統計力學論題 （英文影印版）

《統計力學論題 （英文影印版）》是2006年11月出版的圖書，作者是Brian Cowan。

基本介紹

• 書名：統計力學論題 （英文影印版）
• 作者：[英]Brian Cowan
• 出版社：復旦大學出版社
• 出版時間：2006年11月
• 頁數：338 頁
• 定價：35 元
• 開本：32 開
• 裝幀：平裝
• ISBN：7309052013 

圖書目錄

Contents

Preface

1 The Methodology of Statistical Mechanics

1.1 Terminology and Methodology

1.1.1 Approaches to the subject

1.1.2 Description of states

1.1.3 Extensivity and the thermodynamic limit

1.2 The Fundamental Principles

1.2.1 The laws of thermodynamics

1.2.2 Probabilistic interpretation of the First Law

1.2.3 Microscopic basis for entropy

1.3 Interactions —The Conditions for Equilibrium

1.3.1 Thermal interaction—Temperature

1.3.2 Volume change—Pressure

1.3.3 Particle interchange—Chemical potential

1.3.4 Thermal interaction with the rest of the world—The Boltzmann factor

1.3.5 Particle and energy exchange with the rest of the world —The Gibbs factor

1.4 Thermodynamic Averages

1.4.1 The partition function

1.4.2 Generalised expression for entropy

1.4.3 Free energy

1.4.4 Thermodynamic variables

1.4.5 Fluctuations

1.4.6 The grand partition function

1.4.7 The grand potential

1.4.8 Thermodynamic variables

1.5 Quantum Distributions

1.5.1 Bosons and fermions

1.5.2 Grand potential for identical particles

1.5.3 The Fermi distribution

1.5.4 The Bose distribution

1.5.5 The classical limit—The Maxwell distributior

1.6 Classical Statistical Mechanics

1.6.1 Phase space and classical states

1.6.2 Boltzmann and Gibbs phase spaces

1.6.3 The Fundamental Postulate in the classical case

1.6.4 The classical partition function

1.6.5 The equipartition theorem

1.6.6 Consequences of equipartition

1.6.7 Liouville's theorem

1.6.8 Boltzmann's H theorem

1.7 The Third Law of Thermodynamics

1.7.1 History of the Third Law

1.7.2 Entropy

1.7.3 Quantum viewpoint

1.7.4 Unattainability of absolute zero

1.7.5 Heat capacity at low temperatures

1.7.6 Other consequences of the Third Law

1.7.7 Pessimist's statement of the laws of thermodynamics

2 Practical Calculations with Ideal Systems

2.1 The Density of States

2.1.1 Non-interacting systems

2.1.2 Converting sums to integrals

2.1.3 Enumeration of states

2.1.4 Counting states

2.1.5 General expression for the density of states

2.1.6 General relation between pressure and energy

2.2 Identical Particles

2.2.1 Indistinguishability

2.2.2 Classical approximation

2.3 Ideal Classical Gas

2.3.1 Quantum approach

2.3.2 Classical approach

2.3.3 Thermodynamic properties

2.3.4 The l/N! term in the partition function

2.3.5 Entropy of mixing

2.4 Ideal Fermi Gas

2.4.0 Methodology for quantum gases

2.4.1 Fermi gas at zero temperature

2.4.2 Fermi gas at low temperatures—simple model

2.4.3 Fermi gas at low temperatures—series expansion

Chemical potential

Internal energy

Thermal capacity

2.4.4 More general treatment of low temperature heat capacity

2.4.5 High temperature behaviour—the classical limit

2.5 Ideal Bose Gas

2.5.1 General procedure for treating the Bose gas

2.5.2 Number of particles—chemical potential

2.5.3 Low temperature behaviour of Bose gas

2.5.4 Thermal capacity of Bose gas—below Tc

2.5.5 Comparison with superfluid4 He and other systems

2.5.6 Two-fluid model of superfluid 4He

2.5.7 Elementary excitations

2.6 Black Body Radiation—The Photon Gas

2.6.1 Photons as quantised electromagnetic waves

2.6.2 Photons in thermal equilibrium—black body radiation

2.6.3 Planck's formula

2.6.4 Internal energy and heat capacity

2.6.5 Black body radiation in one dimension

2.7 Ideal Paramagnet

2.7.1 Partition function and free energy

2.7.2 Thermodynamic properties

2.7.3 Negative temperatures

2.7.4 Thermodynamics of negative temperatures

3 Non-Ideal Gases

3.1 Statistical Mechanics

3.1.1 The partition function

3.1.2 Cluster expansion

3.1.3 Low density approximation

3.1.4 Equation of state

3.2 The Virial Expansion

3.2.1 Virial coefficients

3.2.2 Hard core potential

3.2.3 Square-well potential

3.2.4 Lennard-Jones potential

3.2.5 Second virial coefficient for Bose and Fermi gas

3.3 Thermodynamics

3.3.1 Throttling

3.3.2 Joule-Thomson coefficient

3.3.3 Connection with the second virial coefficient..

3.3.4 Inversion temperature

3.4 Van der Waals Equation of State

3.4.1 Approximating the partition function

3.4.2 Van der Waals equation

3.4.3 Microscopic "derivation" of parameters

3.4.4 Virial expansion

3.5 Other Phenomenological Equations of State

3.5.1 The Dieterici equation

3.5.2 Virial expansion

3.5.3 The Berthelot equation

4 Phase Transitions

4.1 Phenomenology

4.1.1 Basic ideas

4.1.2 Phase diagrams

4.1.3 Symmetry

4.1.4 Order of phase transitions

4.1.5 The order parameter

4.1.6 Conserved and non-conserved order parameters

4.1.7 Critical exponents

4.1.8 Scaling theory

4.1.9 Scaling of the free energy

4.2 First-Order Transition—An Example

4.2.1 Coexistence

4.2.2 Van der Waals fluid

4.2.3 The Maxwell construction

4.2.4 The critical point

4.2.5 Corresponding states

4.2.6 Dieterici's equation

4.2.7 Quantum mechanical effects

4.3 Second-Order Transition—An Example

4.3.1 The ferromagnet

4.3.2 The Weiss model

4.3.3 Spontaneous magnetisation

4.3.4 Critical behaviour

4.3.5 Magnetic susceptibility

4.3.6 Goldstone modes

4.4 The Ising and Other Models

4.4.1 Ubiquity of the Ising model

4.4.2 Magnetic case of the Ising model

4.4.3 Ising model in one dimension

4.4.4 Ising model in two dimensions

4.4.5 Mean field critical exponents

4.4.6 The XY model

4.4.7 The spherical model

4.5 Landau Treatment of Phase Transitions

4.5.1 Landau free energy

4.5.2 Landau free energy for the ferromagnet

4.5.3 Landau theory—second-order transitions

4.5.4 Thermal capacity in the Landau model

4.5.5 Ferromagnet in a magnetic field

4.6 Ferroelectricity

4.6.1 Description of the phenomenon

4.6.2 Landau free energy

4.6.3 Second-order case

4.6.4 First-order case

4.6.5 Entropy and latent heat at the transition

4.6.6 Soft modes

4.7 Binary Mixtures

4.7.1 Basic ideas

4.7.2 Model calculation

4.7.3 System energy

4.7.4 Entropy

4.7.5 Free energy

4.7.6 Phase separation—the lever rule

4.7.7 Phase separation curve—the binodal

4.7.8 The spinodal curve

4.7.9 Entropy in the ordered phase

4.7.10 Thermal capacity in the ordered phase

4.7.11 Order of the transition and the critical point

4.7.12 The critical exponent β

4.8 Quantum Phase Transitions

4.8.1 Introduction

4.8.2 The transverse Ising model

4.8.3 Revision of mean field Ising model

4.8.4 Application of a transverse field

4.8.5 Transition temperature

4.8.6 Quantum critical behaviour

4.8.7 Dimensionality and critical exponents

4.9 Retrospective

4.9.1 The existence of order

4.9.2 Validity of mean field theory

4.9.3 Features of different phase transition models

5 Fluctuations and Dynamics

5.1 Fluctuations

5.1.1 Probability distribution functions

5.1.2 Mean behaviour of fluctuations

5.1.3 The autocorrelation function

5.1.4 The correlation time

5.2 Brownian Motion

5.2.1 Kinematics of a Brownian particle

5.2.2 Short time limit

5.2.3 Long time limit

5.3 Langevin's Equation

5.3.1 Introduction

5.3.2 Separation of forces

5.3.3 The Langevin equation

5.3.4 Mean square velocity and equipartition

5.3.5 Velocity autocorrelation function

5.3.6 Electrical analogue of the Langevin equation

5.4 Linear Response—Phenomenology

5.4.1 Definitions

5.4.2 Response to a sinusoidal excitation

5.4.3 Fourier representation

5.4.4 Response to a step excitation

5.4.5 Response to a delta function excitation

5.4.6 Consequence of the reality of X(t)

5.4.7 Consequence of causality

5.4.8 Energy considerations

5.4.9 Static susceptibility

5.4.10 Relaxation time approximation

5.5 Linear Response—Microscopics

5.5.1 Onsager's hypothesis

5.5.2 Nyquist's theorem

5.5.3 Calculation of the step response function

5.5.4 Calculation of the autocorrelation function

Appendixes

Appendix I The Gibbs-Duhem Relation

A.1.1 Homogeneity of the fundamental relation

A.1.2 The Euler relation

A.1.3 A caveat

A.1.4 The Gibbs-Duhem relation

Appendix 2 Thermodynamic Potentials

A.2.1 Equilibrium states

A.2.2 Constant temperature (and volume): the Helmholtz potential

A.2.3 Constant pressure and energy: the Enthalpy function

A.2.4 Constant pressure and temperature: the Gibbs free energy

A.2.5 Differential expressions for the potentials

A.2.6 Natural variables and the Maxwell relations

Appendix 3 Mathematica Notebooks

A.3.1 Chemical potential of Fermi gas at low temperatures

A.3.2 Internal energy of the Fermi gas at low temperatures

A.3.3 Fugacity of the ideal gas at high temperatures—Fermi, Maxwell and Bose cases

A.3.4 Internal energy of the ideal gas at high temperatures—Fermi, Maxwell and Bose cases

Appendix 4 Evaluation of the Correlation Function Integral

A.4.1 Initial domain of integration

A.4.2 Transformation of variables

A.4.3 Jacobian of the transformation

Index

內容提要

全書用一種統一的觀點處理熱力學和統計物理論題。第一、第二章分別講述統計力學的方法論和理想體系的實際計算。其中差不多有一半內容屬於本科期間已有的基礎知識，但採用更高的、完全用統一的觀點，看待熱力學和統計力學。第三章非理想氣體，重點講述維里展開、配分函式、節流和狀態方程。第四章相變，介紹相圖、對稱性、序參量、臨界指數、標度理論、一級相變、二級相變、伊辛模型、朗道理論、鐵電體、二元混合物、量子相變、平均場理論等等。這是全書的重點。第五章講述漲落和動力學行為，重點是漲落的關聯特性、布朗運動、朗之萬方程和線性回響理論。