Classical and Quantum Statistical Physics: Fundamentals and Advanced Topics

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