An edition of Study notes for Statistical Physics
(2015)
Study notes for Statistical Physics
by W. David McComb
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Last edited by Alice Kirk
April 6, 2015 | History
This is an academic textbook for a one-semester course in statistical physics at honours BSc level. It is in three parts and begins with a unified treatment of equilibrium systems, based on the concept of the statistical ensemble, in which the usual combinatorial calculation only has to be worked out once.
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Publish Date
2015
Publisher
Bookboon.com
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Book Details
Table of Contents
Content
1. Introduction
1.1. The isolated assembly
1.2. Method of the most probable distribution
1.3. Ensemble of assemblies: relationship between Gibbs and Boltzmann entropies
2. Stationary ensembles
2.1. Types of ensemble
2.2. Variational method for the most probable distribution
2.3. Canonical ensemble
2.4. Compression of a perfect gas
2.5. The Grand Canonical Ensemble (GCE)
3. Examples of stationary ensembles
3.1. Assembly of distinguishable particles
3.2. Assembly of nonconserved, indistinguishable particles
3.3. Conserved particles: general treatment for Bose-Einstein and Fermi-Dirac statistics
3.4. The Classical Limit: Boltzmann Statistics
4. The bedrock problem: strong interactions
4.1. The interaction Hamiltonian
4.2. Diagonal forms of the Hamiltonian
4.3. Theory of specific heats of solids
4.4. Quasi-particles and renormalization
4.5. Perturbation theory for low densities
4.6. The Debye-Hückel theory of the electron gas
5. Phase transitions
5.1. Critical exponents
5.2. The ferro-paramagnetic transition
5.3. The Weiss theory of ferromagnetism
5.4. Macroscopic mean field theory: the Landau model for phase transitions
5.5. Theoretical models
5.6. The Ising model
5.7. Mean-field theory with a variational principle
5.8. Mean-field critical exponents for the Ising model
6. Classical treatment of the Hamiltonian N-body assembly
6.1. Hamilton’s equations and phase space
6.2. Hamilton’s equations and 6N-dimensional phase space
6.3. Liouville’s theorem for N particles in a box
6.4. Probability density as a fluid
6.5. Liouville’s equation: operator formalism
6.6. The generalised H-theorem (due to Gibbs)
6.7. Reduced probability distributions
6.8. Basic cells in Γ space
7. Derivation of transport equations
7.1. BBGKY hierarchy (Born, Bogoliubov, Green, Kirkwood, Yvon)
7.2. Equations for the reduced distribution functions
7.3. The kinetic equation
7.4. The Boltzmann equation
7.5. The Boltzmann H-theorem
7.6. Macroscopic balance equations
8. Dynamics of Fluctuations
8.1. Brownian motion and the Langevin equation
8.2. Fluctuation-dissipation relations
8.3. The response (or Green) function
8.4. General derivation of the fluctuation-dissipation theorem
9. Quantum dynamics
9.1. Fermi’s master equation
9.2. Applications of the master equation
10. Consequences of time-reversal symmetry
10.1. Detailed balance
10.2. Dynamics of fluctuations
10.3. Onsager’s theorem
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| April 6, 2015 | Edited by Alice Kirk | Edited without comment. |
| April 6, 2015 | Created by Alice Kirk | Added new book. |