Statistical Physics
1st Edition
Published on 11. September 2013
454 pages
978-1-4832-7410-2 (ISBN)
Description
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.
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Butterworth-Heinemann
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Akira Isihara
Statistical Physics
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01/1971
Academic Press
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Content
Preface Acknowledgments Part I. Principles and Elementary Applications 1. Kinetic Theory 1.1. Boltzmann Equation 1.2. Maxwell-Boltzmann Distribution Function 1.3. Calculation of Averages 1.4. Spectral Broadening By the Doppler Effect 1.5. Mean Free Path 1.6. Elementary Treatment of Transport Phenomena 1.7. Boltzmann and Gibbs References 2. Principles of Statistical Mechanics 2.1. Phase Space and the Liouville Theorem 2.2.* Ergodic Theories 2.3. H-Theorem for Systems in Equilibrium 2.4. Meanings of the Constants in the Canonical Distribution Function 2.5. Coarse-Graining 2.6. Product Approximation for the Distribution Function 2.7. H-Theorem Based on the Master Equation 42 Problems References 3. Partition Functions 3.1. Boltzmann Statistics 3.2. Partition Function 3.3. Gibbs'S Paradox 3.4. Grand Ensemble 3.5. Relation Between the Canonical and Grand Canonical Partition Functions 3.6. Fluctuations 3.7. The Elasticity of Rubber 3.8. Lattice Defects Problems References 4. Ideal Bosons and Fermions 4.1. Blackbody Radiation 4.2. Specific Heats of Solids 4.3. Quantum Statistics of Ideal Gases 4.4. Bose-Einstein Condensation 4.5. Phonons and Rotons 4.6. Heat Capacities of Fermi Gases and Fermi Liquids 4.7. Elementary Treatment of Transport Phenomena in Degenerate Gases 4.8. De Haas-Van Alphen Effect 4.9.* Parastatistics Problems References Part II. Classical Interacting Systems 5. Linked Cluster Expansion 5.1. Second Virial Coefficient 5.2. Cluster Expansion 5.3. Virial Expansion 5.4. Irreducible Integrals 5.5. Cumulant Expansion 5.6. Ring Diagram Approximation for a Classical Electron Gas 5.7. Theory of Condensation 5.8. Polarizable Gases 5.9. Bounds of the Free Energy 5.10.* Cluster Expansions for Binary Mixtures Problems References 6. Distribution Functions 6.1. Reduced Liouville Equation and Boltzmann Equation 6.2. Stress Tensor in Nonequilibrium Fluids 6.3. Viscosity Coefficient of Fluids 6.4. Plasmas 6.5. Viri A1 Equation of State 6.6. Determination of Fluid Structure 6.7. Critical Opalescence 6.8. Expansions of Distribution Functions 6.9.* Nodal Expansion 6.10.* HNC and PY Approximations 6.11.* Born-Green Theory Problems References 7. Brownian Motion 7.1. Random Walks and Brownian Motion 7.2.* Random Walks on Lattices 7.3.* Stokes Friction and Einstein Viscosity 7.4. Langevin's Equation 7.5. Friction Coefficient of a Brownian Particle 7.6. Autocorrelation Function 7.7. Neutron Scattering 7.8. The Fokker-Planck Equation 7.9.* Self-Avoiding Walk Problem Problems References 8. Lattice Statistics 8.1. One-Dimensional Lattice 8.2.* Helix-Coil Transition in Polypeptide and "Melting" of DNA 8.3. Duality Principle 8.4.* Rigorous Theory of a Two-Dimensional Rectangular Lattice 8.5. Spin Correlation Functions 8.6. Lattice Gas 8.7. Distribution of Zeros of the Grand Partition Function 8.8. Frequency Spectrum 8.9.* Lattice Green's Function 8.10.* Spherical Model 8.11.* Heisenberg Model References 9. Phenomena Near the Critical Temperature 9.1. Critical Temperature of a Fluid 9.2.
