Study notes for Statistical Physics
Publisher: Bookboon.com
Published: 2015
ISBN-13: 9788740308419
Table of contents: title: Content; title: 1. Introduction; title: 1.1. The isolated assembly; title: 1.2. Method of the most probable distribution; title: 1.3. Ensemble of assemblies: relationship between Gibbs and Boltzmann entropies; title: 2. Stationary ensembles; title: 2.1. Types of ensemble; title: 2.2. Variational method for the most probable distribution; title: 2.3. Canonical ensemble; title: 2.4. Compression of a perfect gas; title: 2.5. The Grand Canonical Ensemble (GCE); title: 3. Examples of stationary ensembles; title: 3.1. Assembly of distinguishable particles; title: 3.2. Assembly of nonconserved, indistinguishable particles; title: 3.3. Conserved particles: general treatment for Bose-Einstein and Fermi-Dirac statistics; title: 3.4. The Classical Limit: Boltzmann Statistics; title: 4. The bedrock problem: strong interactions; title: 4.1. The interaction Hamiltonian; title: 4.2. Diagonal forms of the Hamiltonian; title: 4.3. Theory of specific heats of solids; title: 4.4. Quasi-particles and renormalization; title: 4.5. Perturbation theory for low densities; title: 4.6. The Debye-Hückel theory of the electron gas; title: 5. Phase transitions; title: 5.1. Critical exponents; title: 5.2. The ferro-paramagnetic transition; title: 5.3. The Weiss theory of ferromagnetism; title: 5.4. Macroscopic mean field theory: the Landau model for phase transitions; title: 5.5. Theoretical models; title: 5.6. The Ising model; title: 5.7. Mean-field theory with a variational principle; title: 5.8. Mean-field critical exponents for the Ising model; title: 6. Classical treatment of the Hamiltonian N-body assembly; title: 6.1. Hamilton’s equations and phase space; title: 6.2. Hamilton’s equations and 6N-dimensional phase space; title: 6.3. Liouville’s theorem for N particles in a box; title: 6.4. Probability density as a fluid; title: 6.5. Liouville’s equation: operator formalism; title: 6.6. The generalised H-theorem (due to Gibbs); title: 6.7. Reduced probability distributions; title: 6.8. Basic cells in Γ space; title: 7. Derivation of transport equations; title: 7.1. BBGKY hierarchy (Born, Bogoliubov, Green, Kirkwood, Yvon); title: 7.2. Equations for the reduced distribution functions; title: 7.3. The kinetic equation; title: 7.4. The Boltzmann equation; title: 7.5. The Boltzmann H-theorem; title: 7.6. Macroscopic balance equations; title: 8. Dynamics of Fluctuations; title: 8.1. Brownian motion and the Langevin equation; title: 8.2. Fluctuation-dissipation relations; title: 8.3. The response (or Green) function; title: 8.4. General derivation of the fluctuation-dissipation theorem; title: 9. Quantum dynamics; title: 9.1. Fermi’s master equation; title: 9.2. Applications of the master equation; title: 10. Consequences of time-reversal symmetry; title: 10.1. Detailed balance; title: 10.2. Dynamics of fluctuations; title: 10.3. Onsager’s theorem