Lectures on Selected Topics in Statistical Mechanics (eBook)

International Series in Natural Philosophy

D. ter Haar (Autor)

eBook Download: PDF

2013 | 1. Auflage
132 Seiten
Elsevier Science (Verlag)
978-1-4831-5077-2 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 3.9.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Sozialwissenschaften ► Politik / Verwaltung
• ISBN-10: 1-4831-5077-1 / 1483150771
• ISBN-13: 978-1-4831-5077-2 / 9781483150772