# Statistical Physics

## 1st Edition

**Authors:**A. Isihara

**eBook ISBN:**9781483274102

**Imprint:**Academic Press

**Published Date:**1st January 1971

**Page Count:**454

## 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.

## Table of Contents

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

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.

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

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.

6.10.

*HNC and PY Approximations*

6.11.Born-Green Theory

6.11.

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

7.3.

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

Problems

References

8. Lattice Statistics

8.1. One-Dimensional Lattice

8.2.

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

8.5. Spin Correlation Functions

8.6. Lattice Gas

8.7. Distribution of Zeros of the Grand Partition Function

8.8. Frequency Spectrum

8.9.

8.10.

*Spherical Model*

8.11.Heisenberg Model

8.11.

References

9. Phenomena Near the Critical Temperature

9.1. Critical Temperature of a Fluid

9.2. Relationships among the Critical Exponents

9.3. Magnetic Phase Transitions

9.4. Binary Mixtures

9.5. Quantum Liquid Solution

9.6. Order-Disorder Theory

9.7. Density Fluctuations near Critical Temperature

9.8. Spatial Correlation of a Bose Gas near the Condensation Temperature

9.9. Transport Coefficients near Critical Points

References

Part Iii. Quantum Interacting Systems

10. Propagator Methods for the Partition Functions

10.1. Density Matrix

10.2. Density Matrix in the Canonical Ensemble

10.3. Simple Examples of the Density Matrix

10.4. Propagator in the R-ß Space

10.5. Graphic Representation of Propagators

10.6. Linked Cluster Expansion of the Equation of State

10.7. Equation of State in the Ring Diagram Approximation

10.8.

*The Eigenvalues of Quantum Propagators*

10.9. Correlation Energy of an Electron Gas

Problems

References

11. Propagator Methods for Distribution Functions

11.1. Linked Cluster Expansions of Distribution Functions

11.2. Distribution Functions of Ideal Quantum Gases

11.3. Triplet Distribution Function

11.4. Chain Diagram Approximation

11.5. Classical Electron Gas

11.6.Charged Fermions

10.9. Correlation Energy of an Electron Gas

Problems

References

11. Propagator Methods for Distribution Functions

11.1. Linked Cluster Expansions of Distribution Functions

11.2. Distribution Functions of Ideal Quantum Gases

11.3. Triplet Distribution Function

11.4. Chain Diagram Approximation

11.5. Classical Electron Gas

11.6.

11.7.

*Charged Bosons*

11.8.Phonon Spectrum and Spatial Correlations in a Hard-Sphere Bose Gas

11.8.

11.9.

*Hard-Sphere Fermions*

Problems

References

12. Transport Phenomena in Degenerate Systems

12.1. Uehling-Uhlenbeck Equation

12.2. Transport Coefficients

12.3. Transport Phenomena in Degenerate Systems

12.4. Phonon-Phonon Scattering

12.5. Electrical Conductivity of Metals

12.6.Resistance Minima in Dilute Magnetic Alloys

Problems

References

12. Transport Phenomena in Degenerate Systems

12.1. Uehling-Uhlenbeck Equation

12.2. Transport Coefficients

12.3. Transport Phenomena in Degenerate Systems

12.4. Phonon-Phonon Scattering

12.5. Electrical Conductivity of Metals

12.6.

Problems

References

13. Irreversibility and Transport Coefficients

13.1. Response to External Forces

13.2. Kramers-Kronig Relations for the Response Function

13.3. Symmetry Properties of Response Functions

13.4. Response in Canonical Ensembles

13.5. Transport Coefficients

13.6. Reduction of Transport Coefficients

13.7.

*Cluster Expansion of Time Correlation Functions*

13.8.Master Equation

13.8.

Problems

References

14. Second Quantization

14.1. Number Operator

14.2. Interaction Hamiltonian

14.3. Lattice Vibrations

14.4. Phonon Spectrum in a Degenerate Bose Gas

14.5. Electron Gas

14.6. Electron-Phonon Interaction

14.7. Electron-Electron Interaction Via Phonons

14.8. ⌠-Sum Rule

14.9. Dielectric Constant of a Plasma

14.10.

*Spin and Statistics*

Problems

References

15. Green'S Functions

15.1. Temperature Green's Function

15.2. Properties of the Green's Function

15.3. Contraction

15.4. Perturbation Calculation of the Grand Partition Function

15.5. Interaction Representation and Lehmann Representation

15.6. Applications of a One-Body Time Green's Function

15.7. Response Functions

15.8. Equations of Motion

15.9.Superconductivity

Problems

References

15. Green'S Functions

15.1. Temperature Green's Function

15.2. Properties of the Green's Function

15.3. Contraction

15.4. Perturbation Calculation of the Grand Partition Function

15.5. Interaction Representation and Lehmann Representation

15.6. Applications of a One-Body Time Green's Function

15.7. Response Functions

15.8. Equations of Motion

15.9.

References

Subject Index

## Details

- No. of pages:
- 454

- Language:
- English

- Copyright:
- © Academic Press 1971

- Published:
- 1st January 1971

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483274102