Lectures on Selected Topics in Statistical Mechanics

Preface

Chapter 1. The Occupation Number Representation


1.1 Classical Petit Ensembles


1.2 Classical Grand Ensembles


1.3 Quantal Petit Ensembles


1.4 Quantal Grand Ensembles


1.5 Occupation-Number Representation

Chapter 2. The Green Function Method in Statistical Mechanics


2.1 The Double-Time Temperature-Dependent Green Functions


2.2 Simple Applications


2.3 The Heisenberg Ferromagnet


2.4 Ferromagnetic Resonance


2.5 Antiferromagnetics


2.6 The Paramagnetic Phase of a Heisenberg Ferromagnet


2.7 Lines' Approach to Green Function Decoupling

Chapter 3. The Pair Hamiltonian Model of an Imperfect Bose Gas


3.1 Introduction


3.2 A Green Function Solution of the Problem


3.3 Proof of the Asymptotic Exactness of the Solution


3.4 The Condition for Bose-Einstein Condensation


3.5 A Graphical Solution of the Problem


3.6 Luban's Solution of the Pair Hamiltonian Model


3.7 An Exact Solution of the Pair Hamiltonian Model

References

Appendix - The Bogolyubov Hamiltonian and Transformation

Chapter 4. Fluctuations in a Perfect Bose Gas


4.1 The Use of Gentile Statistics


4.2 Symmetry Breaking in the Ground State of a Bose Gas

Chapter 5. The Equation of State of an Imperfect Gas


5.1 A Hard-Sphere Gas with Attractive Forces


5.2 A One-Dimensional Model of a Van der Waals Gas

Chapter 6. A Simple Derivation of the Bloch Equation

Chapter 7. Statistical Mechanics of Stellar Systems


7.1 Introduction


7.2 The Relaxation Time of Stellar Systems


7.3 Landau Damping


7.4 Lynden-Bell Statistics


7.5 Gravitational Polarization

Chapter 8. Approach to Equilibrium


8.1 A Simple Model


8.2 Linear Response Theory

References

Index

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