Statistical mechanics : methods and applications

목차 (Table of Contents)

• CONTENTS
• Remembering Franz Mohling = ⅴ
• Acknowledgments = xvii
• Preface = xix
• Historical Notes = xxi
• Kinetic Theory of Dilute Gases = xxii
• Classical Statistical Mechanics = xxiv
• Quantum Statistical Mechanics = xxvii
• Irreversible Processes = xxix
• Bibliography = xxx
• Notes to Pertinent Sections of the Text = xxxi
• Text Notation = xxxii
• Chapter Ⅰ Statistical Physics = 1
• 1. Binomial Distribution, Random Walk and Other Applications = 1
• Random Walk and Brownian Motion = 5
• Polymers and Rubber Bands = 6
• Ferromagnetism = 6
• 2. Limit $$N\to \infty $$ Poisson and Normal Distribution = 9
• Stirling's Formula = 10
• Poisson Distribution = 12
• Normal Distribution = 13
• 3. Continuous Distributions, Central Limit Theorem = 16
• Distributions Involving Several Variables = 17
• Stochastic Independence = 18
• Central Limit Theorem = 20
• 4. Maxwell-Boltzmann Distribution for Free Particles, Statistical Entropy = 23
• Maxwell-Boltzmann Distribution = 26
• Information Theory, Statistical Entropy and the Gibbs Paradox = 28
• 5. Counting Problems, Statistical Entropy of Quantum Ideal Gases = 32
• Generating Functions = 36
• Bibliography = 39
• Notes = 40
• Problems = 41
• Chapter Ⅱ Thermodynamics = 47
• 6. Maximum Entropy Principle = 47
• Temperature = 51
• Macroscopic Motion = 53
• 7. Relation of Thermodynamics to Statistical Physics = 55
• Pressure = 58
• Thermodynamic Idenity and First Law of Thermodynamics = 59
• The Clausius Inequality = 61
• 8. Energy Functions of Thermodynamics = 62
• Heat Function W = 63
• Helmholtz Free Energy ψ = 64
• Thermodynamic Potential G = 65
• Chemical Potential g = 66
• Grand Potential f = 68
• Heat Capacity C = 69
• 9. Partial Derivatives in Thermodynamics, Thermodynamic
• Inequalities, Nernst's Theorem 70
• Minimal Conditions for Free Energies 74
• Thermodynamic Inequalities 74
• Nernst's Theorem 77
• 10. Phases in Equilibrium 78
• Clausius - Clapeyron Equation 81
• Surface Pressure 84
• Bibliography 85
• Notes 86
• Problems 88
• Chapter Ⅲ Kinetic Theory of Gases = 93
• 11. Collisions and the Maxwell-Boltzmann Distribution 93
• Collision Integral $$\left( {\partial P/\partial t} \right)_{coll}$$ = 95
• Stosszahlansatz and the Maxwell-Boltzmann Distribution = 98
• Boltzmann Transport Equation = 103
• 12. Boltzmann Transport Equation and Hydrodynamics = 104
• The Conservation Laws = 106
• Derivation of the Conservation Laws = 109
• Transformation to Local Rest System = 111
• Nonviscous Flow = 112
• Examples of Nenviscous Flow = 115
• 13. Viscous Hydrodynamics = 117
• Deviations from Local Equilibrium = 120
• Viscous Flow in a Dilute Gas = 122
• 14. Chapman-Enskog Expansion = 127
• Chapman-Enskog Expansion = 127
• First Order Calculation = 129
• 15. Noise and Brownian Motion = 134
• Calculation of 〈$$x^2$$〉 = 137
• Bibliography = 139
• Notes = 139
• Problems = 141
• Chapter Ⅳ Many-Body Problems in Quantum Mechanics = 147
• 16. Indistinguishhability of Identical Particles, State Descriptions = 147
• Occupation Number Representation = 151
• 17. Fock Space = 153
• Hamiltonian in Terms of Constructure Operators = 155
• Translational Invariance and the Two-Particle Interaction = 160
• 18. Rayleigh-Schr$$\ddot o$$dinger Perturbation Theory = 163
• Non-ideal Fermi Gas = 168
• 19. The Fermi Fluid = 172
• Landau's Theory of a Fermi Fluiod = 174
• Statistically-Averaged Fermi Fluid = 178
• 20. Green's Functions for Many-Particle Systems = 180
• Thermodynamic Green's Function = 182
• Equilibrium Ensemble Averages = 184
• Lehmann Representation = 185
• Bibliography = 189
• Notes = 189
• Problems = 191
• Chapter Ⅴ Statistical Matrix and Classical Distribution Function = 195
• 21. Formal Theory of Statistical Matrix = 195
• The Mixed-State Description = 197
• Calculation of Average Values = 199
• Alternative Treatment = 202
• 22. Example of Spin-1／2 Particles = 203
• Elastic Scattering of Particles with Spin = 207
• 23. Time Evolution of Statistical Matrix ; Liouville's Theorem of Classical Statistical Mechanics = 209
• Classical Statistical Mechanics = 211
• Liouville's Theorem = 213
• Boltzmann Transport Equation = 216
• 24. Reduced Distribution Functions = 219
• Quantum-Mechanical Considerations = 222
• Reduced Density Matrices = 224
• 25. Macroscopic Irreversibihty = 226
• Boltzmann's H-Theorem = 229
• Microscopic Reversibility = 231
• Two Historical Paradoxes = 233
• Ergodic Theory = 236
• Coarse-Grained Distributions = 238
• Bibliography = 240
• Notes = 241
• Problems = 244
• Chapter Ⅵ Macrocanonical Ensembles = 249
• 26. Ensemble Theory, a General Discussion = 249
• Microcanonical Ensembles = 250
• Macrocanonical Ensembles = 253
• Fluctuation = 255
• 27. Method of the Most Probable Distribution, Thermodynamic Analysis = 257
• Proofthat $$\beta =(kT)^{-1}$$ = 261
• Thermodynamic Analysis = 262
• Energy Fluctuations = 265
• 28. Classical Systems = 266
• The Classical Limit = 268
• Equip artition Theorem = 270
• Dilute Gas of Molecules = 273
• 29. Diatomic Gases = 275
• Calculation of $$Z_{\int }$$ = 278
• Effect of Nuclear Identify = 280
• 30. Heat Capacity of Simple Crystals = 283
• Calculation of Heat Capacity = 285
• The Einstein Model = 286
• The Debye Model = 287
• Bibliography = 292
• Notes = 292
• Problems = 295
• Chapter Ⅶ Degenerate Gases = 301
• 31. Partition Function for Ideal Gases = 301
• Use of the Darwin-Fowler Method = 303
• Interpretaion of Results = 305
• Weak Degeneracy = 308
• 32. Ideal Fermi Gas = 309
• Mathematical Procedure = 310
• Low-Temperature Thermodynamics = 314
• 33. Free Electron Theory of Metals = 315
• Heal Capacity = 317
• Thermionic Emission = 318
• Pauli Paramagnetism = 319
• 34. Ideal Bose Gas = 321
• Mathematical Analysis of Bose-Einstein Condensation = 324
• Thermodynamics of Ideal Bose Gas = 326
• Liquid Helium Four = 330
• 35. Blackbody Radiation = 332
• Thermodynamics = 334
• Bibliography = 337
• Notes = 337
• Problems = 339
• Chapter Ⅷ Grand Canonical Ensembles = 343
• 36. Grand Partition Function = 343
• Method of the Most Probable Distribution = 346
• Thermodynamic Identification ofLagrange Multipliers = 348
• 37. Cluster-Integral Expansion of Grand Potential = 351
• The Vrsell Equations = 354
• The Permutation Problem = 358
• 38. Virial Expansion of Equation of State = 360
• Expressions for the $c_N$$ = 362
• Second Virial Coefficient = 364
• 39. Van der Waals' Equation and the Maxwell Construction = 367
• The Maxwell Construction = 370
• Description of a Liquid - Vapor Phase Transition by a Grand Canonical Ensemble = 373
• 40. Ionized Gases = 378
• The Saha Equation = 379
• Debye-H$$\ddot u$$ckel Theory = 382
• Thermodynamic Calculations = 383
• Bibliography = 387
• Notes = 387
• Problems = 390
• Chapter Ⅸ Irreversible Processes = 395
• 41. Fluctuation-Dissipation Theorem for Brownian Motion = 395
• Properties of Time-Correlation Function = 398
• Fluctuation-Dissipation Theorem = 399
• Velocity Correlation Function = 403
• 42. Irreversible Thermodynamics = 404
• Continuous Systems = 407
• Linear Processes = 409
• Onsager Reciprocal Relations = 412
• 43. Applications of Onsager Relations = 413
• Thermoelectric Effects = 416
• Identification of the Kinetic Coefficients = 418
• 44. Nuclear Spin Relaxation = 421
• Polarisation Vectors = 425
• Fourier Analysis and the Spectral Density = 428
• Spin Relaxation Times = 429
• 45. Approach to Equilibrium = 432
• The Master Equation = 433
• Kubo's Method = 435
• Chapman-Kolmogorov Equation = 438
• Derivation of the Master Equation = 441
• Ehrenfests' Urn Model = 442
• Svedberg's Experiment = 446
• Bibliography = 447
• Notes = 448
• Problems = 450
• Chapter Ⅹ One- and Two-Particle Distribution Functions = 455
• 46. One-Particle Distribution Functions = 455
• Momentum Distribution = 459
• 47. Pair Distribution Functions = 462
• Calculation of Pair Distribution Function = 464
• Imperfect Gas = 466
• Measurement of D(r) for Liquids = 468
• Pair Distribution Function in Momentum Space = 469
• 48. Structure Factor and Linear Response Function = 471
• Linear Response Function = 474
• Space-Time Correlation Function = 474
• Measurements of R(q, $$\omega $$) for Liquid Helium = 477
• 49. Long Range Order = 478
• Mathematical Development = 479
• Long Range Order in Crystals = 483
• Fluctuations near the Critical Point = 484
• 50. One-Particle Thermodynamic Green's Function = 488
• Generalization of Wick's Theorem = 491
• Cancellation of Unconnected Terms = 494
• Connected $$\zeta $$ Graphs and the Graphical Expansion of G($$k_2t_2;k_1t_1$$) = 496
• Thermodynamics = 500
• Hartree-Fock Method = 502
• Bibliography = 503
• Notes = 503
• Problems = 507
• Chapter XI Real Systems Idealized = 515
• 51. Paramagnetism = 515
• Quantum Statistical Theory = 517
• Van Vieck Paramagnetism = 520
• 52. Ferromagnetism = 522
• Heisenberg Exchange Interaction = 525
• Behavior Near the Critical Temperature = 527
• 53. Relativistic Statistics = 531
• Degenerate Fermi Gas = 532
• Nondegenerate Fermi Gas = 536
• 54. White Dwarf Star Model = 538
• Equation of State = 540
• Radius and Mass of Star = 542
• 55. Chain Molecules = 545
• Three-Dimensional Folding = 547
• Wool Elasticity = 549
• Bibliography = 550
• Notes = 551
• Appendix A Darwin-Fowler Method of Mean Values = 553
• Generating Function for $P_N$$= 555
• Interpretation of Results = 558
• Application to a Macrocanonical Ensemble = 559
• Bibliography for Appendix A = 562
• Notes = 562
• Appendix B Method of Steepest Descents = 563
• Bibliography for Appendix B 566
• Notes = 567
• Appendix C Carnot Cycle and Absolute Temperature Scale = 569
• Carnot Cycle = 570
• Thermodynamic Temperature Scale = 572
• Second Law of Thermodynamics = 573
• Bibliography for Appendix C = 573
• Notes = 573
• Appendix D Remarks Related to the Collision Integral = 575
• Symmetries of the Transition Probability = 576
• Exact Collision Integral and the Conservation Laws = 578
• Bibliography for Appendix D = 582
• Notes = 582
• Appendix E Wigner Distribution Function = 583
• Calculation of Average Values = 585
• Equation of Motion for $$f_w$$ = 586
• Bibliography for Appendix E = 589
• Note = 589
• Appendix F Graphical Solution to the Permutation Problem of Quantum Statistics = 591
• Grand Potential = 593
• Momentum Distribution = 595
• Bibliography for Appendix F = 596
• Notes = 596
• Index = 597