Quantum many body systems: Cetraro, Italy 2010
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Schriftenreihe: | Lecture notes in mathematics
2051 : CIME Foundation subseries |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 180 S. graph. Darst. 24 cm |
| ISBN: | 9783642295102 9783642295119 |
Internformat
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| 245 | 1 | 0 | |a Quantum many body systems |b Cetraro, Italy 2010 |c Fondazione CIME. Vincent Rivasseau ... Eds.: Alessandro Giuliani ... |
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Datensatz im Suchindex
| _version_ | 1804149512050049024 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION TO THE RENORMALIZATION GROUP WITH APPLICATIONS TO
NON-RELATIVISTIC QUANTUM ELECTRON GASES 1
VINCENT RIVASSEAU . 1.1 INTRODUCTION TO QFT AND RENORMALIZATION 1
1.1.1 GAUSSIAN MEASURES 1
1.1.2 FUNCTIONAL INTEGRALS 2
1.1.3 STATISTICAL MECHANICS AND THERMODYNAMIC QUANTITIES 3 1.1.4
SCHWINGER FUNCTIONS 5
1.1.5 FEYNMAN GRAPHS 7
1.1.6 FEYNMAN RULES 9
1.1.7 SCALE ANALYSIS AND RENORMALIZATION 12
1.1.8 LOCALITY, POWER COUNTING 14
1.1.9 RENORMALIZATION, EFFECTIVE CONSTANTS 15
1.1.10 THE BPHZ THEOREM 16
1.1.11 THE LANDAU GHOST AND ASYMPTOTIC FREEDOM 18
1.1.12 GRASSMANN REPRESENTATIONS O F DETERMINANTS AND PFAFFIANS 20
1.1.13 TREES, FORESTS AND THE PARAMETRIC REPRESENTATION 23
1.1.14 BKAR FOREST FORMULA 26
1.1.15 GRAM AND HADAMARD BOUNDS 28
1.1.16 SINGLE SCALE CONSTRUCTIVE THEORY FOR A TOY MODEL 29
1.2 INTERACTING FERMIONS IN TWO DIMENSIONS 33
1.2.1 INTRODUCTION 33
1.2.2 THE MODELS: J 2 , J J , H 2 34
1.2.3 INTERACTION, LOCALITY 35
1.2.4 A BRIEF REVIEW OF RIGOROUS RESULTS 37
1.2.5 MULTISCALE ANALYSIS, ANGULAR SECTORS 38
1.2.6 RENORMALIZATION 39
1.2.7 2D JELLIUM MODEL: WHY SECTORS WORK 4 0
X I
HTTP://D-NB.INFO/1024815080
IMAGE 2
XII C O N T E N T S
1.2.8 3D JELLIUM MODEL: WHY SECTORS FAIL 4 2
1.2.9 THE HADAMARD METHOD IN X-SPACE 42
1.2.10 2D HUBBARD MODEL 4 4
1.2.11 SCALE ANALYSIS 45
1.2.12 SECTORS 47
1.2.13 SUPPORT PROPERTIES 4 9
1.2.14 MOMENTUM CONSERVATION RULES AT A VERTEX 4 9
1.2.15 MULTISCALE ANALYSIS 51
REFERENCES 52
2 COLD QUANTUM GASES AND BOSE-EINSTEIN CONDENSATION 55
ROBERT SEIRINGER 2.1 INTRODUCTION 55
2.2 QUANTUM MANY-BODY SYSTEMS 56
2.2.1 THE HAMILTONIAN 56
2.2.2 QUANTITIES O F INTEREST 56
2.2.3 CREATION AND ANNIHILATION OPERATORS ON FOCK SPACE 58
2.2.4 IDEAL QUANTUM GASES 59
2.3 BEC FOR INTERACTING SYSTEMS 64
2.3.1 THE CRITERION FOR BEC 6 4
2.3.2 THE HARD-CORE LATTICE GAS 65
2.4 DILUTE BOSE GASES 67
2.4.1 THE MODEL 67
2.4.2 THE TWO-PARTICLE CASE 69
2.4.3 THE GROUND STATE ENERGY O F A DILUTE GAS 70
2.4.4 FURTHER RIGOROUS RESULTS 7 3
2.4.5 THE NEXT ORDER TERM 75
2.5 DILUTE BOSE GASES IN TRAPS 7 6
2.5.1 THE GROSS-PITAEVSKII ENERGY FUNCTIONAL 7 6
2.5.2 BEC O F DILUTE TRAPPED GASES 78
2.5.3 ROTATING BOSE GASES 79
2.5.4 MAIN IDEAS IN THE PROOF 81
2.5.5 COHERENT STATES 84
2.5.6 RAPIDLY ROTATING BOSE GASES 87
REFERENCES 91
3 QUANTUM COULOMB GASES 93
JAN PHILIP SOLOVEJ 3.1 INTRODUCTION 93
3.2 CLASSICAL POINT CHARGES 9 4
3.3 CHARGED QUANTUM GASES 97
3.3.1 QUANTIZED PARTICLES AND CLASSICAL FIELDS 98
3.3.2 STATISTICS OF IDENTICAL PARTICLES 100
3.3.3 GRAND CANONICAL PICTURE 101
3.3.4 SECOND QUANTIZATION AND QUANTIZATION O F FIELDS 102
3.3.5 QUANTIZATION O F THE ELECTROMAGNETIC FIELD 104
IMAGE 3
C O N T E N T S XIII
3.3.6 NON-RELATIVISTIC QED 105
3.3.7 RELATIVISTIC QED HAMILTONIAN 106
3.4 STABILITY 107
3.4.1 STABILITY OF THE FIRST KIND FOR NON-RELATIVISTIC PARTICLES ... 108
3.4.2 GRAND CANONICAL STABILITY 109
3.4.3 EXISTENCE O F THE THERMODYNAMIC LIMIT 114
3.5 INSTABILITY 115
3.5.1 EXAMPLES OF INSTABILITY O F THE FIRST KIND 115
3.5.2 FERMIONIC INSTABILITY OF THE SECOND KIND 117
3.5.3 INSTABILITY O F BOSONIC MATTER 118
REFERENCES 123
4 SUSY STATISTICAL MECHANICS AND RANDOM BAND MATRICES 125
THOMAS SPENCER 4.1 AN OVERVIEW 125
4.1.1 GREEN S FUNCTIONS 127
4.1.2 SYMMETRY AND THE ID SUSY SIGMA MODEL 128
4.1.3 SUSY SIGMA MODELS IN 3D 130
4.2 CLASSICAL MODELS OF QUANTUM DYNAMICS 131
4.2.1 MANHATTAN MODEL 132
4.3 INTRODUCTION RANDOM MATRIX ENSEMBLES AND SUSY 133
4.3.1 SOME CONJECTURES ABOUT RBM AND RANDOM SCHRODINGER 134
4.3.2 CONJECTURED UNIVERSALITY OF GUE AND GOE MODELS 135 4.3.3 GREEN S
FUNCTIONS AND GAUSSIAN INTEGRALS 136
4.4 AVERAGING D E T ( E E - / / ) 137
4.4.1 GAUSSIAN BAND MATRICES AND STATISTICAL MECHANICS 139
4.5 THE DENSITY OF STATES FOR GUE AND RBM 141
4.5.1 DENSITY OF STATES FOR RBM 144
4.6 STATISTICAL MECHANICS, SIGMA MODELS, AND GOLDSTONE MODES 145 4.7
HYPERBOLIC SYMMETRY 149
4.7.1 RANDOM BAND CASE 152
4.8 PHASE TRANSITION FOR A SUSY HYPERBOLIC SIGMA MODEL 155
4.8.1 ROLE OF WARD IDENTITIES IN THE PROOF 159
4.9 EFETOV S SIGMA MODEL 161
4.10 APPENDIX A: GAUSSIAN AND GRASSMANN INTEGRATION 163
4.10.1 GRASSMANN INTEGRATION 164
4.10.2 POLAR COORDINATES FOR GRASSMANN AND BOSONIC MATRICES 166
4.11 APPENDIX B: FORMAL PERTURBATION THEORY 168
4.11.1 LEADING CONTRIBUTION TO DIFFUSION 171
4.11.2 PERTURBATION THEORY FOR RANDOM BAND MATRICES 171
4.12 APPENDIX C: BOUNDS ON GREEN S FUNCTIONS O F DIVERGENCE FORM ... 173
REFERENCES 175
LIST O F PARTICIPANTS 1 79
|
| any_adam_object | 1 |
| author2 | Giuliani, Alessandro |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.133 |
| dewey-search | 530.133 |
| dewey-sort | 3530.133 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| indexdate | 2024-07-10T00:24:12Z |
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| spelling | Quantum many body systems Cetraro, Italy 2010 Fondazione CIME. Vincent Rivasseau ... Eds.: Alessandro Giuliani ... Berlin [u.a.] Springer 2012 XIII, 180 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2051 : CIME Foundation subseries Literaturangaben Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2010 Cetraro gnd-content Vielteilchentheorie (DE-588)4331960-9 s DE-604 Rivasseau, Vincent 1955- Sonstige (DE-588)136009298 oth Giuliani, Alessandro edt Centro Internazionale Matematico Estivo Sonstige (DE-588)1025933-8 oth Erscheint auch als Online-Ausgabe Quantum Many Body Systems Lecture notes in mathematics 2051 : CIME Foundation subseries (DE-604)BV000676446 2051 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025298717&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quantum many body systems Cetraro, Italy 2010 Lecture notes in mathematics Vielteilchentheorie (DE-588)4331960-9 gnd |
| subject_GND | (DE-588)4331960-9 (DE-588)1071861417 |
| title | Quantum many body systems Cetraro, Italy 2010 |
| title_auth | Quantum many body systems Cetraro, Italy 2010 |
| title_exact_search | Quantum many body systems Cetraro, Italy 2010 |
| title_full | Quantum many body systems Cetraro, Italy 2010 Fondazione CIME. Vincent Rivasseau ... Eds.: Alessandro Giuliani ... |
| title_fullStr | Quantum many body systems Cetraro, Italy 2010 Fondazione CIME. Vincent Rivasseau ... Eds.: Alessandro Giuliani ... |
| title_full_unstemmed | Quantum many body systems Cetraro, Italy 2010 Fondazione CIME. Vincent Rivasseau ... Eds.: Alessandro Giuliani ... |
| title_short | Quantum many body systems |
| title_sort | quantum many body systems cetraro italy 2010 |
| title_sub | Cetraro, Italy 2010 |
| topic | Vielteilchentheorie (DE-588)4331960-9 gnd |
| topic_facet | Vielteilchentheorie Konferenzschrift 2010 Cetraro |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025298717&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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