PH4771 Advanced Statistical Physics

Review of thermodynamics. Phase transitions and critical exponents. Ginzburg-Landau theory. Stochastic dynamics and Brownian motion: master equation, Langevin equation, and Fokker-Planck equation. Phase space motion, Liouville theorem. BBGKY hierarchy. Boltzmann equation, H theorem, and entropy. Kinetic theory. Review of equilibrium statistical mechanics and ensemble theory. Information theory. Bose-Einstein condensation, photon gas. Degenerate Fermions: heavily doped semiconductors, degeneracy pressure. Paramagnetism, Curie theory. Ising model of magnetism. Glauber model of time-dependent Ising spins. Widom, Kadanoff scaling theories. Renormalization theory. Onsager relations, linear response theory, fluctuation-dissipation theorem.

Prerequisite

PH3782

Lecture Hours

Lab Hours

Course Learning Outcomes

At the conclusion of this course, students will be able to solve quantitative problems at the graduate level in the following areas:

Thermodynamics of gases and solids from a microscopic perspective, including free energies, specific heats;
Statistical mechanics, including Boltzmann factor, Gibbs factor, and microscopic definition of entropy;
Applications of these concepts from a quantum perspective to common physical systems, including ideal gas, quantum oscillators, photon gas, and paramagnets;
Quantum statistical mechanics of degenerate boson and fermion systems, including degenerate fermi gases and Bose-Einstein condensation;
Kinetic theory, including diffusion, Brownian motion, and transport laws;
Phase transitions, including critical exponents of mean field Ising models;
Selected advanced topics, such as Ginzburg-Landau theory or basic concepts of renormalization theory.