Statistical Mechanics

PrefaceAcknowledgmentsHistorical IntroductionChapter 1. The Statistical Basis of Thermodynamics 1.1 The Macroscopic and the Microscopic Dtates 1.2 Contact between Statistics and Thermodynamics: Physical Significance of Ω{N, V, E) 1.3 Further Contact between Statistics and Thermodynamics 1.4 The Classical Ideal Gas 1.5 The Entropy of Mixing and the Gibbs Paradox 1.6 The "Correct" Enumeration of the Microstates ProblemsChapter 2. Elements of Ensemble Theory 2.1 Phase Space of a Classical System 2.2 Liouville's Theorem and its Consequences 2.3 The Microcanonical Ensemble 2.4 Examples 2.5 Quantum States and the Phase Space 2.6 Two Important Theorems - The "Equipartition" and the "Virial" ProblemsChapter 3. The Canonical Ensemble 3.1 Equilibrium between a System and a Heat Reservoir 3.2 A System in the Canonical Ensemble 3.3 Physical Significance of the Various Statistical Quantities 3.4 Alternative Expressions for the Partition Function 3.5 The Classical Systems 3.6 Energy Fluctuations in the Canonical Ensemble: Correspondence with the Microcanonical Ensemble 3.7 A System of Harmonic Oscillators 3.8 The Statistics of Paramagnetism 3.9 Thermodynamics of Magnetic Systems: Negative Temperatures ProblemsChapter 4. The Grand Canonical Ensemble 4.1 Equilibrium between a System and a Particle-Energy Reservoir 4.2 A system in the Grand Canonical Ensemble 4.3 Physical Significance of the Statistical Quantities 4.4 Examples 4.5 Density and Energy Fluctuations in the Grand Canonical Ensemble: Correspondence with Other Ensembles ProblemsChapter 5. Formulation of Quantum Statistics 5.1 Quantum-Mechanical Ensemble Theory: The Density Matrix 5.2 Statistics of the Various Ensembles 5.3 Examples 5.4 Systems Composed of Indistinguishable Particles 5.5 The Density Matrix and the Partition Function of a System of Free Particles ProblemsChapter 6. The Theory of Simple Gases 6.1 An Ideal Gas in a Quantum-Mechanical Microcanonical Ensemble 6.2 An Ideal Gas in Other Quantum-Mechanical Ensembles 6.3 Statistics of the Occupation Numbers 6.4 Kinetic Considerations 6.5 A Gaseous System in Mass Motion 6.6 Gaseous Systems Composed of Molecules with Internal Motion A. Monatomic Molecules B. Diatomic Molecules C. Polyatomic Molecules ProblemsChapter 7. Ideal Bose Systems 7.1 Thermodynamic Behavior of an Ideal Bose Gas 7.2 Thermodynamics of the Black-Body Radiation 7.3 The Field of Sound Waves 7.4 Inertial Density of the Sound Field 7.5 Elementary Excitations in Liquid Helium II ProblemsChapter 8. Ideal Fermi Systems 8.1 Thermodynamic Behavior of an Ideal Fermi Gas 8.2 Magnetic Behavior of an Ideal Fermi Gas A. Pauli Paramagnetism B. Landau Diamagnetism and de Haas-van Alphen Effect 8.3 The Electron Gas in Metals A. Thermionic Emission B. Photoelectric Emission 8.4 Statistical Equilibrium of White Dwarf Stars 8.5 Statistical Model of the Atom ProblemsChapter 9. Statistical Mechanics of Interacting Systems: The Method of Cluster Expansions 9.1 Cluster Expansion for a Classical Gas 9.2 Virial Expansion of the Equation of State 9.3 Evaluation of the Virial Coefficients 9.4 General Remarks on Cluster Expansions 9.5 Exact Treatment of the Second Virial Coefficient 9.6 Cluster Expansion for a Quantum-Mechanical System 9.7 The Binary Collision Method of Lee and Yang 9.8 Applications of the Binary Collision Method A. A Gas of Noninteracting Particles B. A Gas of Hard Spheres ProblemsChapter 10. Statistical Mechanics of Interacting Systems: The Method of Pseudopotentials 10.1 The Two-Body Pseudopotential 10.2 The N-body Pseudopotential and its Eigenvalues 10.3 Low-Temperature Behavior of an Imperfect Fermi Gas 10.4 Low-Temperature Behavior of an Imperfect Bose Gas 10.5 The Ground State Wave Function of a Bose Fluid 10.6 States with Quantized Circulation 10.7 "Rotation" of the Superfluid 10.8 Quantized Vortex Rings and the Breakdown of Superfluidity ProblemsChapter 11. Statistical Mechanics of Interacting Systems: The Method of Quantized Fields 11.1 The Formalism of Second Quantization 11.2 Low-Lying States of an Imperfect Bose Gas 11.3 Energy Spectrum of a Bose Liquid 11.4 Low-Lying States of an Imperfect Fermi Gas 11.5 Energy Spectrum of a Fermi Liquid: Landau's Phenomenological Theory ProblemsChapter 12. Theory of Phase Transitions 12.1 General Remarks on the Problem of Condensation 12.2 Mayer's Theory of Condensation 12.3 The Theory of Yang and Lee 12.4 Further Comments on the Theory of Yang and Lee A. The Gaseous Phase and the Cluster Integrals B. An Electrostatic Analogue 12.5 A Dynamical Model for Phase Transitions 12.6 The Lattice Gas and the Binary Alloy 12.7 Ising Model in the Zeroth Approximation 12.8 Ising Model in the First Approximation 12.9 Exact Treatments of the One-dimensional Lattice A. The Combinatorial Method B. The Matrix Method C The Zeros of the Grand Partition Function 12.10 Study of the Two- and Three-dimensional Lattices 12.11 The Critical Indices 12.12 The Law of Corresponding States ProblemsChapter 13. Fluctuations 13.1 Thermodynamic Fluctuations 13.2 Spatial Correlations in a Fluid 13.3 Einstein-Smoluchowski Theory of the Brownian Motion 13.4 Langevin Theory of the Brownian Motion 13.5 Approach to Equilibrium: The Fokker-Planck Equation 13.6 Spectral Analysis of Fluctuations: The Wiener-Khintchine Theorem 13.7 The Fluctuation-Dissipation Theorem 13.8 The Onsager Relations ProblemsAppendixes A. Influence of Boundary Conditions on the Distribution of Quantum States B. Certain Mathematical Functions C. "Volume" and "Surface Area" of an n-dimensional Sphere of Radius R D. On the Bose-Einstein Integrals E. On the Fermi-Dirac Integrals F. General Physical Constants G. Defined Values and Equivalents H. General Mathematical ConstantsBibliographyIndex