Page 8 - STATISTICAL MECHANICS: From First Principles to Macroscopic Phenomena

vi Contents

Part II States of matter in equilibrium statistical physics 57
5 Perfect gases 59
Classical perfect gas 60
Molecular ideal gas 62
Quantum perfect gases: general features 69
Quantum perfect gases: details for special cases 71
Perfect Bose gas at low temperatures 74
Perfect Fermi gas at low temperatures 78
References 81
Problems 81
6 Imperfect gases 85
Method I for the classical virial expansion 86
Method II for the virial expansion: irreducible linked clusters 95
Application of cumulants to the expansion of the free energy 102
Cluster expansion for a quantum imperfect gas (extension of
method I) 108
Gross–Pitaevskii–Bogoliubov theory of the low temperature weakly
interacting Bose gas 115
References 122
Problems 122
7 Statistical mechanics of liquids 125
Definitions of n-particle distribution functions 126
Determination of g(r) by neutron and x-ray scattering 128
BBGKY hierarchy 133
Approximate closed form equations for g( r) 135
Molecular dynamics evaluation of liquid properties 136
References 143
Problems 144
8 Quantum liquids and solids 145
Fundamental postulates of Fermi liquid theory 146
Models of magnets 150
Physical basis for models of magnetic insulators: exchange 150
Comparison of Ising and liquid–gas systems 153
Exact solution of the paramagnetic problem 153
High temperature series for the Ising model 154
Transfer matrix 157
Monte Carlo methods 158
References 159
Problems 160