Statistical Mechanics II

Syllabus

Main Texts
Other useful texts:
    See the Book List for a list of useful library texts. We will be referring most frequently to Hansen & McDonald or Huang when the primary texts don't contain a topic of interest.
Course Outline
  1. Introduction
  2. Ising models and lattice gases
    1. Independent spins in a field and equivalent lattice gas.
    2. Interacting spins on a line, the transfer matrix.
    3. Correlation functions.
    4. Reversible work.
    5. Spins with random fields, influence functionals.
    6. Spins on a plane, phase transitions, broken symmetry, interfacial fluctuations.
    7. Monte Carlo simulations of the 2D Ising model.
    8. Mean field theory, Gibbs-Bogoliubov bound.
  3. Atomic and continuum models of liquids
    1. The Lennard-Jones Fluid.
    2. Molecular dynamics simulation.
    3. Correlation functions and measurements, elements of linear response theory.
    4. Linear models
      1. Langevin equations (diffusion, friction and memory).
      2. Gaussian fields (Debye-Huckel and beyond).
    5. The hard sphere model, WCA theory.
    6. Chemical equilibrium and relaxation.
  4. Special topics (if we have time!)
    1. Free energy perturbation
    2. The Jarzynski Equality
    3. Electron transfer, quantum rare events, golden rule, Marcus theory.
    4. Path integrals.
    5. Tunneling, instantons
    6. Ising model / Quantum correspondence
    7. Biased Monte Carlo methods