Lectures on Selected Topics in Statistical Mechanics - 1st Edition - ISBN: 9780080179377, 9781483150772

Lectures on Selected Topics in Statistical Mechanics

1st Edition

International Series in Natural Philosophy

Authors: D. Ter Haar
eBook ISBN: 9781483150772
Imprint: Pergamon
Published Date: 1st January 1977
Page Count: 132
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Lectures on Selected Topics in Statistical Mechanics is a collection of lectures given at the 1971 Simla Summer School of Statistical Mechanics held in India. The lectures explore a wide range of topics related to statistical mechanics, including occupation number representation; the Green function method; the pair Hamiltonian model of an imperfect Bose gas; fluctuations in a perfect Bose gas; and the equation of state of an imperfect gas. A simple derivation of the Bloch equation is also presented, along with the statistical mechanics of stellar systems.

Comprised of eight chapters, this volume begins with a discussion on the occupation number representation by considering some relevant formulae from ensemble theory. Classical petit and grand ensembles are described, together with quanta1 petit and grand ensembles. Subsequent chapters focus on the Green function method in statistical mechanics; the pair Hamiltonian model of the imperfect Bose gas and its solution in the absence of Bose-Einstein condensation using Green function methods and diagrammatic techniques; fluctuations in a perfect Bose gas; the equation of state of an imperfect gas; and a simple derivation of the Bloch equation. Finally, the statistical mechanics of stellar systems and an approach to equilibrium are described.

This book will be of interest to physicists.

Table of Contents


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


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



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About the Author

D. Ter Haar

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