Syllabus: Statistical Mechanics

PCS 8301

A. Objectives

To teach the foundation of statistical mechanics developed by Boltzmann,
Gibbs and others, presented from a modern perspective, using quantum
mechanics. In the initial phase the canonical ensemble theory is
developed to treat many-body models with a fixed number of particles. A
quantum prescription is given using the second law of thermodynamics. The
canonical ensembles are applied to physical problems such as solids of
Einstein and Debye, photon gas of Planck, magnetic models. These studies
are intended to illustrated the workings of modern statistical mechanics

B. Topics

1. Review of thermodynamics
2. Boltzmann's method and canonical ensembles
3. LaGrange's method of multipliers, temperature and chemical potential
4. Two level systems
5. Quantum partition function and Helmholtz free energy
6, Energy fluctuations and the specific heat
7. Einstein and Debye models of solids
8. Planck's radiation law, the sun's spectra, cosmological background
9. Phase transitions in fluids and magnets