Beale Statistical Mechanics

3. Auflage 2011
ISBN: 978-0-12-382189-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 744 Seiten

Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations. This edition includes new topics such as BoseEinstein condensation and degenerate Fermi gas behavior in ultracold atomic gases and chemical equilibrium. It also explains the correlation functions and scattering; fluctuationdissipation theorem and the dynamical structure factor; phase equilibrium and the Clausius-Clapeyron equation; and exact solutions of one-dimensional fluid models and two-dimensional Ising model on a finite lattice. New topics can be found in the appendices, including finite-size scaling behavior of Bose-Einstein condensates, a summary of thermodynamic assemblies and associated statistical ensembles, and pseudorandom number generators. Other chapters are dedicated to two new topics, the thermodynamics of the early universe and the Monte Carlo and molecular dynamics simulations. This book is invaluable to students and practitioners interested in statistical mechanics and physics. - Bose-Einstein condensation in atomic gases - Thermodynamics of the early universe - Computer simulations: Monte Carlo and molecular dynamics - Correlation functions and scattering - Fluctuation-dissipation theorem and the dynamical structure factor - Chemical equilibrium - Exact solution of the two-dimensional Ising model for finite systems - Degenerate atomic Fermi gases - Exact solutions of one-dimensional fluid models - Interactions in ultracold Bose and Fermi gases - Brownian motion of anisotropic particles and harmonic oscillators

Paul D. Beale is a Professor of Physics at the University of Colorado Boulder. He earned a B.S. in Physics with Highest Honors at the University of North Carolina Chapel Hill in 1977, and Ph.D. in Physics from Cornell University in 1982. He served as a postdoctoral research associate at the Department of Theoretical Physics at Oxford University from 1982-1984. He joined the faculty of the University of Colorado Boulder in 1984 as an assistant professor, was promoted to associate professor in 1991, and professor in 1997. He served as the Chair of the Department of Physics from 2008-2016. He also served as Associate Dean for Natural Sciences in the College of Arts and Sciences, and Director of the Honors Program. He is currently Director of the Buffalo Bicycle Classic, the largest scholarship fundraising event in the State of Colorado. Beale is a theoretical physicist specializing in statistical mechanics, with emphasis on phase transitions and critical phenomena. His work includes renormalization group methods, finite-size scaling in spin models, fracture modes in random materials, dielectric breakdown in metal-loaded dielectrics, ferroelectric switching dynamics, exact solutions of the finite two-dimensional Ising model, solid-liquid phase transitions of molecular systems, and ordering in layers of molecular dipoles. His current interests include scalable parallel pseudorandom number generators, and interfacing quantum randomness with cryptographically secure pseudorandom number generators. He is coauthor with Raj Pathria of the third and fourth editions of the graduate physics textbook Statistical Mechanics. The Boulder Faculty Assembly has honored him with the Excellence in Teaching and Pedagogy Award, and the Excellence in Service and Leadership Award. Beale is a private pilot and an avid cyclist. He is married to Erika Gulyas, and has two children: Matthew and Melanie.

Autoren/Hrsg.

Beale, Paul D.

Inhaltsverzeichnis

1;Front Cover;1
2;Statistical Mechanics;4
3;Copyright;5
4;Table of Contents;6
5;Preface to the Third Edition;14
6;Preface to the Second Edition;18
7;Preface to the First Edition;20
8;Historical Introduction;22
9;Chapter 1. The Statistical Basis of Thermodynamics;28
9.1;1.1 The macroscopic and the microscopic states;28
9.2;1.2 Contact between statistics and thermodynamics: physical significance of the number O(N, V, E);30
9.3;1.3 Further contact between statistics and thermodynamics;33
9.4;1.4 The classical ideal gas;36
9.5;1.5 The entropy of mixing and the Gibbs paradox;43
9.6;1.6 The "correct" enumeration of the microstates;47
9.7;Problems;49
10;Chapter 2. Elements of Ensemble Theory;52
10.1;2.1 Phase space of a classical system;52
10.2;2.2 Liouville's theorem and its consequences;54
10.3;2.3 The microcanonical ensemble;57
10.4;2.4 Examples;59
10.5;2.5 Quantum states and the phase space;62
10.6;Problems;64
11;Chapter 3. The Canonical Ensemble;66
11.1;3.1 Equilibrium between a system and a heat reservoir;67
11.2;3.2 A system in the canonical ensemble;68
11.3;3.3 Physical significance of the various statistical quantities in the canonical ensemble;77
11.4;3.4 Alternative expressions for the partition function;79
11.5;3.5 The classical systems;81
11.6;3.6 Energy fluctuations in the canonical ensemble: correspondence with the microcanonical ensemble;85
11.7;3.7 Two theorems — the "equipartition" and the "virial";88
11.8;3.8 A system of harmonic oscillators;92
11.9;3.9 The statistics of paramagnetism;97
11.10;3.10 Thermodynamics of magnetic systems: negative temperatures;104
11.11;Problems;110
12;Chapter 4. The Grand Canonical Ensemble;118
12.1;4.1 Equilibrium between a system and a particle-energy reservoir;118
12.2;4.2 A system in the grand canonical ensemble;120
12.3;4.3 Physical significance of the various statistical quantities;122
12.4;4.4 Examples;125
12.5;4.5 Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles;130
12.6;4.6 Thermodynamic phase diagrams;132
12.7;4.7 Phase equilibrium and the Clausius–Clapeyron equation;136
12.8;Problems;138
13;Chapter 5. Formulation of Quantum Statistics;142
13.1;5.1 Quantum-mechanical ensemble theory: the density matrix;142
13.2;5.2 Statistics of the various ensembles;146
13.3;5.3 Examples;149
13.4;5.4 Systems composed of indistinguishable particles;155
13.5;5.5 The density matrix and the partition function of a system of free particles;160
13.6;Problems;166
14;Chapter 6. The Theory of Simple Gases;168
14.1;6.1 An ideal gas in a quantum-mechanical microcanonical ensemble;168
14.2;6.2 An ideal gas in other quantum-mechanical ensembles;173
14.3;6.3 Statistics of the occupation numbers;176
14.4;6.4 Kinetic considerations;179
14.5;6.5 Gaseous systems composed of molecules with internal motion;182
14.6;6.6 Chemical equilibrium;197
14.7;Problems;200
15;Chapter 7. Ideal Bose Systems;206
15.1;7.1 Thermodynamic behavior of an ideal Bose gas;207
15.2;7.2 Bose–Einstein condensation in ultracold atomic gases;218
15.3;7.3 Thermodynamics of the blackbody radiation;227
15.4;7.4 The field of sound waves;232
15.5;7.5 Inertial density of the sound field;239
15.6;7.6 Elementary excitations in liquid helium II;242
15.7;Problems;250
16;Chapter 8. Ideal Fermi Systems;258
16.1;8.1 Thermodynamic behavior of an ideal Fermi gas;258
16.2;8.2 Magnetic behavior of an ideal Fermi gas;265
16.3;8.3 The electron gas in metals;274
16.4;8.4 Ultracold atomic Fermi gases;285
16.5;8.5 Statistical equilibrium of white dwarf stars;286
16.6;8.6 Statistical model of the atom;291
16.7;Problems;296
17;Chapter 9. Thermodynamics of the Early Universe;302
17.1;9.1 Observational evidence of the Big Bang;302
17.2;9.2 Evolution of the temperature of the universe;307
17.3;9.3 Relativistic electrons, positrons, and neutrinos ;309
17.4;9.4 Neutron fraction;312
17.5;9.5 Annihilation of the positrons and electrons;314
17.6;9.6 Neutrino temperature;316
17.7;9.7 Primordial nucleosynthesis;317
17.8;9.8 Recombination;320
17.9;9.9 Epilogue;322
17.10;Problems;323
18;Chapter 10. Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions;326
18.1;10.1 Cluster expansion for a classical gas;326
18.2;10.2 Virial expansion of the equation of state;334
18.3;10.3 Evaluation of the virial coefficients;336
18.4;10.4 General remarks on cluster expansions;342
18.5;10.5 Exact treatment of the second virial coefficient;347
18.6;10.6 Cluster expansion for a quantum-mechanical system;352
18.7;10.7 Correlations and scattering;358
18.8;Problems;367
19;Chapter 11. Statistical Mechanics of Interacting Systems: The Method of Quantized Fields;372
19.1;11.1 The formalism of second quantization;372
19.2;11.2 Low-temperature behavior of an imperfect Bose gas;382
19.3;11.3 Low-lying states of an imperfect Bose gas;388
19.4;11.4 Energy spectrum of a Bose liquid;393
19.5;11.5 States with quantized circulation;397
19.6;11.6 Quantized vortex rings and the breakdown of superfluidity;403
19.7;11.7 Low-lying states of an imperfect Fermi gas;406
19.8;11.8 Energy spectrum of a Fermi liquid: Landau's phenomenological theory;412
19.9;11.9 Condensation in Fermi systems;419
19.10;Problems;421
20;Chapter 12. Phase Transitions: Criticality, Universality, and Scaling;428
20.1;12.1 General remarks on the problem of condensation;429
20.2;12.2 Condensation of a van der Waals gas;434
20.3;12.3 A dynamical model of phase transitions;438
20.4;12.4 The lattice gas and the binary alloy;444
20.5;12.5 Ising model in the zeroth approximation;447
20.6;12.6 Ising model in the first approximation;454
20.7;12.7 The critical exponents;462
20.8;12.8 Thermodynamic inequalities;465
20.9;12.9 Landau's phenomenological theory;469
20.10;12.10 Scaling hypothesis for thermodynamic functions;473
20.11;12.11 The role of correlations and fluctuations;476
20.12;12.12 The critical exponents v and .;483
20.13;12.13 A final look at the mean field theory;487
20.14;Problems;490
21;Chapter 13. Phase Transitions: Exact (or Almost Exact) Results for Various Models;498
21.1;13.1 One-dimensional fluid models;498
21.2;13.2 The Ising model in one dimension;503
21.3;13.3 The n-vector models in one dimension;509
21.4;13.4 The Ising model in two dimensions;515
21.5;13.5 The spherical model in arbitrary dimensions;535
21.6;13.6 The ideal Bose gas in arbitrary dimensions;546
21.7;13.7 Other models;553
21.8;Problems;557
22;Chapter 14. Phase Transitions: The Renormalization Group Approach;566
22.1;14.1 The conceptual basis of scaling;567
22.2;14.2 Some simple examples of renormalization;570
22.3;14.3 The renormalization group: general formulation;579
22.4;14.4 Applications of the renormalization group;586
22.5;14.5 Finite-size scaling;597
22.6;Problems;606
23;Chapter 15. Fluctuations and Nonequilibrium Statistical Mechanics;610
23.1;15.1 Equilibrium thermodynamic fluctuations;611
23.2;15.2 The Einstein–Smoluchowski theory of the Brownian motion;614
23.3;15.3 The Langevin theory of the Brownian motion;620
23.4;15.4 Approach to equilibrium: the Fokker–Planck equation;630
23.5;15.5 Spectral analysis of fluctuations: the Wiener–Khintchine theorem;636
23.6;15.6 The fluctuation–dissipation theorem;644
23.7;15.7 The Onsager relations;653
23.8;Problems;659
24;Chapter 16. Computer Simulations;664
24.1;16.1 Introduction and statistics;664
24.2;16.2 Monte Carlo simulations;667
24.3;16.3 Molecular dynamics;670
24.4;16.4 Particle simulations;673
24.5;16.5 Computer simulation caveats;677
24.6;Problems;678
25;Appendices;680
25.1;A. Influence of boundary conditions on the distribution of quantum states;680
25.2;B. Certain mathematical functions;682
25.3;C. "Volume" and "surface area" of an n-dimensional sphere of radius R;689
25.4;D. On Bose–Einstein functions;691
25.5;E. On Fermi–Dirac functions;694
25.6;F. A rigorous analysis of the ideal Bose gas and the onset of Bose–Einstein condensation;697
25.7;G. On Watson functions;702
25.8;H. Thermodynamic relationships;703
25.9;I. Pseudorandom numbers;710
26;Bibliography;714
27;Index;734