# Course of Theoretical Physics

## 3rd Edition

**Authors:**L. D. Landau E. M. Lifshitz

**eBook ISBN:**9781483106236

**Imprint:**Pergamon

**Published Date:**1st January 1980

**Page Count:**562

## Description

Course of Theoretical Physics, Volume 5: Statistical Physics, Third Edition, Part 1 covers the fundamental principles of statistical physics and thermodynamic quantities.

The book discusses the Gibbs and Maxwellian distributions; the Boltzmann distribution for ideal gases; and the Fermi and Bose distributions. Solids are tackled with regard to their application of statistical methods of calculating the thermodynamic quantities. The book describes the deviations of gases from the ideal state, conditions of phase equilibrium, solutions, and chemical reactions. The text also discusses the properties of matter at very high density; the Gaussian distribution; fluctuations of the fundamental thermodynamic quantities; and fluctuations in solids and ideal gases. The symmetry of crystals; phase transitions of the second kind and critical phenomena; and surfaces are considered as well.

Students taking statistical physics and those involved in the areas of statistical physics will find the book invaluable.

## Table of Contents

Preface to the Third Russian Edition

From the Prefaces to Previous Russian Editions

Notation

I. The Fundamental Principles of Statistical Physics

§ 1. Statistical Distributions

§ 2. Statistical Independence

§ 3. Liouville's Theorem

§ 4. The Significance of Energy

§ 5. The Statistical Matrix

§ 6. Statistical Distributions in Quantum Statistics

§ 7. Entropy

§ 8. The Law of Increase of Entropy

II. Thermodynamic Quantities

§ 9. Temperature

§ 10. Macroscopic Motion

§ 11. Adiabatic Processes

§ 12. Pressure

§ 13. Work and Quantity of Heat

§ 14. The Heat Function

§ 15. The Free Energy and the Thermodynamic Potential

§ 16. Relations Between the Derivatives of Thermodynamic Quantities

§ 17. The Thermodynamic Scale of Temperature

§ 18. The Joule-Thomson Process

§ 19. Maximum Work

§ 20. Maximum Work Done by a Body in an External Medium

§ 21. Thermodynamic Inequalities

§ 22. Le Chatelier's Principle

§ 23. Nernst's Theorem

§ 24. The Dependence of the Thermodynamic Quantities on the Number of Particles

§ 25. Equilibrium of a Body in an External Field

§ 26. Rotating Bodies

§ 27. Thermodynamic Relations in the Relativistic Region

III. The Gibbs Distribution

§ 28. The Gibbs Distribution

§ 29. The Maxwellian Distribution

§ 30. The Probability Distribution for an Oscillator

§ 31. The Free Energy in the Gibbs Distribution

§ 32. Thermodynamic Perturbation Theory

§ 33. Expansion in Powers of h

§ 34. The Gibbs Distribution for Rotating Bodies

§ 35. The Gibbs Distribution for a Variable Number of Particles

§ 36. The Derivation of the Thermodynamic Relations from the Gibbs Distribution

IV. Ideal Gases

§ 37. The Boltzmann Distribution

§ 38. The Boltzmann Distribution in Classical Statistics

§ 39. Molecular Collisions

§ 40. Ideal Gases Not in Equilibrium

§ 41. The Free Energy of an Ideal Boltzmann Gas

§ 42. The Equation of State of an Ideal Gas

§ 43. Ideal Gases With Constant Specific Heat

§ 44. The Law of Equipartition

§ 45. Monatomic Ideal Gases

§ 46. Monatomic Gases. The Effect of the Electronic Angular Momentum

§ 47. Diatomic Gases With Molecules of Unlike Atoms. Rotation of Molecules

§ 48. Diatomic Gases With Molecules of Like Atoms. Rotation of Molecules

§ 49. Diatomic Gases. Vibrations of Atoms

§ 50. Diatomic Gases. The Effect of the Electronic Angular Momentum

§ 51. Polyatomic Gases

§ 52. Magnetism of Gases

V. The Fermi and Bose Distributions

§ 53. The Fermi Distribution

§ 54. The Bose Distribution

§ 55. Fermi and Bose Gases Not in Equilibrium

§ 56. Fermi and Bose Gases of Elementary Particles

§ 57. A Degenerate Electron Gas

§ 58. The Specific Heat of a Degenerate Electron Gas

§ 59. Magnetism of an Electron Gas. Weak Fields

§ 60. Magnetism of an Electron Gas. Strong Fields

§ 61. A Relativistic Degenerate Electron Gas

§ 62. A Degenerate Bose Gas

§ 63. Black-Body Radiation

VI. Solids

§ 64. Solids at Low Temperatures

§ 65. Solids at High Temperatures

§ 66. Debye's Interpolation Formula

§ 67. Thermal Expansion of Solids

§ 68. Highly Anisotropic Crystals

§ 69. Crystal Lattice Vibrations

§ 70. Number Density of Vibrations

§ 71. Phonons

§ 72. Phonon Creation and Annihilation Operators

§ 73. Negative Temperatures

VII. Non-Ideal Gases

§ 74. Deviations of Gases from the Ideal State

§ 75. Expansion in Powers of the Density

§ 76. Van Der Waals' Formula

§ 77. Relationship of the Virial Coefficient and the Scattering Amplitude

§ 78. Thermodynamic Quantities for a Classical Plasma

§ 79. The Method of Correlation Functions

§ 80. Thermodynamic Quantities for a Degenerate Plasma

VIII. Phase Equilibrium

§ 81. Conditions of Phase Equilibrium

§ 82. The Clapeyron-Clausius Formula

§ 83. The Critical Point

§ 84. The Law of Corresponding States

IX. Solutions

§ 85. Systems Containing Different Particles

§ 86. The Phase Rule

§ 87. Weak Solutions

§ 88. Osmotic Pressure

§ 89. Solvent Phases in Contact

§ 90. Equilibrium With Respect To the Solute

§ 91. Evolution of Heat and Change of Volume on Dissolution

§ 92. Solutions of Strong Electrolytes

§ 93. Mixtures of Ideal Gases

§ 94. Mixtures of Isotopes

§ 95. Vapor Pressure Over Concentrated Solutions

§ 96. Thermodynamic Inequalities for Solutions

§ 97. Equilibrium Curves

§ 98. Examples of Phase Diagrams

§ 99. Intersection of Singular Curves on the Equilibrium Surface

§ 100. Gases and Liquids

X. Chemical Reactions

§ 101. The Condition for Chemical Equilibrium

§ 102. The Law of Mass Action

§ 103. Heat of Reaction

§ 104. Ionization Equilibrium

§ 105. Equilibrium With Respect To Pair Production

XI. Properties of Matter at Very High Density

§ 106. The Equation of State of Matter at High Density

§ 107. Equilibrium of Bodies of Large Mass

§ 108. The Energy of a Gravitating Body

§ 109. Equilibrium of a Neutron Sphere

XII. Fluctuations

§ 110. The Gaussian Distribution

§ 111. The Gaussian Distribution for More Than One Variable

§ 112. Fluctuations of the Fundamental Thermodynamic Quantities

§ 113. Fluctuations in an Ideal Gas

§ 114. Poisson's Formula

§ 115. Fluctuations in Solutions

§ 116. Spatial Correlation of Density Fluctuations

§ 117. Correlation of Density Fluctuations in a Degenerate Gas

§ 118. Correlations of Fluctuations in Time

§ 119. Time Correlations of the Fluctuations of More Than One Variable

§ 120. The Symmetry of the Kinetic Coefficients

§ 121. The Dissipative Function

§ 122. Spectral Resolution of Fluctuations

§ 123. The Generalized Susceptibility

§ 124. The Fluctuation-Dissipation Theorem

§ 125. The Fluctuation-Dissipation Theorem for More Than One Variable

§ 126. The Operator Form of the Generalized Susceptibility

§ 127. Fluctuations in the Curvature of Long Molecules

XIII. The Symmetry of Crystals

§ 128. Symmetry Elements of a Crystal Lattice

§ 129. The Bravais Lattice

§ 130. Crystal Systems

§ 131. Crystal Classes

§ 132. Space Groups

§ 133. The Reciprocal Lattice

§ 134. Irreducible Representations of Space Groups

§ 135. Symmetry Under Time Reversal

§ 136. Symmetry Properties of Normal Vibrations of a Crystal Lattice

§ 137. Structures Periodic in One and Two Dimensions

§ 138. The Correlation Function in Two-Dimensional Systems

§ 139. Symmetry With Respect To Orientation of Molecules

§ 140. Nematic and Cholesteric Liquid Crystals

§ 141. Fluctuations in Liquid Crystals

XIV. Phase Transitions of the Second Kind and Critical Phenomena

§ 142. Phase Transitions of the Second Kind

§ 143. The Discontinuity of Specific Heat

§ 144. Effect of an External Field on a Phase Transition

§ 145. Change in Symmetry in a Phase Transition of the Second Kind

§ 146. Fluctuations of the Order Parameter

§ 147. The Effective Hamiltonian

§ 148. Critical Indices

§ 149. Scale Invariance

§ 150. Isolated and Critical Points of Continuous Transition

§151. Phase Transitions of the Second Kind in a Two-Dimensional Lattice

§ 152. Van Der Waals Theory of the Critical Point

§ 153. Fluctuation Theory of the Critical Point

XV. Surfaces

§ 154. Surface Tension

§ 155. Surface Tension of Crystals

§ 156. Surface Pressure

§ 157. Surface Tension of Solutions

§ 158. Surface Tension of Solutions of Strong Electrolytes

§ 159. Adsorption

§ 160. Wetting

§ 161. The Angle of Contact

§ 162. Nucleation in Phase Transitions

§ 163. The Impossibility of the Existence of Phases in One-Dimensional Systems

Index

Contents of Part 2

Preface

Notation

I. The Normal Fermi Liquid

§ 1. Elementary Excitations in a Quantum Fermi Liquid

§ 2. Interaction of Quasi-Particles

§ 3. Magnetic Susceptibility of a Fermi Liquid

§ 4. Zero Sound

§ 5. Spin Waves in a Fermi Liquid

§ 6. A Degenerate Almost Ideal Fermi Gas With Repulsion Between the Particles

II. Green's Functions in a Fermi System at T = O

§ 7. Green's Functions in a Macroscopic System

§ 8. Determination of the Energy Spectrum from the Green's Function

§ 9. Green's Function of an Ideal Fermi Gas

§ 10. Particle Momentum Distribution in a Fermi Liquid

§ 11. Calculation of Thermodynamic Quantities from the Green's Function

§ 12. Ø Operators in the Interaction Representation

§ 13. The Diagram Technique for Fermi Systems

§ 14. The Self-Energy Function

§ 15. The Two-Particle Green's Function

§ 16. The Relation of the Vertex Function To the Quasi-Particle Scattering Amplitude

§ 17. The Vertex Function for Small Momentum Transfers

§ 18. The Relation of the Vertex Function To the Quasi-Particle Interaction Function

§ 19. Identities for Derivatives of the Green's Function

§ 20. Derivation of the Relation Between the Limiting Momentum and the Density

§ 21. Green's Function of an Almost Ideal Fermi Gas

III. Superfluidity

§ 22. Elementary Excitations in a Quantum Bose Liquid

§ 23. Superfluidity

§ 24. Phonons in a Liquid

§ 25. A Degenerate Almost Ideal Bose Gas

§ 26. The Wave Function of the Condensate

§ 27. Temperature Dependence of the Condensate Density

§ 28. Behavior of the Superfluid Density Near the λ-Point

§ 29. Quantized Vortex Filaments

§ 30. A Vortex Filament in an Almost Ideal Bose Gas

§ 31. Green's Functions in a Bose Liquid

§ 32. The Diagram Technique for a Bose Liquid

§ 33. Self-Energy Functions

§ 34. Disintegration of Quasi-Particles

§ 35. Properties of the Spectrum Near Its Termination Point

IV. Green's Functions at Non-Zero Temperatures

§ 36. Green's Functions at Non-Zero Temperatures

§ 37. Temperature Green's Functions

§ 38. The Diagram Technique for Temperature Green's Functions

V. Superconductivity

§ 39. A Superfluid Fermi Gas. The Energy Spectrum

§ 40. A Superfluid Fermi Gas. Thermodynamic Properties

§ 41. Green's Functions in a Superfluid Fermi Gas

§ 42. Temperature Green's Functions in a Superfluid Fermi Gas

§ 43. Superconductivity in Metals

§ 44. The Superconductivity Current

§ 45. The Ginzburg-Landau Equations

§ 46. Surface Tension at the Boundary of Superconducting and Normal Phases

§ 47. The Two Types of Superconductor

§ 48. The Structure of the Mixed State

§ 49. Diamagnetic Susceptibility Above the Transition Point

§ 50. The Josephson Effect

§ 51. Relation Between Current and Magnetic Field in a Superconductor

§ 52. Depth of Penetration of a Magnetic Field Into a Superconductor

§ 53. Superconducting Alloys

§ 54. The Cooper Effect for Non-Zero Orbital Angular Momenta of the Pair

VI. Electrons in the Crystal Lattice

§ 55. an Electron in a Periodic Field

§ 56. Effect of an External Field on Electron Motion in a Lattice

§ 57. Quasi-Classical Trajectories

§ 58. Quasi-Classical Energy Levels

§ 59. The Electron Effective Mass Tensor in the Lattice

§ 60. Symmetry of Electron States in a Lattice in a Magnetic Field

§ 61. Electron Spectra of Normal Metals

§ 62. Green's Function of Electrons in a Metal

§ 63. The De Haas-Van Alphen Effect

§ 64. Electron-Phonon Interaction

§ 65. Effect of Electron-Phonon Interaction on the Electron Spectrum in a Metal

§ 66. The Electron Spectrum of Solid Insulators

§ 67. Electrons and Holes in Semiconductors

§ 68. The Electron Spectrum Near the Degeneracy Point

VII. Magnetism

§ 69. Equation of Motion of the Magnetic Moment in a Ferromagnet

§ 70. Magnons in a Ferromagnet. The Spectrum

§ 71. Magnons in a Ferromagnet. Thermodynamic Quantities

§ 72. The Spin Hamiltonian

§ 73. Interaction of Magnons

§ 74. Magnons in an Antiferromagnet

VIII. Electromagnetic Fluctuations

§ 75. Green's Function of a Photon in a Medium

§ 76. Electromagnetic Field Fluctuations

§ 77. Electromagnetic Fluctuations in an Infinite Medium

§ 78. Current Fluctuations in Linear Circuits

§ 79. Temperature Green's Function of a Photon in a Medium

§ 80. The Van Der Waals Stress Tensor

§ 81. Forces of Molecular Interaction Between Solid Bodies. The General Formula

§ 82. Forces of Molecular Interaction Between Solid Bodies. Limiting Cases

§ 83. Asymptotic Behavior of the Correlation Function in a Liquid

§ 84. Operator Expression for the Permittivity

§ 85. A Degenerate Plasma

IX. Hydrodynamic Fluctuations

§ 86. Dynamic Form Factor of a Liquid

§ 87. Summation Rules for the Form Factor

§ 88. Hydrodynamic Fluctuations

§ 89. Hydrodynamic Fluctuations in an Infinite Medium

§ 90. Operator Expressions for the Transport Coefficients

§ 91. Dynamic Form Factor of a Fermi Liquid

Index

## Details

- No. of pages:
- 562

- Language:
- English

- Copyright:
- © Pergamon 1980

- Published:
- 1st January 1980

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483106236