Ter Haar Lectures on Selected Topics in Statistical Mechanics

International Series in Natural Philosophy
1. Auflage 2013
ISBN: 978-1-4831-5077-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 132 Seiten, Web PDF

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.

Autoren/Hrsg.

Ter Haar, D.

Inhaltsverzeichnis

1;Front Cover;1
2;Lectures on Selected Topics in Statistical Mechanics;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. THE OCCUPATION NUMBER REPRESENTATION;10
6.1;1.1 Classical Petit Ensembles;10
6.2;1.2 Classical Grand Ensembles;12
6.3;1.3 Quantal Petit Ensembles;13
6.4;1.4 Quantal Grand Ensembles;13
6.5;1.5 Occupation-number Representation;14
7;CHAPTER 2. THE GREEN FUNCTION METHOD IN STATISTICAL MECHANICS;18
7.1;2.1 The Double-time Temperature-dependent Green Functions;18
7.2;2.2 Simple Applications;21
7.3;2.3 The Heisenberg Ferromagnet;25
7.4;2.4 Ferromagnetic Eesonance;30
7.5;2.5 Antiferromagnetics;33
7.6;2.6 The Paramagnetic Phase of a Heisenberg Ferromagnet;35
7.7;2.7 Lines' Approach to Green Function Decoupling;43
8;CHAPTER 3. THE PAIR HAMILTONIAN MODEL OF AN IMPERFECT BOSE GAS;46
8.1;3.1 Introduction;46
8.2;3.2 A Green Function Solution of the Problem;47
8.3;3.3 Proof of the Asymptotic Exactness of the Solution;51
8.4;3.4 The Condition for Bose-Einstein Condensation;54
8.5;3.5 A Graphical Solution of the Problem;55
8.6;3.6 Luban's Solution of the Pair Hamiltonian Model;59
8.7;3.7 An Exact Solution of the Pair Hamiltonian Model;60
8.8;Eeferences;64
8.9;Appendix- The Bogolyubov Hamiltonian and Transformation;64
9;CHAPTER 4. FLUCTUATIONS IN A PERFECT BOSE GAS;66
9.1;4.1 The Use of Gentile Statistics;66
9.2;4.2 Symmetry Breaking in the Ground State of a Bose Gas;73
10;CHAPTER 5. THE EQUATION OF STATE OF AN IMPERFECT GAS;80
10.1;5.1 A Hard-sphere Gas with Attractive Forces;80
10.2;5.2 A One-Dimensional Model of a van der Waals Gas;89
11;CHAPTER 6. A SIMPLE DERIVATION OF THE BLOCH EQUATION;100
12;CHAPTER 7. STATISTICAL MECHANICS OF STELLAR SYSTEMS;106
12.1;7.1 Introduction;106
12.2;7.2 The Relaxation Time of Stellar Systems;108
12.3;7.3 Landau Damping;112
12.4;7.4 Lynden-Bell Statistics;114
12.5;7.5 Gravitational Polarization;116
13;CHAPTER 8. APPROACH TO EQUILIBRIUM;120
13.1;8.1 A Simple Model;120
13.2;8.2 Linear Response Theory;123
14;REFERENCES;128
15;INDEX;132
16;OTHER TITLES IN THE SERIES IN
NATURAL PHILOSOPHY;133