR SYSTEMS AND THE CBA . . . . X . 18
2.3 FERMIONIC SYSTEM 26
2.4 BOUNDARY CONDITION IN THE BETHE ANSATZ 33
2.4.1 SEMI-INFINITE AXIS 35
2.5 HEISENBERG SPIN CHAIN 37
2.6 SPIN OF THE BETHE ANSATZ STATE 42
2.7 OTHER INTEGRABLE MODELS 43
2.7.1 SUPERSYMMETRIC NLS EQUATION 44
2.7.2 THREE-WAVE INTERACTION PROBLEM 47
3 YANG-BAXTER EQUATION 51
3.1 INTRODUCTION 51
3.2 GENERAL DESCRIPTION 51
3.3 FACTORIZED SCATTERING 57
3.4 BAXTER S STAR-TRIANGLE RELATION 68
3.5 VERTEX MODELS 74
3.6 REFLECTION EQUATION ALGEBRA 83
4 CONTINUOUS INTEGRABLE SYSTEMS 97
4.1 INTRODUCTION 97
4.2 QUANTUM CONTINUOUS INTEGRABLE SYSTEMS 97
4.2.1 NONLINEAR SCHRODINGER MODEL 98
IMAGE 3
4.2.2 THIRRING MODEL 102
4.3 CONSERVED QUANTITIES 105
4.4 NONULTRALOCAL SYSTEMS AND THE YBE 107
4.4.1 QUANTIZATION OF NONULTRALOCAL SYSTEMS I LL
4.5 OPERATOR PRODUCT EXPANSION AND THE YBE 114
4.6 FINITE BOUNDARY CONDITIONS 119
4.7 MODIFIED CLASSICAL YANG-BAXTER EQUATION 124
ALGEBRAIC BETHE ANSATZ 133
5.1 INTRODUCTION 133
5.2 DISCRETE SELF-TRAPPING MODEL 133
5.3 ASYMMETRIC XXZ MODEL IN A MAGNETIC FIELD 138 5.4 ANALYTICAL BETHE
ANSATZ 143
5.5 OFF-SHELL BETHE ANSATZ 152
5.6 NESTED BETHE ANSATZ 159
5.7 FUSION PROCEDURE 166
5.8 FUSION PROCEDURE FOR OPEN CHAINS 175
5.9 FUSION PROCEDURE FOR TRANSFER MATRICES 177
5.10 APPLICATION OF FUSION PROCEDURE . . . . 180
INTEGRABLE LONG-RANGE MODELS 189
6.1 INTRODUCTION 189
6.2 LONG-RANGE MODELS FROM THE ABA 190
6.3 SYMMETRY TRANSFORMATION 197
6.4 CALOGERO-MOSER MODELS 201
6.4.1 QUANTUM CALOGERO-MOSER MODEL 203
6.4.2 GENERALIZATIONS OF THE CM MODEL 205
SEPARATION OF VARIABLES 209
7.1 INTRODUCTION 209
7.2 HAMILTON-JACOBI EQUATION 210
7.3 SKLYANIN S METHOD FOR SOV 215
7.4 GORYACHEV-CHAPLYGIN TOP 222
7.5 QUANTUM CASE AND THE ROLE OF LIE ALGEBRA 226
7.5.1 GAUDIN MODEL 227
7.5.2 QUANTUM DST MODEL 234
7.6 BI-HAMILTONIAN STRUCTURE AND SOV 239
7.6.1 JAULENT-MIODEK SPECTRAL PROBLEM 240
7.7 SOV FOR GCM MODEL 245
7.7.1 QUANTUM GENERALIZED CALOGERO-MOSER MODEL . . . 249
IMAGE 4
7.8 SOV AND BOUNDARY CONDITIONS 252
7.8.1 PERIODIC TODA LATTICE 252
7.8.2 NONPERIODIC CASE 256
7.8.3 QUANTUM DETERMINANT 259
8 BACKLUND TRANSFORMATIONS 263
8.1 INTRODUCTION . . 263
8.2 PERMUTABILITY THEOREM 264
8.3 BACKLUND TRANSFORMATIONS AND CLASSICAL INVERSE SCATTERING 266
8.4 BACKLUND TRANSFORMATIONS FROM THE RICCATI EQUATION . 270 8.5
DARBOUX-BACKLUND TRANSFORMATIONS 273
8.6 THE EXPONENTIAL LATTICE 276
8.7 CANONICAL TRANSFORMATIONS 281
8.8 GROUP PROPERTY OF BACKLUND TRANSFORMATIONS 287 8.9 RECENT
DEVELOPMENTS IN THE BACKLUND TRANSFORMATION THEORY 289
8.9.1 SPECTRALITY 291
8.9.2 PROPERTIES OF THE Q OPERATOR 292
8.9.3 APPLICATION OF SPECTRALITY TO THE SEPARATION OF VARIABLES 293
8.10 SKLYANIN S FORMALISM FOR CANONICAL BACKLUND TRANSFORMATIONS 294
8.11 EXTENDED-PHASE SPACE METHOD 300
8.12 QUANTIZATION OF BACKLUND TRANSFORMATIONS 306 . 8.12.1 ANALYTICAL
PROPERTIES OF THE Q OPERATOR 323 8.13 METHOD OF PROJECTION OPERATORS 325
9 QUANTUM GLM EQUATION 335
9.1 INTRODUCTION . 335
9.2 QUANTUM GLM EQUATION . 336
9.3 QUANTUM FLOQUET FUNCTION 337
9.4 EXACT QUANTIZATION 347
9.5 QUANTUM GLM EQUATION IN A CONTINUOUS SYSTEM . . . 354 9.5.1 QUANTUM
GLM EQUATION 357
9.6 BOUND STATES AND AN ALTERNATIVE APPROACH 360
A DIRECT PRODUCT CALCULUS 369
B GRASSMAN ALGEBRA 375
IMAGE 5
C THE BETHE ANSATZ EQUATION 379
C.I THE BAE FOR AN ELEMENTARY SPIN SYSTEM 379
C.2 COMPLEX ROOTS 387
D THE AKNS PROBLEM 389
REFERENCES 399
INDEX 410
|
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| language | English |
| lccn | 2003061849 |
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| spelling | Roy Chowdhury, Asesh Verfasser (DE-588)122367685 aut Quantum integrable systems Asesh Roy Chowdhury and Anindya Ghose Choudhury Boca Raton [u.a.] Chapman & Hall/CRC 2004 412 S. Ill., graph. Darst. 23 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC research notes in mathematics series 435 Includes bibliographical references (p. 399-409) and index Hamiltonianen gtt Mathematische fysica gtt Physique mathématique Systèmes hamiltoniens aHamiltonian systems aMathematical physics Integrables System (DE-588)4114032-1 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 gnd rswk-swf Bäcklund-Transformation (DE-588)4143891-7 gnd rswk-swf Bethe-Ansatz (DE-588)4121011-6 gnd rswk-swf Nichtlineares System (DE-588)4042110-7 s DE-604 Bethe-Ansatz (DE-588)4121011-6 s Integrables System (DE-588)4114032-1 s Bäcklund-Transformation (DE-588)4143891-7 s Choudhury, Anindya Ghose Sonstige oth Chapman & Hall/CRC research notes in mathematics series 435 (DE-604)BV012456897 435 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Roy Chowdhury, Asesh Quantum integrable systems Chapman & Hall/CRC research notes in mathematics series Hamiltonianen gtt Mathematische fysica gtt Physique mathématique Systèmes hamiltoniens aHamiltonian systems aMathematical physics Integrables System (DE-588)4114032-1 gnd Nichtlineares System (DE-588)4042110-7 gnd Bäcklund-Transformation (DE-588)4143891-7 gnd Bethe-Ansatz (DE-588)4121011-6 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4042110-7 (DE-588)4143891-7 (DE-588)4121011-6 |
| title | Quantum integrable systems |
| title_auth | Quantum integrable systems |
| title_exact_search | Quantum integrable systems |
| title_full | Quantum integrable systems Asesh Roy Chowdhury and Anindya Ghose Choudhury |
| title_fullStr | Quantum integrable systems Asesh Roy Chowdhury and Anindya Ghose Choudhury |
| title_full_unstemmed | Quantum integrable systems Asesh Roy Chowdhury and Anindya Ghose Choudhury |
| title_short | Quantum integrable systems |
| title_sort | quantum integrable systems |
| topic | Hamiltonianen gtt Mathematische fysica gtt Physique mathématique Systèmes hamiltoniens aHamiltonian systems aMathematical physics Integrables System (DE-588)4114032-1 gnd Nichtlineares System (DE-588)4042110-7 gnd Bäcklund-Transformation (DE-588)4143891-7 gnd Bethe-Ansatz (DE-588)4121011-6 gnd |
| topic_facet | Hamiltonianen Mathematische fysica Physique mathématique Systèmes hamiltoniens aHamiltonian systems aMathematical physics Integrables System Nichtlineares System Bäcklund-Transformation Bethe-Ansatz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012849144&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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