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      Statistical mechanics : methods and applications

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      https://www.riss.kr/link?id=M439626

      • 저자
      • 발행사항

        Jamaica, Queens, N. Y. : Publishers Creative Services ; New York : Distributed by Halsted Press, c1982

      • 발행연도

        1982

      • 작성언어

        영어

      • 주제어
      • ISBN

        0470273402

      • 자료형태

        일반단행본

      • 발행국(도시)

        New York(State)

      • 서명/저자사항

        Statistical mechanics : methods and applications / Franz Mohling.

      • 형태사항

        xxxii, 608 p. : ill. ; 25 cm.

      • 일반주기명

        Includes bibliographies and index.

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      목차 (Table of Contents)

      • CONTENTS
      • Remembering Franz Mohling = ⅴ
      • Acknowledgments = xvii
      • Preface = xix
      • Historical Notes = xxi
      • 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
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