Classical and Quantum Statistical Physics: Fundamentals and Advanced Topics

✍ Scribed by Carlo Heissenberg, Augusto Sagnotti

• Publisher: Cambridge University Press
• Year: 2022
• Tongue: English
• Leaves: 383
• Edition: New
• Category: Library

✦ Synopsis

Statistical physics examines the collective properties of large ensembles of particles, and is a powerful theoretical tool with important applications across many different scientific disciplines. This book provides a detailed introduction to classical and quantum statistical physics, including links to topics at the frontiers of current research. The first part of the book introduces classical ensembles, provides an extensive review of quantum mechanics, and explains how their combination leads directly to the theory of Bose and Fermi gases. This allows a detailed analysis of the quantum properties of matter, and introduces the exotic features of vacuum fluctuations. The second part discusses more advanced topics such as the two-dimensional Ising model and quantum spin chains. This modern text is ideal for advanced undergraduate and graduate students interested in the role of statistical physics in current research. 140 homework problems reinforce key concepts and further develop readers' understanding of the subject.

✦ Table of Contents

Front matter
Copyright
Contents
Preface
Acknowledgements
PartI
1 Elements of Thermodynamics
1.1 The Laws of Thermodynamics
1.2 Thermodynamic Potentials
1.3 Comparison between CP and CV
1.4 Fluctuations
1.5 Stability
1.6 Specific Heat and Compressibility
1.7 The Ideal Monatomic Gas
Bibliographical Notes
Problems
2 The Classical Ensembles
2.1 Time Averages and Ensemble Averages
2.2 The Microcanonical Ensemble
2.3 The Canonical Ensemble
2.4 Two Examples
Bibliographical Notes
Problems
3 Aspects of Quantum Mechanics
3.1 Some General Properties
3.2 The Free Particle
3.3 The Harmonic Oscillator
3.4 Evolution Kernels and Path Integrals
3.5 The Free Particle on a Circle
3.6 The Hydrogen Atom
3.7 The WKB Approximation
3.8 Instantons
3.9 The Density Matrix
Bibliographical Notes
Problems
4 Systems of Quantum Oscillators
4.1 The Effect of an Energy Gap
4.2 Blackbody Radiation
4.3 Debye Theory of Specific Heats
Bibliographical Notes
Problems
5 Vacuum Fluctuations
5.1 The Casimir Effect
5.2 The Lamb Shift
5.3 The Cosmological-Constant Problem
Bibliographical Notes
6 The van der Waals Theory
6.1 The Role of Interactions
6.2 The Partition Function
6.3 The van der Waals Equation of State
6.4 Phase Equilibria and the van der Waals Gas
6.5 The Gibbs Phase Rule
Bibliographical Notes
Problems
7 The Grand Canonical Ensemble
7.1 The Grand Canonical Equations
7.2 Two Instructive Examples
Bibliographical Notes
8 Quantum Statistics
8.1 Identical Particles in Quantum Mechanics
8.2 Identical Oscillators in the Canonical Ensemble
8.3 Nonrelativistic Fermi and Bose Gases
8.4 High-Temperature Limits
8.5 The Free Fermi Gas at Low Temperatures
8.6 Fermi Gases in Solids
8.7 The Free Bose Gas at Low Temperatures
8.8 Bosons in an External Potential
8.9 Atomic and Molecular Spectra
8.10 Some Applications
Bibliographical Notes
Problems
9 Magnetism in Matter, I
9.1 Orbits in a Uniform Magnetic Field
9.2 Landau Levels
9.3 Landau Diamagnetism
9.4 High-T Paramagnetism
9.5 Low-T Paramagnetism
Bibliographical Notes
Problems
10 Magnetism in Matter, II
10.1 Effective Spin–Spin Interactions
10.2 The One-Dimensional Ising Model
10.3 The Role of Boundary Conditions
10.4 The Continuum Limit
10.5 The Infinite-Range Ising Model
10.6 Mean-Field and Variational Method
10.7 Mean-Field Analysis of the Ising Model
10.8 Critical Exponents and Scaling Relations
10.9 Landau–Ginzburg Theory
10.10 A Toy Model of a Phase Transition
Bibliographical Notes
Problems
PartII
11 The 2D Ising Model
11.1 Closed Polygons in Two Dimensions
11.2 Kramers–Wannier Duality
11.3 The Onsager Solution
Bibliographical Notes
12 The Heisenberg Spin Chain
12.1 Noninteracting Systems
12.2 The Spectrum of the Heisenberg Model
12.3 Thermodynamic Bethe Ansatz
Bibliographical Notes
13 Conformal Invariance and the Renormalization Group
13.1 Conformal Invariance
13.2 1D Ising Model and Renormalization Group
13.3 Percolation
13.4 The XY Model
13.5 ǫ-Expansion and the D =3 Ising Model
Bibliographical Notes
14 The Approach of Equilibrium
14.1 The Langevin Equation
14.2 The Fokker–Planck Equation
14.3 The Boltzmann Equation
14.4 The H-Theorem
14.5 Transport Phenomena
14.6 Nondissipative Hydrodynamics
14.7 The Emergence of Viscosity
14.8 The Fluctuation–Dissipation Theorem
Bibliographical Notes
Appendix A Probability Distributions
Appendix B Equilibrium and Combinatorics
Appendix C WKB at the Bottom
Appendix D Some Analytic Functions
Appendix E Euler–Maclaurin and Abel–Plana Formulas
Appendix F Spin and the Pauli Equation
Appendix G The Gn,m Operator
References
Index