Isihara Statistical Physics

1. Auflage 2013
ISBN: 978-1-4832-7410-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 454 Seiten, Web PDF

Statistical Physics provides an introduction to the basic principles of statistical mechanics. Statistical mechanics is one of the fundamental branches of theoretical physics and chemistry, and deals with many systems such as gases, liquids, solids, and even molecules which have many atoms. The book consists of three parts. Part I gives the principles, with elementary applications to noninteracting systems. It begins with kinetic theory and discusses classical and quantum systems in equilibrium and nonequilibrium. In Part II, classical statistical mechanics is developed for interacting systems in equilibrium and nonequilibrium. Finally, in Part III, quantum statistics is presented to an extent which enables the reader to proceed to advanced many-body theories. This book is written for a one-year graduate course in statistical mechanics or a half-year course followed by a half-year course on related subjects, such as special topics and applications or elementary many-body theories. Efforts are made such that discussions of each subject start with an elementary level and end at an advanced level.

Autoren/Hrsg.

Isihara, A.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Physics;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;14
7;Acknowledgments;16
8;Part I. PRINCIPLES AND ELEMENTARY APPLICATIONS;18
9;Chapter 1. Kinetic Theory;20
9.1;I.1. BOLTZMANN EQUATION;20
9.2;1.2. MAXWELL–BOLTZMANN DISTRIBUTION FUNCTION;24
9.3;1.3. CALCULATION OF AVERAGES;26
9.4;1.4. SPECTRAL BROADENING BY THE DOPPLER EFFECT;28
9.5;1.5. MEAN FREE PATH;29
9.6;1.6. ELEMENTARY TREATMENT OF TRANSPORT PHENOMENA;30
9.7;1.7. BOLTZMANN AND GIBBS;34
9.8;REFERENCES;36
10;Chapter 2. Principles of Statistical Mechanics;37
10.1;2.1. PHASE SPACE AND THE LIOUVILLE THEOREM;38
10.2;2.2. ERGODIC THEORIES;40
10.3;2.3. H-THEOREM FOR SYSTEMS IN EQUILIBRIUM;47
10.4;2.4. MEANINGS OF THE CONSTANTS IN THE CANONICAL DISTRIBUTION FUNCTION;50
10.5;2.5. COARSE-GRAINING;56
10.6;2.6. PRODUCT APPROXIMATION FOR THE DISTRIBUTION FUNCTION;57
10.7;2.7. H-THEOREM BASED ON THE MASTER EQUATION;59
10.8;PROBLEMS;62
10.9;REFERENCES;64
11;Chapter 3. Partition Functions;65
11.1;3.1. BOLTZMANN STATISTICS;65
11.2;3.2. PARTITION FUNCTION;68
11.3;3.3. GIBBS'S PARADOX;71
11.4;3.4. GRAND ENSEMBLE;74
11.5;3.5. RELATION BETWEEN THE CANONICAL AND GRAND CANONICAL PARTITION FUNCTIONS;76
11.6;3.6. FLUCTUATIONS;80
11.7;3.7. THE ELASTICITY OF RUBBER;82
11.8;3.8. LATTICE DEFECTS;85
11.9;PROBLEMS;86
11.10;REFERENCES;87
12;Chapter 4. Ideal Bosons and Fermions;88
12.1;4.1. BLACKBODY RADIATION;88
12.2;4.2. SPECIFIC HEATS OF SOLIDS;92
12.3;4.3. QUANTUM STATISTICS OF IDEAL GASES;97
12.4;4.4. BOSE-EINSTEIN CONDENSATION;101
12.5;4.5. PHONONS AND ROTONS;106
12.6;4.6. HEAT CAPACITIES OF FERMI GASES AND FERMI LIQUIDS;108
12.7;4.7. ELEMENTARY TREATMENT OF TRANSPORT PHENOMENA IN DEGENERATE GASES;115
12.8;4.8. DE HAAS-VAN ALPHEN EFFECT;118
12.9;4.9. PARASTATISTICS;122
12.10;PROBLEMS;124
12.11;REFERENCES;126
13;Part II. CLASSICAL INTERACTING SYSTEMS;128
13.1;Chapter 5. Linked Cluster Expansion;130
13.1.1;5.1. SECOND VIRIAL COEFFICIENT;130
13.1.2;5.2. CLUSTER EXPANSION;137
13.1.3;5.3. VIRIAL EXPANSION;144
13.1.4;5.4. IRREDUCIBLE INTEGRALS;145
13.1.5;5.5. CUMULANT EXPANSION;148
13.1.6;5.6. RING DIAGRAM APPROXIMATION FOR A CLASSICALELECTRON GAS;151
13.1.7;5.7. THEORY OF CONDENSATION;153
13.1.8;5.8. POLARIZABLE GASES;157
13.1.9;5.9. BOUNDS OF THE FREE ENERGY;161
13.1.10;5.10. CLUSTER EXPANSIONS FOR BINARY MIXTURES;165
13.1.11;PROBLEMS;167
13.1.12;REFERENCES;169
14;Chapter 6. Distribution Functions;170
14.1;6.1. REDUCED LIOUVILLE EQUATION AND BOLTZMANN EQUATION;170
14.2;6.2. STRESS TENSOR IN NONEQUILIBRIUM FLUIDS;174
14.3;6.3. VISCOSITY COEFFICIENT OF FLUIDS;175
14.4;6.4. PLASMAS;178
14.5;6.5. VIRI AL EQUATION OF STATE;180
14.6;6.6. DETERMINATION OF FLUID STRUCTURE;182
14.7;6.7. CRITICAL OPALESCENCE;183
14.8;6.8. EXPANSIONS OF DISTRIBUTION FUNCTIONS;186
14.9;6.9. NODAL EXPANSION;189
14.10;6.10. HNC AND PY APPROXIMATIONS;191
14.11;6.11. BORN–GREEN THEORY;193
14.12;PROBLEMS;196
14.13;REFERENCES;197
15;Chapter 7. Brownian Motion;199
15.1;7.1. RANDOM WALKS AND BROWNIAN MOTION;200
15.2;7.2. RANDOM WALKS ON LATTICES;203
15.3;7.3. STOKES FRICTION AND EINSTEIN VISCOSITY;205
15.4;7.4. LANGEVIN'S EQUATION;209
15.5;7.5. FRICTION COEFFICIENT OF A BROWNIAN PARTICLE;212
15.6;7.6. AUTOCORRELATION FUNCTION;216
15.7;7.7. NEUTRON SCATTERING;219
15.8;7.8. THE FOKKER-PLANCK EQUATION;222
15.9;7.9. SELF-AVOIDING WALK PROBLEM;224
15.10;PROBLEMS;228
15.11;REFERENCES;230
16;Chapter 8. Lattice Statistics;231
16.1;8.1. ONE-DIMENSIONAL LATTICE;232
16.2;8.2. HELIX-COIL TRANSITION IN POLYPEPTIDE AND " MELTING "OF DNA;234
16.3;8.3. DUALITY PRINCIPLE;236
16.4;8.4. RIGOROUS THEORY OF A TWO-DIMENSIONAL RECTANGULAR LATTICE;239
16.5;8.5. SPIN CORRELATION FUNCTIONS;247
16.6;8.6. LATTICE GAS;252
16.7;8.7. DISTRIBUTION OF ZEROS OF THE GRAND PARTITION FUNCTION;253
16.8;8.8. FREQUENCY SPECTRUM;256
16.9;8.9. LATTICE GREEN'S FUNCTION;261
16.10;8.10. SPHERICAL MODEL;263
16.11;8.11. HEISENBERG MODEL;264
16.12;REFERENCES;267
17;Chapter 9. Phenomena near the Critical Temperature;269
17.1;9.1. CRITICAL TEMPERATURE OF A FLUID;269
17.2;9.2. RELATIONSHIPS AMONG THE CRITICAL EXPONENTS;273
17.3;9.3. MAGNETIC PHASE TRANSITIONS;274
17.4;9.4. BINARY MIXTURES;276
17.5;9.5. QUANTUM LIQUID SOLUTION;278
17.6;9.6. ORDER-DISORDER THEORY;280
17.7;9.7. DENSITY FLUCTUATIONS NEAR CRITICAL TEMPERATURE;283
17.8;9.8. SPATIAL CORRELATION OF A BOSE GAS NEAR THE CONDENSATION TEMPERATURE;287
17.9;9.9. TRANSPORT COEFFICIENTS NEAR CRITICAL POINTS;288
17.10;REFERENCES;289
18;Part III. QUANTUM INTERACTING SYSTEMS;292
18.1;Chapter 10. Propagator Methods for the Partition Functions;294
18.1.1;10.1. DENSITY MATRIX;295
18.1.2;10.2. DENSITY MATRIX IN THE CANONICAL ENSEMBLE;297
18.1.3;10.3. SIMPLE EXAMPLES OF THE DENSITY MATRIX;300
18.1.4;10.4. PROPAGATOR IN THE r-ß Space;303
18.1.5;10.5. GRAPHIC REPRESENTATION OF PROPAGATORS;307
18.1.6;10.6. LINKED CLUSTER EXPANSION OF THE EQUATION OF STATE;310
18.1.7;10.7. EQUATION OF STATE IN THE RING DIAGRAM APPROXIMATION;312
18.1.8;10.8. THE EIGENVALUES OF QUANTUM PROPAGATORS;316
18.1.9;10.9. CORRELATION ENERGY OF AN ELECTRON GAS;321
18.1.10;PROBLEMS;324
18.1.11;REFERENCES;326
19;Chapter 11. Propagator Methods for Distribution Functions;327
19.1;11.1. LINKED CLUSTER EXPANSIONS OF DISTRIBUTION FUNCTIONS;328
19.2;11.2. DISTRIBUTION FUNCTIONS OF IDEAL QUANTUM GASES;330
19.3;11.3. TRIPLET DISTRIBUTION FUNCTION;333
19.4;11.4. CHAIN DIAGRAM APPROXIMATION;334
19.5;11.5. CLASSICAL ELECTRON GAS;337
19.6;11.6. CHARGED FERMIONS;341
19.7;11.7. CHARGED BOSONS;344
19.8;11.8. PHONON SPECTRUM AND SPATIAL CORRELATIONS IN AHARD-SPHERE BOSE GAS;345
19.9;11.9. HARD-SPHERE FERMIONS;349
19.10;PROBLEMS;352
19.11;REFERENCES;354
20;Chapter 12. Transport Phenomena in Degenerate Systems;355
20.1;12.1. UEHLING-UHLENBECK EQUATION;355
20.2;12.2. TRANSPORT COEFFICIENTS;358
20.3;12.3. TRANSPORT PHENOMENA IN DEGENERATE SYSTEMS;360
20.4;12.4. PHONON–PHONON SCATTERING;365
20.5;12.5. ELECTRICAL CONDUCTIVITY OF METALS;369
20.6;12.6. RESISTANCE MINIMA IN DILUTE MAGNETIC ALLOYS;372
20.7;PROBLEMS;375
20.8;REFERENCES;376
21;Chapter 13. Irreversibility and Transport Coefficients;377
21.1;13.1. RESPONSE TO EXTERNAL FORCES;378
21.2;13.2. KRAMERS-KRONIG RELATIONS FOR THE RESPONSE FUNCTION;381
21.3;13.3. SYMMETRY PROPERTIES OF RESPONSE FUNCTIONS;383
21.4;13.4. RESPONSE IN CANONICAL ENSEMBLES;384
21.5;13.5. TRANSPORT COEFFICIENTS;386
21.6;13.6. REDUCTION OF TRANSPORT COEFFICIENTS;389
21.7;13.7. CLUSTER EXPANSION OF TIME CORRELATION FUNCTIONS;392
21.8;13.8. MASTER EQUATION;393
21.9;PROBLEMS;396
21.10;REFERENCES;397
22;Chapter 14. Second Quantization;399
22.1;14.1. NUMBER OPERATOR;400
22.2;14.2. INTERACTION HAMILTONIAN;402
22.3;14.3. LATTICE VIBRATIONS;403
22.4;14.4. PHONON SPECTRUM IN A DEGENERATE BOSE GAS;405
22.5;14.5. ELECTRON GAS;407
22.6;14.6. ELECTRON-PHONON INTERACTION;409
22.7;14.7. ELECTRON-ELECTRON INTERACTION VIA PHONONS;412
22.8;14.8. f-SUM RULE;414
22.9;14.9. DIELECTRIC CONSTANT OF A PLASMA;415
22.10;14.10. SPIN AND STATISTICS;417
22.11;PROBLEMS;420
22.12;REFERENCES;421
23;Chapter 15. Green's Functions;422
23.1;15.1. TEMPERATURE GREEN'S FUNCTION;422
23.2;15.2. PROPERTIES OF THE GREEN'S FUNCTION;424
23.3;15.3. CONTRACTION;426
23.4;15.4. PERTURBATION CALCULATION OF THE GRAND PARTITION FUNCTION;429
23.5;15.5. INTERACTION REPRESENTATION AND LEHMANN REPRESENTATION;433
23.6;15.6. APPLICATIONS OF A ONE-BODY TIME GREEN'S FUNCTION;435
23.7;15.7. RESPONSE FUNCTIONS;439
23.8;15.8. EQUATIONS OF MOTION;443
23.9;15.9. SUPERCONDUCTIVITY;444
23.10;REFERENCES;449
24;Subject Index;450