The Bethe wavefunction:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2014
|
| Ausgabe: | Engl. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. 314-322 |
| Beschreibung: | XV, 324 S. graph Darst. |
| ISBN: | 9781107045859 |
Internformat
MARC
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| 245 | 1 | 0 | |a The Bethe wavefunction |c Michel Gaudin |
| 250 | |a Engl. ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2014 | |
| 300 | |a XV, 324 S. |b graph Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804152047379939328 |
|---|---|
| adam_text | The
Bethe
aveTunction
Michel Gaudin s book
La fonction
d onde de
Bethe is a uniquely influential
masterpiece on exactly solvable models of quantum mechanics and statistical
physics. Available in English for the first time, this translation brings his classic work
to a new generation of graduate students and researchers in physics. It presents a
mixture of mathematics interspersed with powerful physical intuition, retaining the
author s unmistakably honest tone.
The book begins with the
Heisenberg
spin chain, starting from the coordinate
Bethe
Ansatz
and culminating in a discussion of its thermodynamic properties.
Delta-interacting bosons (the Lieb-Liniger model) are then explored, and extended
1o exactly solvable models associated with a reflection group. After discussing
the continuum limit of spin chains, the book covers six- and eight-vertex models in
extensive detail, from their lattice definition to their thermodynamics. Later chapters
examine advanced topics such as multicomponent delta-interacting systems,
Gaudin magnets and the
Toda
chain.
MICHEL GAUDIN is recognized as one of the foremost experts in this field, and
has worked at Commissariat
à l Énergie Atomique
(CEA)
and the Service
de
Physique
Théorique. Saclay.
His numerous scientific contributions to the theory of
exactly solvable models are well known, including his famous formula for the norm
of Bethe wavefunctions.
JEAN-SÉBASTIEN CAUX
is a Professor in the theory of low-dimensional
quantum condensed
matterat
the University of Amsterdam. He has made
significant contributions to the calculation of experimentally observable dynamical
—
operties of these systems.
r
iiustrattcn:
a represen;
ie
Yang-Baxter relation by John Coilingwood-
Cover designed by Hart McLeod Ltd
Cambridge
UNIVERSITY PRESS
www. cambr idge.org
1O7-O4585-5
045859
Contents
Foreword page
ix
Translator s note
x
introduction
xii
The chain of spin-1
/2
atoms
1
1.1
Model for a one-dimensional metal
1
1.2
Bethe s method
3
1.3
Parameters and quantum numbers
8
1.4
Asymptotic positioning of complex momenta
15
1.5
State classification and counting
19
Thermodynamic limit of the Heisenberg-Ising chain
27
2.1
Results for the ground state and elementary excitations
27
2.2
Calculation method for the elementary excitations
30
2.3
Thermodynamics at nonzero temperature: Energy and
entropy functionals
(Δ
> 1) 33
2.4
Thermodynamics at nonzero temperature: Thermodynamic
functions
37
Appendix A
42
Thermodynamics of the spin-
1/2
chain: Limiting cases
44
3.1
The Ising limit
44
3.2
The
T
= ±0
limits
46
3.3
Τ = σο
limit
52
¿-Interacting bosons
54
4.1
The elementary symmetric wavefunctions
54
4.2
Normalization of states in the continuum
56
4.3
Periodic boundary conditions
63
4.4
Thermodynamic limit
67
Appendix
В
70
vi
Contents
Appendix
С
75
Appendix
D
77
5
Bethe wavefunctions associated with a reflection group
79
5.1
Bosonic gas on a finite interval
79
5.2
The generalized kaleidoscope
83
5.3
The open chain
89
Appendix
E
91
6
Continuum limit of the spin chain
94
6.1
¿-Interacting bosons and the Heisenberg-Ising chain
94
6.2
Luttinger and Thirring models
99
6.3
Massive Thirring model
105
6.4
Diagonalization of H*r
107
7
The six-vertex model
112
7.1
The ice model
112
7.2
The transfer matrix
114
7.3
Diagonalization
119
7.4
The free energy
124
Appendix
F
137
Appendix
G
140
8
The eight-vertex model
142
8.1
Definition and equivalences
142
8.2
The transfer matrix and the symmetries of the self-dual model
146
8.3
Relation of the XYZ Hamiltonian to the transfer matrix
150
8.4
One-parameter family of commuting transfer matrices
153
8.5
A representation of the symmetric group
π ν
158
8.6
Diagonalization of the transfer matrix
162
8.7
The coupled equations for the spectrum
167
Appendix
Η
173
Appendix I
175
9
The eight-vertex model: Eigenvectors and thermodynamics
179
9.1
Reduction to an Ising-type model
179
9.2
Equivalence to a six-vertex model
185
9.3
The thermodynamic limit
194
9.4
Various results on the critical exponents
199
10
Identical particles with ¿-interactions
203
10.1
The Bethe hypothesis
203
10.2
Yang s representation
207
Contents
vii
10.3
Ternary relations algebra and integrability
211
10.4
On the models of Hubbard and Lai
220
11
Identical particles with ¿-interactions: General solution for two
internal states
223
11.1
The spin-
1 /2
fermion problem
223
1
1.2
The operatorial method
231
11.3
Sketch of the original solution of the fermion problem
233
11.4
On the thermodynamic limit of the fermion system
in the vicinity of its ground state
236
Appendix
J
244
Appendix
К
249
Appendix
L
250
12
Identical particles with
б
-interactions: General solution for
n
components and limiting cases
253
12.1
The transfer matrix
Z (k)
in a symmetry-adapted basis
253
12.2
Recursive diagonalization of matrix
Z
257
12.3
Zero coupling limit
264
13
Various corollaries and extensions
268
13.1
A class of completely
integrable
spin Hamiltonians
268
13.2
Other examples of
integrable
systems
275
13.3
Ternary relation and star-triangle relation
279
13.4
Ternary relation with Z5 symmetry
282
13.5
Ternary relations with Z| symmetry
287
13.6
Notes on a system of distinguishable particles
292
Appendix
M
294
Appendix
N 298
14
On the
Toda
chain
301
14.1
Definition
301
14.2
Bäcklund
transformation
301
14.3
The solitary wave
303
14.4
Complete integrability
304
14.5
The M-soliton solution for the infinite chain
307
14.6
The quantum chain
308
14.7
The integral equation for the eigenfunctions
310
14.8
Ternary relations and action-angle variables
311
References
314
Index
323
|
| any_adam_object | 1 |
| author | Gaudin, Michel 1931- |
| author_GND | (DE-588)1072248727 |
| author_facet | Gaudin, Michel 1931- |
| author_role | aut |
| author_sort | Gaudin, Michel 1931- |
| author_variant | m g mg |
| building | Verbundindex |
| bvnumber | BV041749973 |
| classification_rvk | UK 1000 UK 1200 |
| classification_tum | PHY 057f |
| ctrlnum | (OCoLC)880631757 (DE-599)BSZ401650014 |
| discipline | Physik |
| edition | Engl. ed. |
| format | Book |
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| id | DE-604.BV041749973 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:04:30Z |
| institution | BVB |
| isbn | 9781107045859 |
| language | English |
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| physical | XV, 324 S. graph Darst. |
| publishDate | 2014 |
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| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Gaudin, Michel 1931- Verfasser (DE-588)1072248727 aut La fonction d'onde de Bethe The Bethe wavefunction Michel Gaudin Engl. ed. Cambridge [u.a.] Cambridge Univ. Press 2014 XV, 324 S. graph Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 314-322 Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Bethe-Ansatz (DE-588)4121011-6 gnd rswk-swf Wellenfunktion (DE-588)4189547-2 gnd rswk-swf Exakte Lösung (DE-588)4348289-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Bethe-Salpeter-Gleichung (DE-588)4144979-4 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 s Mathematisches Modell (DE-588)4114528-8 s Exakte Lösung (DE-588)4348289-2 s Bethe-Ansatz (DE-588)4121011-6 s DE-604 Wellenfunktion (DE-588)4189547-2 s Bethe-Salpeter-Gleichung (DE-588)4144979-4 s 1\p DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027196373&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027196373&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gaudin, Michel 1931- The Bethe wavefunction Statistische Mechanik (DE-588)4056999-8 gnd Bethe-Ansatz (DE-588)4121011-6 gnd Wellenfunktion (DE-588)4189547-2 gnd Exakte Lösung (DE-588)4348289-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Bethe-Salpeter-Gleichung (DE-588)4144979-4 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4121011-6 (DE-588)4189547-2 (DE-588)4348289-2 (DE-588)4114528-8 (DE-588)4144979-4 |
| title | The Bethe wavefunction |
| title_alt | La fonction d'onde de Bethe |
| title_auth | The Bethe wavefunction |
| title_exact_search | The Bethe wavefunction |
| title_full | The Bethe wavefunction Michel Gaudin |
| title_fullStr | The Bethe wavefunction Michel Gaudin |
| title_full_unstemmed | The Bethe wavefunction Michel Gaudin |
| title_short | The Bethe wavefunction |
| title_sort | the bethe wavefunction |
| topic | Statistische Mechanik (DE-588)4056999-8 gnd Bethe-Ansatz (DE-588)4121011-6 gnd Wellenfunktion (DE-588)4189547-2 gnd Exakte Lösung (DE-588)4348289-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Bethe-Salpeter-Gleichung (DE-588)4144979-4 gnd |
| topic_facet | Statistische Mechanik Bethe-Ansatz Wellenfunktion Exakte Lösung Mathematisches Modell Bethe-Salpeter-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027196373&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027196373&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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