Statistical mechanics made simple : a guide for students and researchers / Daniel C. Mattis.

Format:

Book

Author/Creator:

Mattis, Daniel Charles, 1932-

Language:

English

Subjects (All):

Statistical mechanics.

Physical Description:

xvi, 252 pages : illustrations ; 25 cm

Other Title:

Title appears on item as: Guide for students and researchers : Statistical mechanics made simple

Place of Publication:

River Edge, N.J. : World Scientific, [2003]

Summary:

This graduate textbook develops the rudiments of thermodynamics and statistical physics, then describes the quantum statistics of bosons and fermions, the kinetic theory of dilute gases, the transfer matrix applied to the two-dimensional Ising model, and a quantum field theory approach to diffusion-limited chemical reactions. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)

Contents:

Introduction: Theories of Thermodynamics, Kinetic Theory and Statistical Mechanics xiii

Chapter 1 Elementary Concepts in Statistics and Probability 1

1.1. The Binomial Distribution 1

1.2. Length of a Winning Streak 3

1.3. Brownian Motion and the Random Walk 4

1.4. Poisson versus Normal (Gaussian) Distributions 5

1.5. Central Limit Theorem (CLT) 9

1.6. Multinomial Distributions, Statistical Thermodynamics 12

1.7. The Barometer Equation 14

1.8. Other Distributions 14

Chapter 2 The Ising Model and the Lattice Gas 17

2.1. Some Background and Motivation 17

2.2. First-Principles Statistical Theory of Paramagnetism 18

2.3. More on Entropy and Energy 21

2.4. Some Other Relevant Thermodynamic Functions 21

2.5. Mean-Field Theory, Stable and Metastable Solutions 23

2.6. The Lattice Gas 26

2.7. The Nearest-Neighbor Chain: Thermodynamics in 1D 26

2.8. The Disordered Ising Chain 28

2.9. Other Magnetic Systems in One Dimension 28

Chapter 3 Elements of Thermodynamics 31

3.1. The Scope of Thermodynamics 31

3.2. Equations of State and Some Definitions 32

3.3. Maxwell Relations 35

3.4. Three Important Laws of Thermodynamics 35

3.5. The Second Derivatives of the Free Energy 38

3.6. Phase Diagrams for the van der Waals Gas 39

3.7. Clausius-Clapeyron Equation 43

3.8. Phase Transitions 46

3.9. The Carnot Cycle 49

3.10. Superconductivity 51

Chapter 4 Statistical Mechanics 55

4.1. The Formalism

and a False Start 55

4.2. Gibbs' Paradox and Its Remedy 58

4.3. The Gibbs Factor 59

4.4. The Grand Ensemble 60

4.5. Non-Ideal Gas and the 2-Body Correlation Function 62

4.6. The Virial Equation of State 64

4.7. Weakly Non-Ideal Gas 65

4.8. Two-body Correlations 68

4.9. Configurational Partition Function in 1D 73

4.10. One Dimension versus Two 75

4.11. Two Dimensions versus Three: The Debye-Waller Factors 77

Chapter 5 The World of Bosons 83

5.1. Two Types of Bosons and Their Operators 83

5.2. Number Representation and the Many-Body Problem 86

5.3. The Adiabatic Process and Conservation of Entropy 88

5.4. Many-Body Perturbations 89

5.5. Photons 90

5.6. Phonons 93

5.7. Ferromagnons 96

5.8. Conserved Bosons and the Ideal Bose Gas 99

5.9. Nature of "Ideal" Bose-Einstein Condensation 101

5.10. Ideal Bose-Einstein Condensation in Low Dimensions 104

5.11. Consequences of a Hard Core Repulsion in 1D 106

5.12. Bosons in 3D Subject to Weak Two-Body Forces 109

5.13. Superfluid Helium (He II) 114

Chapter 6 All About Fermions: Theories of Metals, Superconductors, Semiconductors 119

6.1. Fermi-Dirac Particles 119

6.2. Slater Determinant: The Ground State 120

6.3. Ideal Fermi-Dirac Gas 121

6.4. Ideal Fermi-Dirac Gas with Spin 123

6.5. Fermi Integrals 124

6.6. Thermodynamic Functions of an Ideal Metal 125

6.7. Quasiparticles and Elementary Excitations 128

6.8. Semiconductor Physics: Electrons and Holes 130

6.9. n-Type Semiconductor Physics: The Statistics 131

6.10. Correlations and the Coulomb Repulsion 132

6.11. Miscellaneous Properties of Semiconductors 135

6.12. Aspects of Superconductivity: Cooper Pairs 137

6.13. Aspects of BCS Theory 140

6.14. Contemporary Developments in Superconductivity 146

Chapter 7 Kinetic Theory 149

7.2. Quasi-Equilibrium Flows and the Second Law 150

7.3. The Collision Integral 151

7.4. Approach to Equilibrium of a "Classical" Non-Ideal Gas 154

7.5. A New Look at "Quantum Statistics" 156

7.6. Master Equation: Application to Radioactive Decay 158

7.7. Boltzmann Equation 160

7.8. Electrical Currents in a Low-Density Electron Gas 162

7.9. Diffusion and the Einstein Relation 165

7.10. Electrical Conductivity of Metals 165

7.11. Exactly Solved "Backscattering" Model 166

7.12. Electron-Phonon Scattering 169

7.13. Approximating the Boltzmann Equation 170

7.14. Crossed Electric and Magnetic Fields 171

7.15. Propagation of Sound Waves in Fluids 173

7.16. The Calculations and Their Result 178

Chapter 8 The Transfer Matrix 183

8.1. The Transfer Matrix and the Thermal Zipper 183

8.2. Opening and Closing a "Zipper Ladder" or Polymer 186

8.3. The Full Zipper (N [greater than sign] 2) 190

8.4. The Transfer Matrix and Gaussian Potentials 191

8.5. Transfer Matrix in the Ising Model 192

8.6. The Ising Ladder or Polymer 195

8.7. Ising Model on the Isotropic Square Lattice (2D) 196

8.8. The Phase Transition 201

8.9. A Question of Long-Range Order 202

8.10. Ising Model in 2D and 3D 204

8.11. Antiferromagnetism and Frustration 206

8.12. Maximal Frustration 208

8.13. Separable Model Spin-Glass without Frustration 210

8.14. Critical Phenomena and Critical Exponents 212

8.15. Potts Models 215

Chapter 9 Some Uses of Quantum Field Theory in Statistical Physics 219

9.1. Outline of the Chapter 219

9.2. Diffusion on a Lattice: Standard Formulation 219

9.3. Diffusion as Expressed in QFT 222

9.4. Diffusion plus One-Body Recombination Processes 225

9.5. Diffusion and Two-Body Recombination Processes 226

9.6. Questions Concerning Long-Range Order 228

9.7. Mermin-Wagner Theorem 230

9.8. Proof of Bogolubov Inequality 233

9.9. Correlation Functions and the Free Energy 234

9.10. Introduction to Thermodynamic Green's Functions 237.

Notes:

Includes bibliographical references and index.

ISBN:

9812381651

981238166X

OCLC:

51586651