# Statistical Mechanics, 2ed, (An Indian Adaptation)

ISBN: 9789354247736

576 pages

## Description

Statistical Mechanics by Kerson Huang is a comprehensive textbook on the framework of statistical mechanics, in which the macroscopic thermodynamic behavior of complex systems is explained by the application of probability and statistics to the dynamics of their microscopic constituents. The book is directed mainly at advanced undergraduate physics majors, graduate students in physics, as well as researchers in the field. This adaptation of the second edition of the textbook is a revision that has been developed from detailed feedback obtained from long-standing users in India.

Part A Thermodynamics and Kinetic Theory

Chapter 1 Review of The Laws of Thermodynamics

1.1 Preliminaries

1.2 The First Law of Thermodynamics

1.3 The Second Law of Thermodynamics

1.4 Entropy

1.5 Some Immediate Consequences of the Second Law

1.6 Thermodynamic Potentials

1.7 The Third Law of Thermodynamics

1.8 Worked Problems

Chapter 2 Some Applications of Thermodynamics

2.1 Thermodynamic Description of Phase Transitions

2.2 Surface Effects in Condensation

2.3 Van Der Waals Equation of State

2.4 Osmotic Pressure

2.5 The Limit of Thermodynamics

2.6 Worked Problems

Chapter 3 The Problem of Kinetic Theory

3.1 Formulation of the Problem

3.2 Binary Collisions

3.3 The Boltzmann Transport Equation

3.4 The Gibbsian Ensemble

3.5 Worked Problems

Chapter 4 The Equilibrium State of A Dilute Gas

4.1 Boltzmann’s H Theorem

4.2 The Maxwell-Boltzmann Distribution

4.3 The Method of the Most Probable Distribution

4.4 Analysis of the H Theorem

4.5 The Poincaré Cycle

4.6 Worked Problems

Chapter 5 Transport Phenomena

5.1 The Mean Free Path

5.2 Effusion

5.3 The Conservation Laws

5.4 Viscosity

5.5 Viscous Hydrodynamics

5.6 The Navier-Stokes Equation

5.7 Examples in Hydrodynamics

5.8 Worked Problems

Part B Statistical Mechanics

Chapter 6 Classical Statistical Mechanics

6.1 The Postulate of Classical Statistical Mechanics

6.2 Microcanonical Ensemble

6.3 Derivation of Thermodynamics

6.4 Equipartition Theorem

6.5 Classical Ideal Gas

6.6 Gibbs Paradox

6.7 Worked Problems

Chapter 7 Canonical Ensemble and Grand Canonical Ensemble

7.1 Canonical Ensemble

7.2 Classical Ideal Gas in the Canonical Ensemble

7.3 Energy Fluctuations in the Canonical Ensemble

7.4 Grand Canonical Ensemble

7.5 Density Fluctuations in the Grand Canonical Ensemble

7.6 The Chemical Potential

7.7 Equivalence of the Canonical Ensemble and the Grand Canonical Ensemble

7.8 Behavior of W (N)

7.9 Worked Problems

Chapter 8 Quantum Statistical Mechanics

8.1 The Postulates of Quantum Statistical Mechanics

8.2 Density Matrix

8.3 Ensembles in Quantum Statistical Mechanics

8.4 Third Law of Thermodynamics

8.5 The Ideal Gases: Microcanonical Ensemble

8.6 The Ideal Gases: Grand Canonical Ensemble

8.7 Foundations of Statistical Mechanics

8.8 Density of States

8.9 Worked Problems

Chapter 9 Fermi Systems

9.1 The Equation of State of an Ideal Fermi Gas

9.2 The Theory of White Dwarf Stars

9.3 Landau Diamagnetism

9.4 The De Haas-Van Alphen Effect

9.5 The Quantized Hall Effect

9.6 Pauli Paramagnetism

9.7 Magnetic Properties of an Imperfect Gas

9.8 Worked Problems

Chapter 10 Bose Systems

10.1 Photons

10.2 Phonons in Solids

10.3 Bose-Einstein Condensation

10.4 An Imperfect Bose Gas

10.5 The Superfluid Order Parameter

10.6 Worked Problems

Part C Special Topics in Statistical Mechanics

Chapter 11 Superfluids

11.1 Liquid Helium

11.2 Tisza’s Two-Fluid Model

11.3 The Bose-Einstein Condensate

11.4 Landau’s Theory

11.5 Superfluid Velocity

11.6 Superfluid Flow

11.7 The Phonon Wave Function

11.8 Dilute Bose Gas

11.9 Worked Problems

Chapter 12 The Ising Model

12.1 Definition of the Ising Model

12.2 Equivalence of the Ising Model to other Models

12.3 Spontaneous Magnetization

12.4 The Bragg-Williams Approximation

12.5 The Bethe-Peierls Approximation

12.6 The One-Dimensional Ising Model

12.7 Worked Problems

Chapter 13 The Onsager Solution

13.1 Formulation of the Two-Dimensional Ising Model

13.2 Mathematical Digression

13.3 The Solution

13.4 Worked Problem

Chapter 14 Critical Phenomena

14.1 The Order Parameter

14.2 The Correlation Function and the Fluctuation-Dissipation Theorem

14.3 Critical Exponents

14.4 The Scaling Hypothesis

14.5 Scale Invariance

14.6 Goldstone Excitations

14.7 The Importance of Dimensionality

14.8 Worked Problems

Chapter 15 The Landau Approach

15.1 The Landau Free Energy

15.2 Mathematical Digression

15.3 Derivation in Simple Models

15.4 Mean-Field Theory

15.5 The Van Der Waals Equation of State

15.6 The Tricritical Point

15.7 The Gaussian Model

15.8 The Ginzburg Criterion

15.9 Anomalous Dimensions

15.10 Worked Problems

Chapter 16 Renormalization Group

16.1 Block Spins

16.2 The One-Dimensional Ising Model

16.3 Renormalization-Group Transformation

16.4 Fixed Points and Scaling Fields

16.5 Momentum-Space Formulation

16.6 The Gaussian Model

16.7 The Landau-Wilson Model

16.8 Worked Problems

Appendix A General Properties of The Partition Function

A.1 The Darwin-Fowler Method

A.2 Classical Limit of the Partition Function

A.3 Singularities and Phase Transitions

A.4 The Lee-Yang Circle Theorem

Appendix B Approximate Methods

B.1 Classical Cluster Expansion

B.2 Quantum Cluster Expansion

B.3 The Second Virial Coefficient

B.4 Variational Principles

Appendix C N-Body System of Identical Particles

C.1 The Two Kinds of Statistics

C.2 N-Body Wave Functions

C.3 Method of Quantized Fields

C.4 Longitudinal Sum Rules

Appendix D Monte Carlo Simulations

D.1 Introduction to Monte Carlo Methods

D.2 Metropolis Algorithm for the Ising Model

D.3 Metropolis Algorithm for Bose-Einstein Condensation

Answer of MCQS

Index