Exactly solvable models in many-body theory:
"The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to model...
Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2016]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Zusammenfassung: | "The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed. The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments"... |
| Beschreibung: | xvi, 330 Seiten Diagramme |
| ISBN: | 9789813140141 9813140143 |
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| adam_text | EXACTLY SOLVABLE MODELS FOR CLUSTER AND MANY-BODY CONDENSED MATTER
SYSTEMS
/ MARCH, NORMAN H.YYQ(NORMAN HENRY)YYD1927-YYEAUTHOR
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
LOW ORDER DENSITY MATRICES
SOLVABLE MODELS FOR SMALL CLUSTERS OF FERMIONS
SMALL CLUSTERS OF BOSONS
ANYON STATISTICS WITH MODELS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
EXACT RESULTS FOR AN ISOLATED IMPURITY IN A SOLID
PAIR POTENTIAL AND MANY-BODY FORCE MODELS FOR LIQUIDS
ANDERSON LOCALIZATION IN DISORDERED SYSTEMS
STATISTICAL FIELD THEORY: ESPECIALLY MODELS OF CRITICAL EXPONENTS
RELATIVISTIC FIELDS
TOWARDS QUANTUM GRAVITY
DIESES SCHRIFTSTCK WURDE MASCHINELL ERZEUGT.
Titel: Exactly solvable models in many-body theory
Autor: March, Norman H
Jahr: 2016
Contents
Preface vii
Acknowledgments ix
1. Low-order density matrices 1
1.1 Low-order spinless density matrix theory 1
1.1.1 Natural orbitals and occupation numbers 3
1.1.2 V-representability 4
1.2 Gilbert theorem 6
1.2.1 Exchange and correlation energy in terms of first
order reduced density matrices 8
1.3 Differential virial theorem 9
1.3.1 Definition of kinetic energy density 9
1.3.2 Derivation of differential virial theorem 9
2. Solvable models for small Clusters of fermions 13
2.1 Ground-state energy as a functional of the electron density 13
2.2 Moshinsky model for a two-electron atom 14
2.2.1 Schrödinger equation for the relative motion ... 16
2.2.2 First-order spinless density matrix 16
2.2.3 Kinetic energy density 17
2.2.4 Virial equation 18
2.3 An exactly solvable model for a two-electron spin-
compensated atom 18
2.4 Low-order density gradient contributions to the kinetic en¬
ergy 21
xi
xii
Exactly solvable models in many-body theory
2.5 Exactly solvable ground-state energies for some series of
light atomic ions with non-integral nuclear charges to
within Statistical error of QMC 24
2.5.1 Discussion of QMC results for He- to B-like isoelec-
tronic series of atomic ions 26
3. Small Clusters of bosons 31
3.1 Efimov trimers 31
3.1.1 Hyperspherical coordinates 33
3.1.2 Schrödinger equation for the 3-body problem: adi-
abatic hyperspherical approximation 34
3.1.3 Low-energy limit: Faddeev equations 36
3.1.4 Efimov states in the resonant limit 39
3.2 Efimov resonances and experimental evidence thereof ... 41
3.2.1 Relevance of Efimov trimers for helium Clusters . . 42
3.2.2 Feshbach resonances in ultracold atoms 42
4. Anyon statistics with models 45
4.1 Anyon exchange statistics in d — 2 dimensions 47
4.1.1 Statistical interaction via Chern-Simons fields . . 49
4.2 Anyon exclusion statistics in arbitrary dimensions 54
4.2.1 Exclusons distribution function 55
4.2.2 Thermodynamic properties of exclusons 59
4.3 Statistical correlations in an excluson gas 64
4.3.1 Pair correlation function for non-interacting exclu¬
sons 65
4.3.2 Friedel oscillations in the excluson pair correlation
function at T ^ 0 67
4.3.3 Friedel oscillations in the excluson pair correlation
function at T = 0 69
4.4 Concluding remarks 72
5. Superconductivity and superfluidity 75
5.1 Superconductivity 75
5.1.1 BCS theory 76
5.1.2 Richardson model 82
5.1.3 Geminals for pairing correlations 86
5.2 Superfluidity 91
Contents xiii
5.2.1 General introduction to the Bose-Einstein conden-
sation and superfluidity 91
5.2.2 Experimental manifestations of superfluidity and
BEC 94
5.2.3 Superfluidity without BEC: the two-dimensional
Bose fluid 95
5.2.4 BEC of magnons 97
5.2.5 Mesoscopic condensation: relevance of pairing cor-
relations 100
5.2.6 An exactly solvable model for an interacting Boson
gas in one dimension 103
5.2.7 Quench dynamics of a one-dimensional interacting
Bose gas 110
6. Exact results for an isolated impurity in a solid 113
6.1 Derivation of the expression of the Dirac density matrix
from Schrödinger equation 113
6.2 Priedel sum rule and integrated density of states 115
6.3 Second-order perturbation corrections for Dirac density
matrix around an impurity in a metal 118
6.4 Effect of impurities on the resistivity of a metal 119
7. Pair potential and many-body force models for liquids 123
7.1 Force equation for pair potentials 124
7.2 Pair potentials for liquid Na near freezing 125
7.3 Possible empirical extrapolation of the valence-valence elec-
tron partial structure factor for liquid Mg near freezing . . 127
7.3.1 Treating pure s-p liquid metals like Na near freez¬
ing as a two-component system 128
7.3.2 Comparison of first-order theory for Siv(k) with
Computer Simulation results 128
7.3.3 Treatment of electron-electron structure factor
Svv(k) byDFT 129
7.3.4 Analytic relation between ÖSi(k) and SiV(k) . . . 131
7.4 Magnetic susceptibility of expanded fluid alkali metals . . 132
8. Anderson localization in disordered Systems 135
8.1 Anderson s model for localization in random lattices . . . 136
xiv Exactly solvable models in many-body theory
8.2 Beyond simple scaling 138
8.2.1 Current relaxation in disordered conductors .... 139
8.3 Hopping conductivity in disordered systems: reduction to
a percolation problem 142
8.4 Icosahedra in amorphous Ni-Al alloys 145
9. Statistical field theory: especially models of critical exponents 147
9.1 Ising model 148
9.1.1 Exact Solution in one dimension 149
9.1.2 Exact Solution in two dimensions 151
9.1.3 Ising model in one- and four-dimensions in a mag-
netic field of arbitrary strength 154
9.2 Yang-Lee theory of phase transitions 156
9.2.1 Yang-Lee zeroes 157
9.2.2 Yang-Lee theory of the Ising model 161
9.2.3 Fisher zeroes 165
9.2.4 Concluding remarks 171
9.3 Tonks 1D model and its generalization 172
9.4 Critical exponents in terms of d and r/ 174
9.4.1 String theory model of critical exponents 174
9.4.2 Proof that ILM model embraces Gaussian case . . 177
9.5 Baxter model 181
9.5.1 The Baxter or eight-vertex model 181
9.5.2 Correlation functions for the XYZ model having
spin 185
9.5.3 Generalization to the continuum 187
9.5.4 Critical exponents 190
10. Relativistic fields 193
10.1 Dirac wave equation 193
10.2 Central field solutions of the Dirac s equation 195
10.2.1 Dirac equation for a hydrogenic atom 197
10.3 Dirac equation in a magnetic field 199
10.3.1 Pauli equation 200
10.3.2 Dirac propagator 202
10.4 Semiclassical limit of Dirac s relativistic wave equation . . 211
10.5 Spinless Salpeter equation 215
11. Towards quantum gravity 217
Contents xv
11.1 The graviton and its relevance for quantum gravity .... 220
11.1.1 Mass and spin of the quantum of gravitation . . . 220
11.1.2 Comments on polarization 221
11.2 The Schrödinger-Newton equation 222
11.2.1 Solutions of the Schrödinger-Newton equation . . 224
11.3 Concluding remarks 226
Appendix A Feynman propagator for an arbitrary DFT-like
one-body potential 229
A. 1 Generalization of the March-Murray equation for the Slater
sum to d 1 230
Appendix B Phonons in Wigner crystals near melting 233
B.l Jellium model 233
B.2 Low-density limit: Wigner crystallization 235
B.2.1 Experimental Observation of Wigner crystallization 237
B.3 Elementary excitations in Wigner crystals 238
B.3.1 Wigner crystals in 2DEG at high magnetic field . 239
Appendix C Lattice chains, Bethe Ansatz and polynomials
for energies E of ground and excited states 241
Appendix D Kondo lattices 247
D.l The Kondo effect 247
D.2 Kondo lattices 248
Appendix E Luttinger liquid: spinons and holons 253
E.l 1D Hubbard model in an arbitrary magnetic field 254
Appendix F States with fractional Fermion charge in both
Condensed matter and relativistic field theories 257
F.l Relativistic field theory 257
F.2 Bröken symmetry ground state 258
F.3 Soliton excitations 259
F.4 SSH model for polyacetylene 261
F. 5 Discussion 264
Appendix G Haidane gap 265
xvi Exactly solvable models in many-body theory
G.l Valence bond states for spin-i chains 265
G.2 Higher spin chains: the Haidane gap 265
G.3 Experimental tests of the Haidane conjecture 268
Appendix H Quantum mechanics and number theory 273
H. 1 Quantum zeta function, and some properties of power Po¬
tentials 274
Bibliography 279
Index 327
|
| any_adam_object | 1 |
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| id | DE-604.BV043744972 |
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| indexdate | 2024-07-10T07:33:57Z |
| institution | BVB |
| isbn | 9789813140141 9813140143 |
| language | English |
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| spelling | March, Norman H. 1927- Verfasser (DE-588)136632661 aut Exactly solvable models in many-body theory N H March, G G N Angilella New Jersey World Scientific [2016] © 2016 xvi, 330 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier "The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed. The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments"... Mathematisches Modell Condensed matter Mathematical models Many-body problem Mathematical models Microclusters Mathematical models Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf Exakte Lösung (DE-588)4348289-2 gnd rswk-swf Vielteilchentheorie (DE-588)4331960-9 s Exakte Lösung (DE-588)4348289-2 s DE-604 Angilella, Giuseppe G. N. Verfasser aut LoC Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029156622&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029156622&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | March, Norman H. 1927- Angilella, Giuseppe G. N. Exactly solvable models in many-body theory Mathematisches Modell Condensed matter Mathematical models Many-body problem Mathematical models Microclusters Mathematical models Vielteilchentheorie (DE-588)4331960-9 gnd Exakte Lösung (DE-588)4348289-2 gnd |
| subject_GND | (DE-588)4331960-9 (DE-588)4348289-2 |
| title | Exactly solvable models in many-body theory |
| title_auth | Exactly solvable models in many-body theory |
| title_exact_search | Exactly solvable models in many-body theory |
| title_full | Exactly solvable models in many-body theory N H March, G G N Angilella |
| title_fullStr | Exactly solvable models in many-body theory N H March, G G N Angilella |
| title_full_unstemmed | Exactly solvable models in many-body theory N H March, G G N Angilella |
| title_short | Exactly solvable models in many-body theory |
| title_sort | exactly solvable models in many body theory |
| topic | Mathematisches Modell Condensed matter Mathematical models Many-body problem Mathematical models Microclusters Mathematical models Vielteilchentheorie (DE-588)4331960-9 gnd Exakte Lösung (DE-588)4348289-2 gnd |
| topic_facet | Mathematisches Modell Condensed matter Mathematical models Many-body problem Mathematical models Microclusters Mathematical models Vielteilchentheorie Exakte Lösung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029156622&sequence=000001&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=029156622&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT marchnormanh exactlysolvablemodelsinmanybodytheory AT angilellagiuseppegn exactlysolvablemodelsinmanybodytheory |
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