Statistical Mechanics

Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.

Kerson Huang is Professor of Physics at the Massachusetts Institute of Technology, Cambridge, USA, and a leading authority on quantum physics. He is a highly experienced textbook writer and has written Statistical Mechanics, also published by Wiley. Professor Huang?s research interests focus on Bose-Einstein condensates and non-renormalizable theories.

PART A THERMODYNAMICS AND KINETIC THEORY

1

(124)

The Laws of Thermodynamics

3

(28)

Preliminaries

3

(4)

The First Law of Thermodynamics

7

(2)

The Second Law of Thermodynamics

9

(5)

Entroy

14

(5)

Some Immediate Consequences of the Second Law

19

(3)

Thermodynamic Potentials

22

(3)

The Third Law of Thermodynamics

25

(6)

Some Applications of Thermodynamics

31

(21)

Thermodynamic Description of Phase Transitions

31

(4)

Surface Effects in Condensation

35

(3)

Van der Waals Equation of State

38

(5)

Osmotic Pressure

43

(5)

The Limit of Thermodynamics

48

(4)

The Problem of Kinetic Theory

52

(21)

Formulation of the Problem

52

(4)

Binary Collisions

56

(4)

The Boltzmann Transport Equation

60

(2)

The Gibbsian Ensemble

62

(3)

The BBGKY Hierarchy

65

(8)

The Equilibrium state of a Dilute Gas

73

(20)

Boltzmann's H Theorem

73

(2)

The Maxwell-Boltzmann Distribution

75

(4)

The Method of the Most Probable Distribution

79

(6)

Analysis of the H Theorem

85

(5)

The Poincare Cycle

90

(3)

Transport Phenomena

93

(32)

The Mean Free Path

93

(2)

Effusion

95

(1)

The Conservation Laws

96

(4)

The Zero-Order Approximation

100

(4)

The First-Order Approximation

104

(4)

Viscosity

108

(3)

Viscous Hydrodynamics

111

(2)

The Navier-Stokes Equation

113

(4)

Example in Hydrodynamics

117

(8)

PART B STATISTICAL MECHANICS

125

(180)

Classical Statistical Mechanics

127

(16)

The Postulate of Classical Statistical Mechanics

127

(3)

Microcanonical Ensemble

130

(5)

Derivationi of Thermodynamics

135

(1)

Equipartition Theorem

136

(2)

Classical Ideal Gas

138

(2)

Gibbs Paradox

140

(3)

Canonical Ensemble and Grand Canonical Ensemble

143

(28)

Canonical Ensemble

143

(2)

Energy Fluctuations in the Canonical Ensemble

145

(4)

Grand Canonical Ensemble

149

(3)

Density Fluctuations in the Grand Canonical Ensemble

152

(2)

The Chemical Potential

154

(3)

Equivalence of the Canonical Ensemble and the Grand Canonical Ensemble

157

(4)

Behavior of W(N)

161

(2)

The Meaning of the Maxwell Construction

163

(8)

Quantum statistical mechanics

171

(22)

The Postulates of Quantum Statistical Mechanics

171

(3)

Density Matrix

174

(2)

Ensembles in Quantum Statistical Mechanics

176

(2)

The Third Law of Thermodynamics

178

(1)

The Ideal Gases: Microcanonical Ensemble

179

(6)

The Ideal Gases: Grand Canonical Ensemble

185

(4)

Foundations of Statistical Mechanics

189

(4)

General Properties of the Partition Function

193

(20)

The Darwin-Fowler Method

193

(6)

Classical Limit of the Partition Function

199

(7)

Singularities and Phase Transitions

206

(4)

The Lee-Yang Circle Theorem

210

(3)

Approximate Methods

213

(28)

Classical Cluster Expansion

213

(7)

Quantum Cluster Expansion

220

(4)

The Second Virial Coefficient

224

(4)

Variational Principles

228

(2)

Imperfect Gases at Low Temperatures

230

(11)

Fermi Systems

241

(37)

The Equation of State of an Ideal Fermi Gas

241

(6)

The Theory of White Dwarf Stars

247

(6)

Landau Diamagnetism

253

(7)

The De Haas-Van Alphen Effect

260

(1)

The Quantized Hall Effect

261

(6)

Pauli Paramagnetism

267

(5)

Magnetic Properties of an Imperfect Gas

272

(6)

Bose Systems

278

(27)

Photons

278

(5)

Phonons in Solids

283

(3)

Bose-Einnstein Condensation

286

(8)

An Imperfect Bose Gas

294

(4)

The Superfluid Order Parameter

298

(7)

PART C SPECIAL TOPICS IN STATISTICAL MECHANICS

305

(163)

Superfluids

307

(34)

Liquid Helium

307

(4)

Tisza's Two-Fluid Model

311

(2)

The Bose-Einstein Condensate

313

(2)

Landau's Theory

315

(2)

Superfluid Velocity

317

(4)

Superfluid Flow

321

(4)

The Phonon Wave Function

325

(4)

Dilute Bose Gas

329

(12)

The Ising Model

341

(27)

Definition of the Ising Model

341

(3)

Equivalence of the Ising Model to Other Models

344

(4)

Spontaneous Magnetization

348

(4)

The Bragg-Williams Approximation

352

(5)

The Bethe-Peierls Approximation

357

(4)

The One-Dimensional Ising Model

361

(7)

The Onsager Solution

368

(24)

Formulation of the Two-Dimensional Ising Model

368

(6)

Mathematical Digression

374

(4)

The Solution

378

(14)

Critical Phenomena

392

(24)

The Order Parameter

392

(2)

The Correlation Function and the Fluctuation-Dissipation Theorem

394

(2)

Critical Exponents

396

(3)

The Scaling Hypothesis

399

(4)

Scale Invariance

403

(3)

Goldstone Excitations

406

(1)

The Importance of Dimensionality

407

(9)

The Landau Approach

416

(25)

The Landau Free Energy

416

(2)

Mathematical Digression

418

(2)

Derivation in Simple Models

420

(2)

Mean-Field Theory

422

(4)

The Van der Waals Equation of State

426

(2)

The Tricritical Point

428

(6)

The Gaussian Model

434

(3)

The Ginzburg Criterion

437

(1)

Anomalous Dimensions

438

(3)

Renoremalization Group

441

(27)

Block Spins

441

(2)

The One-Dimensional Ising Model

443

(3)

Renormalization-Group Transformation

446

(3)

Fixed Points and Scaling Fields

449

(3)

Momentum-Space Formulation

452

(3)

The Gaussian Model

455

(3)

The Landau-Wilson Model

458

(10)

APPENDIX N-BODY SYSTEM OF IDENTICAL PARTICLES

468

(19)

A.1 The Two Kinds of Statistics

468

(2)

A.2 N-Body Wave Functions

470

(7)

A.3 Method of Quantized Fields

477

(7)

A.4 Longitudinal Sum Rules

484

(3)

Index

487

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Statistical Mechanics

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Author Biography

Table of Contents

Supplemental Materials