Physics 418: Statistical Mechanics I
Prof. S. Teitel ----- Spring 2006

Lecture Notes

My hand written class lecture notes are being scanned and uploaded for you to view. Please be warned that these are the notes I prepare for myself to lecture from - they are not in general carefully prepared for others to read. I make no guarentees about their legibility, or that they are totally free of errors. I hope, nevertheless that you will find them useful. The lectures are uploaded as pdf files, so you will need Adobe Acrobat Reader in order to read them. You can download Acrobat Reader for free here.

The lecture note files correspond roughly to the material presented in a given day's lecture. But you may on occassion find the end of one day's lecture at the start of the file for the next day's lecture, so please look there if you think there might be something missing.

  • Lecture 1 - Postulates of classical thermodynamics; extensive and intensive variables

  • Lecture 2 - Thermal, mechanical and chemical equilibrium; concavity of the entropy; Euler relation; equations of state; Gibbs-Duhem relation

  • Lecture 3 - Entropy of the ideal gas; energy minimum principal

  • Lecture 4 - Legendre transformations; Helmholtz free energy, enthalpy, Gibbs free energy and the grand potential

  • Lecture 5 - Extrema principals for various thermodynamic potentials; reservoirs; Maxwell relations; response functions and relations among them

  • Lecture 6 - Thermodynamic stability within various potentials and consequences for response functions; kinetic theory of the ideal gas and Maxwell velocity distribution; statistical ensembles and the ergodic hypothesis

  • Lecture 7 - Liouville's Theorem; microcanonical and canonical ensemble, density of states; connection to entropy

  • Lecture 8 - Entropy of the ideal gas revisited; entropy of mixing and Gibbs parodox; indistiguishable particles

  • Lecture 9 - The canonical ensemble; energy fluctuations

  • Lecture 10 - Equivalence of the canonical and microcanonical ensembles in the thermodynamic limit; ideal gas in the canonical ensemble; virial and equipartition theorems.

  • Lecture 11 - Elastic vibartions of a solid and the Law of Dulong and Petit; Curie Law for paramagnetism; entropy and information

  • Lecture 12 - Entropy and information continued

  • Lecture 13 - The grand canonical ensemble

  • Lecture 14 - The grand canonical ensemble for non-interacting particles; chemical equilibrium

  • Lecture 15 - Quantum ensembles; the density matrix

  • Lecture 16 - Many particle quantum systems; Fermi-Dirac and Bose-Einstein statistics; non-interacting particles; two particle density matrix and effective interaction

  • Lecture 17 - N-particle canonical partition function in real space representation; corrections to classical result due to particle exchanges; the grand canonical partition function for non-interacting fermions, bosons, and classical particles

  • Lecture 18 - Average occupation numbers; comparision of quantum vs classical single particle partition function; the classical limit; harmonic oscillator vs bosons

  • Lecture 19 - Debye model for the specific heat of a solid; black body radiation and Stefan-Boltzmann Law

  • Lecture 20 - Ideal quantum gas of fermions or bosons; the "standard" functions; non-degenerate limit and leading quantum corrections to the ideal gas equation of state; degenerate fermi gas and the Sommerfeld model of electrons in a conductor

  • Lecture 21 - Degenerate ideal fermi gas: Sommerfeld expansion (not covered in class); specific heat; Pauli paramagnetism

  • Lecture 22 - Degenerate ideal bose gas: Bose-Einstein condensation

  • Lecture 23 - Bose-Einstein condensation continued; BEC of laser cooled gases in magnetic traps

  • Lecture 24 - Classical spin models; magnetic ensembles; phase transitions and the thermodynamic limit; phase diagram for the Ising model

  • Lecture 25 - Mean field solution of the Ising model; critical exponents

  • Lecture 26 - Landau theory of phase transition

  • Lecture 27 - Critical exponents within Landau theory; exact solution of one dimensional Ising model

  • Lecture 28 - Landau-Ginzburg theory - including fluctuations; correlation function; fluctuation corrections to specific heat; upper critical dimension

Last update: Wednesday, August 22, 2007 at 3:55:03 PM.