Holdings: Statistical physics

Statistical physics: 2 Nonequilibrium statistical mechanics

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Bibliographic Details
Main Author:	Kubo, Ryōgo 1920-1995 (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 1991
Edition:	2. ed.
Series:	Springer series in solid-state sciences 31
Online Access:	Inhaltsverzeichnis
Physical Description:	XVI, 279 S. graph. Darst.
ISBN:	354053833X 038753833X

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MARC


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adam_text	R. KUBO M. TODA N. HASHITSUME STATISTICAL PHYSICS II NONEQUILIBRIUM STATISTICAL MECHANICS SECOND EDITION WITH 28 FIGURES SPRINGER-VERLAG BERLIN HEIDELBERG NEW YORK LONDON PARIS TOKYO HONGKONG BARCELONA BUDAPEST CONTENTS 1. BROWNIAN MOTION 1 1.1 BROWNIAN MOTION AS A STOCHASTIC PROCESS 2 1.2 THE CENTRAL LIMIT THEOREM AND BROWNIAN MOTION 8 1.3 THE LANGEVIN EQUATION AND HARMONIE ANALYSIS 14 1.4 GAUSSIAN PROCESSES 22 1.5 BROWNIAN MOTION MODELED BY A GAUSSIAN PROCESS 27 1.6 THE FLUCTUATION-DISSIPATION THEOREM 31 2. PHYSICAL PROCESSES AS STOCHASTIC PROCESSES 40 2.1 RANDOM FREQUENCY MODULATION 40 2.2 BROWNIAN MOTION REVISITED 48 2.3 MARKOVIAN PROCESSES 55 2.4 FOKKER-PLANCK EQUATION 62 2.5 CONTRACTION OF INFORMATION. PROJECTED PROCESSES 69 2.6 DERIVATION OF MASTER EQUATIONS 77 2.7 BROWNIAN MOTION OF A QUANTAL SYSTEM 84 2.8 BOLTZMANN EQUATION 90 2.9 GENERALIZED LANGEVIN EQUATION AND THE DAMPING THEORY . . 97 3. RELAXATION AND RESONANCE ABSORPTION 109 3.1 LINEAR IRREVERSIBLE PROCESSES 109 3.1.1 MECHANICAL AND THERMAL FORCES VS DISPLACEMENTS AND CURRENTS 110 3.1.2 LINEAR RELATIONS 110 3.1.3 RESPONSE TO A PULSED FORCE 112 3.1.4 RELAXATION PHENOMENA 114 3.2 COMPLEX ADMITTANCE 115 3.2.1 HARMONIE (FOURIER) ANALYSIS 116 3.2.2 ENERGY DISSIPATION 117 3.3 DEBYE RELAXATION 120 3.3.1 DIELECTRIC RELAXATION 120 3.3.2 RESPONSE FUNCTIONS WITH EXPONENTIAL DAMPING . . . . 121 3.3.3 SOLUTION OF POLAR MOLECULES 123 3.4 RESONANCE ABSORPTION 125 3.4.1 VAN VLECK-WEISSKOPF-FROEHLICH TYPE RESONANCE ABSORPTION 126 XIV CONTENTS 3.4.2 NUCLEAR MAGNETIC RESONANCE 128 3.4.3 FAILURE AT HIGH FREQUENCIES 131 3.5 WAVE NUMBER-DEPENDENT COMPLEX ADMITTANCE 131 3.5.1 NON-MARKOVIAN NONLOCAL LINEAR RELATIONS 132 3.5.2 COMPLEX ADMITTANCE FOR THE DIFFUSION PHENOMENON . . 134 3.6 DISPERSION RELATIONS 136 3.6.1 PROOF OF THE DISPERSION RELATIONS 136 3.6.2 DISPERSION RELATIONS AND CAUSALITY 138 3.6.3 ANALYTICAL CONTINUATION INTO THE COMPLEX PLANE . . . 138 3.7 SUM RULES AND INTERPOLATION FORMULAS 139 3.7.1 MOMENT SUM RULES 140 3.7.2 NON-MARKOVIAN LAW OF DIFFUSION 143 4. STATISTICAL MECHANICS OF LINEAR RESPONSE 146 4.1 STATIC RESPONSE TO EXTERNAL FORCE 146 4.1.1 STATIC ADMITTANCE AND THE CANONICAL CORRELATION . . . . 147 4.2 DYNAMIC RESPONSE TO EXTERNAL FORCE 150 4.2.1 THE RESPONSE FUNCTION AND THE POISSON BRACKET . . . . 150 4.2.2 KUBO FORMULA 154 4.2.3 INITIAL VALUES OF THE RESPONSE FUNCTION AND ITS DERIVATIVES 158 4.3 SYMMETRY AND THE DISPERSION RELATIONS 158 4.3.1 SPECTRAL FUNCTION AND ITS SYMMETRY 158 4.3.2 SYMMETRY IN THE CURRENT RESPONSE 162 4.3.3 SYMMETRY IN THE DISPLACEMENT RESPONSE 163 4.3.4 PROOF OF THE DISPERSION RELATIONS 164 4.4 FLUCTUATION AND DISSIPATION THEOREM 167 4.4.1 SYMMETRIZED CORRELATION 167 4.4.2 THE EQUIVALENCE BETWEEN THE SYMMETRIZED CORRELATION FUNCTION AND THE RESPONSE OR THE RELAXATION FUNCTION . 168 4.4.3 FLUCTUATION-DISSIPATION THEOREM 170 4.5 DENSITY RESPONSE, CONDUCTION AND DIFFUSION 171 4.5.1 DENSITY AND CURRENT IN RESPONSE TO THE EXTERNAL FIELD 171 4.5.2 RELAXATION OF THE DENSITY RESPONSE AND THE DENSITY FLUCTUATION 174 4.5.3 SHIELDING OF THE EXTERNAL POTENTIAL 176 4.5.4 RESISTIVITY FORMULA 178 4.5.5 DIELECTRIC SHIELDING AND ELECTRIC CONDUCTIVITY 179 4.5.6 KRAMERS-KRONIG RELATIONS AND THE SUM RULES 181 4.6 RESPONSE TO THERMAL INTERNAL FORCES 183 4.6.1 ONSAGER S POSTULATE 184 4.6.2 FLUCTUATION OF MACROVARIABLES AS BROWNIAN MOTION . . . 185 4.6.3 A GENERAL FORMULATION OF ONSAGER S POSTULATE 187 4.6.4 NONEQUILIBRIUM DENSITY MATRIX 190 CONTENTS XV 4.7 SOME REMARKS ON THE LINEAR-RESPONSE THEORY 196 4.7.1 THE KINETIC METHOD VERSUS THE LINEAR-RESPONSE THEORY 196 4.7.2 VAN KAMPEN S OBJECTION 198 4.7.3 SPURIOUS SINGULARITIES AT THE ZERO VALUE OF THE EXTERNAL FIELD 199 4.7.4 SINGULARITIES AT K = 0, CO = 0 200 5. QUANTUM FIELD THEORETICAL METHODS IN STATISTICAL MECHANICS . . . 203 5.1 DOUBLE-TIME GREEN S FUNCTIONS 203 5.1.1 RETARDED GREEN S FUNCTIONS 204 5.1.2 ADVANCED GREEN S FUNCTIONS 206 5.2 CHAIN OF EQUATIONS OF MOTION AND THE DECOUPLING APPROXIMATION 207 5.2.1 CHAIN OF EQUATIONS OF MOTION 208 5.2.2 COMPLEX DIELECTRIC FUNCTION OF A PLASMA IN A DECOUPLING APPROXIMATION 210 5.3 RELATION TO THE KINETIC EQUATION 216 5.3.1 KLIMONTOVICH OPERATOR 216 5.3.2 SELF-CONSISTENT FIELD APPROXIMATION 217 5.3.3 PLASMA OSCILLATION 220 5.4 SINGLE-PARTICLE GREEN S FUNCTION AND THE CAUSAL GREEN S FUNCTION 222 5.4.1 SINGLE-PARTICLE GREEN S FUNCTIONS 222 5.4.2 SINGLE-PARTICLE GREEN S FUNCTIONS FOR FREE PARTICLES . . . 224 5.4.3 CAUSAL GREEN S FUNCTIONS 225 5.5 BASIC FORMULA FOR PERTURBATIONAL EXPANSION 226 5.5.1 PERTURBATIONAL EXPANSION OF THE EQUILIBRIUM DENSITY MATRIX 227 5.5.2 PERTURBATIONAL EXPANSION OF THE THERMODYNAMIC POTENTIAL 228 5.6 TEMPERATURE GREEN S FUNCTION 229 5.6.1 TEMPERATURE GREEN S FUNCTIONS (MATSUBARA-GREEN S FUNCTIONS) 229 5.6.2 FOURIER ANALYSIS OF THE TEMPERATURE GREEN S FUNCTION . 230 5.6.3 SINGLE-PARTICLE TEMPERATURE GREEN S FUNCTION FOR NONINTERACTING PARTICLES 232 5.6.4 ABRIKOSOV-GOR KOV-DZYALOSHINSKII-FRADKIN THEOREM . 233 5.7 DIAGRAM TECHNIQUE 235 5.7.1 BLOCH-DE DOMINICIS THEOREM 235 5.7.2 PERTURBATIONAL EXPANSION OF ^09) 0 238 5.7.3 CORRESPONDENCE WITH FEYNMAN DIAGRAMS 240 5.7.4 MATSUBARA FORMULA 242 5.8 DYSON EQUATION 244 5.8.1 SINGLE-PARTICLE TEMPERATURE GREEN S FUNCTION 244 XVI CONTENTS 5.8.2 GRAPHICAL SUMMATION 246 5.8.3 FEYNMAN RULES 248 5.9 RELATIONSHIP BETWEEN THE THERMODYNAMIC POTENTIAL AND THE TEMPERATURE GREEN S FUNCTION 253 5.10 SPECIAL CASE OF THE TWO-PARTICLE GREEN S FUNCTION 255 5.10.1 TWO-PARTICLE GREEN S FUNCTION OF ZEROTH-ORDER FOR A PLASMA 257 5.10.2 POLARIZATION OPERATOR 258 5.10.3 ELECTRIC CHARGE DENSITY GREEN S FUNCTION 260 GENERAL BIBLIOGRAPHY OF TEXTBOOKS 265 REFERENCES 266 SUBJECT INDEX 271
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author	Kubo, Ryōgo 1920-1995
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author_facet	Kubo, Ryōgo 1920-1995
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language	English
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spelling	Kubo, Ryōgo 1920-1995 Verfasser (DE-588)133977277 aut Tokei butsurigaku Statistical physics 2 Nonequilibrium statistical mechanics R. Kubo ; M. Toda ; N. Hashitsume 2. ed. Berlin [u.a.] Springer 1991 XVI, 279 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 31 Springer series in solid-state sciences ... Toda, Morikazu Sonstige oth Kubo, Ryogo Sonstige oth Saitō, Nobuhiko Sonstige oth (DE-604)BV001234348 2 Springer series in solid-state sciences 31 (DE-604)BV000016582 31 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004228078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Kubo, Ryōgo 1920-1995 Statistical physics Springer series in solid-state sciences
title	Statistical physics
title_alt	Tokei butsurigaku
title_auth	Statistical physics
title_exact_search	Statistical physics
title_full	Statistical physics 2 Nonequilibrium statistical mechanics R. Kubo ; M. Toda ; N. Hashitsume
title_fullStr	Statistical physics 2 Nonequilibrium statistical mechanics R. Kubo ; M. Toda ; N. Hashitsume
title_full_unstemmed	Statistical physics 2 Nonequilibrium statistical mechanics R. Kubo ; M. Toda ; N. Hashitsume
title_short	Statistical physics
title_sort	statistical physics nonequilibrium statistical mechanics
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004228078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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