Advanced Statistical Mechanics

This course covers the theory of statistical mechanics at the intermediate level, in particular:

1. The formalism of statistical mechanics and its relation to thermodynamics,

   • Ensemble theory.

2. Systems of non-interacting particles,

   • classical, quantum.

3. Classical systems of interacting particles,

   • Perturbation theory: Cluster expansion;

   • Phase transitions: van der Waals, mean field theory, exact solutions, quantum phase transitions;

   • Phase transitions: scaling and renormalization.

4. Fluctuations, dissipation and non-equilibrium statistical mechanics.