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Spring 2009 – Lecture Notes on Statistical Mechanics


Note: I am posting updated versions of these files as we go along. Comments are most welcome.

List of Available Files

  00. Course Information

Introductory Topics
  01. Introduction to the Course; Review of Probability and Statistics [updated 20 jan 09].
  02. Statistical Mechanics and the Distribution Function [updated 2 feb 09].
  03. Equilibrium Distribution Functions and the Microcanonical Ensemble [updated 6 feb 09].
  04. The Canonical and Grand Canonical Distribution Functions [updated 6 feb 09].
  05. Mixed States in Quantum Mechanics and Quantum Canonical Distribution [updated 11 feb 09].
  06. Review of Thermodynamics. 1: Basic Laws [updated 20 feb 09].
  07. Review of Thermodynamics. 2: Thermodynamic Potentials [updated 16 feb 09].
  08. Review of Thermodynamics. 3: Useful relations [updated 16 feb 09].
  09. Thermodynamics from Statistical Mechanics; Monatomic Ideal Gas [updated 8 mar 09].
  10. Effect of Quantum Statistics on the Semiclassical Limit [updated 25 feb 09].

Examples of Systems
  11. The Free Fermion Gas and Electrons in Metals [updated 8 mar 09].
  12. The Photon Gas [updated 11 mar 09 – small notation change].
  13. The Free Quantum Molecular Gas [updated 8 mar 09].
  14. The Phonon Gas [8 mar 09; major changes 11 mar 09].
  15. Non-Ideal Gases. 1: The Virial Expansion and Cluster Method [23 mar 09; updated 25 mar 09].
  16. Non-Ideal Gases. 2: Classical Approximation and Two Important Examples [updated 8 apr 09].
  17. Phase Equilibrium and Phase Transitions in Thermodynamics [30 mar 09].
  18. The Free Boson Gas and Bose-Einstein Condensation [6 apr 09; updated 13 apr 09].
  19. Magnetism. 1: Paramagnetism [13 apr 09; updated 15 apr 09].
  20. Magnetism. 2: Ferromagnetism [15 apr 09; updated 22 apr 09].

Special Techniques and Application to the Ising Model
  21. The 1D Ising Model (and Renormalization Group Approach) [17 apr 09; updated 22 apr 09].
  22. The 2D Ising Model (Renormalization Group and Monte Carlo) [22 apr 09; updated 1 may 09].
  23. The Monte Carlo Method [22 apr 09; updated 29 apr 09].
Applications of the Monte Carlo Method
Mathematica 5 notebooks for: Simple example and 2D Ising Model [29 apr 09; updated 1 may 09].

Additional Topics not Covered This Year
Critical Phenomena: Scaling and Universality
Non-Equilibrium Statistical Mechanics: Transport Phenomena.
Non-Equilibrium Statistical Mechanics: The Fluctuation-Dissipation Theorem.

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page by luca bombelli <bombelli at olemiss.edu>, modified 1 may 2009