Thermodynamics, Kinetic Theory and Statistical Mechanics.

Instructor: Duncan Haldane (Jadwin 327, x8-5856, haldane@princeton.edu)
Class meets: Jadwin A06, TTh 1:30-2:50pm.

This class will study the physical principles and mathematical formulation of statistical physics, with emphasis on applications in thermodynamics, condensed matter, physical chemistry and astrophysics.

Students will be asked to participate in class discussion of challenging problems taken from past departmental generals exams (prelims).

The class will aim at a balance between material useful for Generals and more advanced topics.

Homework sets will emphasize previous prelims problems.

Recommended text: A Modern Course in Statistical Physics (L. E. Reichl, Wiley Interscience 1998, second edition)

Some Planned Topics:

• Review of Thermodynamics: entropy, thermodynamic potentials, stability, phase transitions. phase diagrams, mixtures, non-ideal gases, chemical reactions.

• Equilibrium Statistical Mechanics: Microcanonical, canonical and grand canonical ensemble, partition functions, density matrix. Ideal classical and quantum gases, Bose condensation and Fermi gases. Mean field theory, Landau theory, Ising model. Polymers. Virial expansion for non-ideal gases. Superconductors.

• Correlation functions, Ornstein-Zernike equations. Critical phenomena: Landau-Ginzburg theory, Renormalization group, XY model, Kosterlitz-Thouless transition. Magnetism, Heisenberg model. Monte Carlo calculations. Percolation.

• Kinetics: Boltzmann equation, Fokker-Plank equation. Onsager relations.

• more (or less) as time permits $\ldots$