Lectures on Selected Topics in Statistical Mechanics

Lectures on Selected Topics in Statistical Mechanics

International Series in Natural Philosophy

First published on January 1, 1977

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  • eBook ISBN: 9781483150772

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Description

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


  • 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

    Other Titles in the Series

Product details

  • No. of pages: 132
  • Language: English
  • Copyright: © Pergamon 1977
  • Published: January 1, 1977
  • Imprint: Pergamon
  • eBook ISBN: 9781483150772

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