粒子的统计物理学

Preface

1 Thermodynamics

1.1 Introduction

1.2 The zeroth law

1.3 The first law

1.4 The second law

1.5 Carnot engines

1.6 Entropy

1.7 Approach to equilibrium and thermodynamic potentials

1.8 Useful mathematical results

1.9 Stability conditions

1.10 The third law

Problems

2 Probability

2.1 General definitions

2.2 One random variable

2.3 Some important probability distributions

2.4 Many random variables

2.5 Sums of random variables and the central limit theorem

2.6 Rules for large numbers

2.7 Information, entropy, and estimation

Problems

3 Kinetic theory of gases

3.1 General definitions

3.2 Liouvilles theorem

3.3 The Bogoliubov-Born--Green-Kirkwood-Yvon hierarchy

3.4 The Boltzmann equation

3.5 The H-theorem and irreversibility

3.6 Equilibrium properties

3.7 Conservation laws

3.8 Zeroth-order hydrodynamics

3.9 First-order hydrodynamics

Problems

4 Classical statistical mechanics

4.1 General definitions

4.2 The microcanonical ensemble

4.3 Two-level systems

4.4 The ideal gas

4.5 Mixing entropy and the Gibbs paradox

4.6 The canonical ensemble

4.7 Canonical examples

4.8 The Gibbs canonical ensemble

4.9 The grand canonical ensemble

Problems

5 Intenmeting particles

5.1 The cumulant expansion

5.2 The cluster expansion

5.3 The second virial coefficient and van der Waals equation

5.4 Breakdown of the van der Waals equation

5.5 Mean-field theory of condensation

5.6 Variational methods

5.7 Corresponding states

5.8 Critical point behavior

Problems

6 Quantum statistical mechanics

6.1 Dilute polyatomic gases

6.2 Vibrations of a solid

6.3 Black-body radiation

6.4 Quantum microstates

6.5 Quantum macrostates

Problems

7 Ideal quantum gases

7.1 Hilbert space of identical particles

7.2 Canonical formulation

7.3 Grand canonical formulation

7.4 Non-relativistic gas

7.5 The degenerate fermi gas

7.6 The degenerate bose gas

7.7 Superfiuid Hen

Problems

Solutions to selected problems

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Index

统计物理是利用物质基本组成成份来研究物质的整体性质，它在量子力学发展中发挥了重要的作用。本书根据作者20多年来在麻省理工学院讲授粒子统计物理的课程讲义编写而成，主要讲解统计物理学的基本概念和处理实际问题的方法。在讲述完热力学基础后，作者专门讲解了常用数学工具如概率论和中心极限定理。本书内容还包括相互作用粒子，van der Waals方程及其推导，经典和量子统计力学以及信息论中的相关问题。本书附有习题，并在全书结尾处给出部分答案。阅读本书时可以参考作者的另外一本专著《场的统计物理》，主要介绍利用重整化群等非平均场方法研究标度律和临界现象。目次：热力学；概率论；气体动力学理论；经典统计力学；相互作用的粒子；量子统计力学；理想量子气体；部分习题解答；索引。