Mathematical theory of thermodynamic limits: Thomas-Fermi type models
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
1998
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| Schriftenreihe: | Oxford mathematical monographs
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 277 S. graph. Darst. |
| ISBN: | 0198501617 |
Internformat
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Datensatz im Suchindex
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| adam_text | THE MATHEMATICAL THEORY OF THERMODYNAMIC LIMITS: THOMAS-FERMI TYPE
MODELS ISABELLE CATTO CNRS URA 749, UNIVERSITE PARIS DAUPHINE, PARIS,
FRANCE CLAUDE LE BRIS ECOLE NATIONALE DES PONTS ET CHAUSSEES, MARNE LA
VALLEE, FRANCE PIERRE-LOUIS LIONS CNRS URA 749, UNIVERSITE PARIS
DAUPHINE AND ECOLE POLYTECHNIQUE, PARIS, FRANCE CLARENDON PRESS * OXFORD
1998 CONTENTS 1 GENERAL PRESENTATION 1 1.1 INTRODUCTION 1 1.2 THE
THERMODYNAMIC LIMIT FROM THE MATHEMATICAL VIEWPOINT 1 1.3 PHYSICAL
BACKGROUND 6 1.3.1 THE THERMODYNAMIC LIMIT OF MICROSCOPIC SYSTEMS 7
1.3.2 SOME BASICS OF SOLID STATE THEORY 8 1.4 HISTORICAL SURVEY 11 1.4.1
STATISTICAL MECHANICS WORKS 11 1.4.2 THE THOMAS-FERMI THEORY 14 1.5 THE
THERMODYNAMIC LIMIT IN THE TFW SETTING 16 1.5.1 DESCRIPTION OF THE
MODELS AND STATEMENT OF THE MAIN RESULTS 17 1.5.2 COROLLARIES 28 1.6 THE
THERMODYNAMIC LIMIT IN THE HARTREE*FOCK SETTING 31 2 CONVERGENCE OF THE
ENERGY FOR THE THOMAS*FERMI*VON WEIZSAECKER MODEL WITH YUKAWA POTENTIAL
34 2.1 INTRODUCTION 34 2.2 PRELIMINARIES: A PRIORI ESTIMATES 38 2.3
LOWER BOUND FOR THE ENERGY 52 2.4 UPPER BOUND FOR THE ENERGY 57 2.5
PROOF OF THE MAIN THEOREM 69 2.6 RECOVERING THE COULOMB POTENTIAL:
COMPACTNESS 70 2.7 EXTENSIONS 80 2.7.1 SMEARED OUT NUCLEI 80 2.7.2
REPLACING P 5 / 3 BY SOME OTHER FUNCTION 82 2.7.3 DEFAULT AND EXCESS OF
CHARGE 83 2.7.4 OTHER SHAPES OF PERIODIC CELLS 84 3 CONVERGENCE OF THE
ENERGY FOR THE THOMAS*FERMI*VON WEIZSAECKER MODEL 85 3.1 INTRODUCTION 85
3.2 PRELIMINARIES: A PRIORI ESTIMATES 91 3.2.1 THE CASE OF SMEARED
NUCLEI 91 3.2.2 THE POINT NUCLEI CASE 97 3.3 PROOF OF COMPACTNESS 104
3.3.1 SMEARED OUT NUCLEI 105 3.3.2 CONVEXITY ARGUMENT 106 3.3.3 SCALING
ARGUMENT 107 CONTENTS 3.3.4 GENERAL ARGUMENT 109 3.3.5 AN ARGUMENT VIA
THE ESTIMATION OF THE OUTSIDE CHARGE 111 3.3.6 COMPACTNESS IN THE TF
CASE 112 3.4 LOWER BOUND FOR THE ENERGY 113 3.4.1 COMPARISON PROOF 4 113
3.4.2 DIRECT PROOF FOR THE {CB * M) PROGRAM 115 3.4.3 DIRECT PROOF FOR
THE {CB * 6) PROGRAM 119 3.4.4 ADAPTATION TO THE YUKAWA CASE 126 3.5
UPPER BOUND FOR THE ENERGY 127 3.6 SOME EXTENSIONS 136 3.6.1 OTHER SIZES
OF ELEMENTARY CUBIC CELLS 136 3.6.2 OTHER SHAPES OF NUCLEUS 141 3.6.3
THE THOMAS-FERMI-DIRAC-VON WEIZSAECKER MODEL 142 3.7 APPENDIX 152 4
CONVERGENCE OF THE DENSITY FOR THE THOMAS*FERMI*VON WEIZSAECKER MODEL
WITH YUKAWA POTENTIAL 156 4.1 INTRODUCTION 156 4.2 PRELIMINARY
CONVERGENCE RESULTS ON THE DENSITY 160 4.2.1 LOCAL CONVERGENCE 160 4.2.2
CONVERGENCE OF THE ^-TRANSFORM 162 4.2.3 PERIODICITY UP TO A TRANSLATION
162 4.3 PERIODICITY OF THE LIMIT DENSITY 165 4.3.1 BOUNDS FROM ABOVE FOR
SOLUTIONS 166 4.3.2 BOUNDS FROM BELOW FOR SOLUTIONS 170 4.3.3 UNIQUENESS
RESULT WITHOUT THE CONVOLUTION TERM 176 4.3.4 UNIQUENESS RESULT FOR THE
FULL EQUATION: CONCLUSION 180 5 CONVERGENCE OF THE DENSITY FOR THE
THOMAS*FERMI*VON WEIZSAECKER MODEL 194 5.1 INTRODUCTION 194 5.2
PRELIMINARY CONVERGENCE RESULTS 196 5.2.1 CONVERGENCE OF THE ~-TRANSFORM
196 5.2.2 CONVERGENCE UP TO A TRANSLATION 197 5.3 A UNIQUENESS RESULT
FOR A SYSTEM OF PDE S 199 5.3.1 THE SMEARED NUCLEI CASE 199 5.3.2 THE
POINT NUCLEI CASE 206 5.3.3 COROLLARIES AND REMARKS 217 5.4 CONVERGENCE
OF THE DENSITY 219 5.5 UNIFORM CONVERGENCE ON INTERIOR DOMAINS 222 6
CONVERGENCE OF THE ENERGY VIA THE CONVERGENCE OF THE DENSITY 228 6.1
INTRODUCTION 228 6.2 A NEW PROOF OF THE CONVERGENCE OF THE ENERGY 231
CONTENTS ** 6.2.1 PROOF OF THEOREM 6.6 232 6.2.2 ADAPTATION TO THE TF
CASE 240 6.3 A GENERAL RESULT FOR EXISTENCE AND UNIQUENESS 246 6.3.1
PROOF OF THEOREM 6.10 247 6.3.2 WHEN THERE IS NO UNIQUENESS 251 6.4
GEOMETRIES WHICH ARE NOT THAT NON-PERIODIC 254 6.4.1 GENERAL PERIODIC
LATTICES, IMPURITIES. 255 6.4.2 TOWARDS QUASICRYSTALS: ALMOST PERIODIC
MEASURES 258 6.5 NON-NEUTRAL SYSTEMS 264 6.5.1 NEGATIVE IONS 265 6.5.2
POSITIVE IONS 267 REFERENCES 272
|
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| indexdate | 2024-07-09T18:17:25Z |
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| isbn | 0198501617 |
| language | English |
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| physical | XIII, 277 S. graph. Darst. |
| publishDate | 1998 |
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| spelling | Catto, Isabelle Verfasser aut Mathematical theory of thermodynamic limits Thomas-Fermi type models Isabelle Catto ; Claude LeBris ; Pierre-Louis Lions Oxford [u.a.] Oxford Univ. Press 1998 XIII, 277 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Chimie quantique ram Equations différentielles non linéaires - Solutions numériques ram Physique mathématique ram Thermodynamica gtt Thomas Fermi theorie gtt Thomas-Fermi, Modèle de ram Théorie quantique ram Mathematische Physik Quantentheorie Differential equations, Nonlinear Numerical solutions Mathematical physics Quantum chemistry Quantum theory Thomas-Fermi theory Thomas-Fermi-Modell (DE-588)4185321-0 gnd rswk-swf Thomas-Fermi-Modell (DE-588)4185321-0 s DE-604 Le Bris, Claude 1966- Verfasser (DE-588)12235138X aut Lions, Pierre-Louis 1956- Sonstige (DE-588)1038560152 oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008004515&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Catto, Isabelle Le Bris, Claude 1966- Mathematical theory of thermodynamic limits Thomas-Fermi type models Chimie quantique ram Equations différentielles non linéaires - Solutions numériques ram Physique mathématique ram Thermodynamica gtt Thomas Fermi theorie gtt Thomas-Fermi, Modèle de ram Théorie quantique ram Mathematische Physik Quantentheorie Differential equations, Nonlinear Numerical solutions Mathematical physics Quantum chemistry Quantum theory Thomas-Fermi theory Thomas-Fermi-Modell (DE-588)4185321-0 gnd |
| subject_GND | (DE-588)4185321-0 |
| title | Mathematical theory of thermodynamic limits Thomas-Fermi type models |
| title_auth | Mathematical theory of thermodynamic limits Thomas-Fermi type models |
| title_exact_search | Mathematical theory of thermodynamic limits Thomas-Fermi type models |
| title_full | Mathematical theory of thermodynamic limits Thomas-Fermi type models Isabelle Catto ; Claude LeBris ; Pierre-Louis Lions |
| title_fullStr | Mathematical theory of thermodynamic limits Thomas-Fermi type models Isabelle Catto ; Claude LeBris ; Pierre-Louis Lions |
| title_full_unstemmed | Mathematical theory of thermodynamic limits Thomas-Fermi type models Isabelle Catto ; Claude LeBris ; Pierre-Louis Lions |
| title_short | Mathematical theory of thermodynamic limits |
| title_sort | mathematical theory of thermodynamic limits thomas fermi type models |
| title_sub | Thomas-Fermi type models |
| topic | Chimie quantique ram Equations différentielles non linéaires - Solutions numériques ram Physique mathématique ram Thermodynamica gtt Thomas Fermi theorie gtt Thomas-Fermi, Modèle de ram Théorie quantique ram Mathematische Physik Quantentheorie Differential equations, Nonlinear Numerical solutions Mathematical physics Quantum chemistry Quantum theory Thomas-Fermi theory Thomas-Fermi-Modell (DE-588)4185321-0 gnd |
| topic_facet | Chimie quantique Equations différentielles non linéaires - Solutions numériques Physique mathématique Thermodynamica Thomas Fermi theorie Thomas-Fermi, Modèle de Théorie quantique Mathematische Physik Quantentheorie Differential equations, Nonlinear Numerical solutions Mathematical physics Quantum chemistry Quantum theory Thomas-Fermi theory Thomas-Fermi-Modell |
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