Syllabus for Statistical Mechanics II

Other Useful Texts:

  • The principles of statistical mechanics, by Richard Chace Tolman,  (QC 175.T584p)
  • Theory of Simple Liquids, by Jean-Pierre Hansen and Ian McDonald,  (QC 145.2.H36 1986)
  • Understanding molecular simulation, by Daan Frenkel and Berend Smit,  (QD 461 .F86 1996)
  • Computer Simulation of Liquids, by M.P. Allen and D.J. Tildesley,  (QC 145.2.A43 1992)
  • Classical Mechanics, by Herbert Goldstein, (QA 805 .G6 1980)
  • A modern course in statistical physics, by L. E. Reichl, (QC 174.8.R44)
  • Statistical Mechanics, by Kerson Huang, (QC 174.8 .H83 1987)
  • Statistical Mechanics, by Shang-Keng Ma, (QC 174.8 .M2513 1985)
  • Mathematical Methods in the Physical Sciences, by Mary L. Boas, (QA 37.B662)
  • Statistical Mechanics: a Set of Lectures, by R.P. Feynman (QC 174.8 .F48)
  • Statistical thermodynamics of surfaces, interfaces, and membranes, by Samuel A. Safran, (QC 173.4 .S94 S24 1994)
  • Hydrodynamic fluctuations, broken symmetry, and correlation functions, by Dieter Forster, (QC 20.7 .C6 F67)
  • An Introduction to Statistical Thermodynamics, by Terrell L. Hill,  (QC 20.7 .C6 F67)

Course Outline:

  1. Review of Statistical Mechanical concepts
  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
    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