Prof. Andrew Cumming
ERP 219, email: cumming-at-physics.mcgill.ca
Office hours: MTF 2-3.30pm
MWF 11.35am-12.25pm, WONG 1050
Bertrand Chapleau, Lu Egang
Here is a list of topics that we hope to cover during the course. Statistical mechanics has broad applicability across physics (and other fields), and we will illustrate this throughout the course with examples drawn from condensed matter physics, biophysics, astrophysics, and elsewhere.
1. Fundamentals. Ergodicity and principle of equal equilibrium probabilities. The microcanonical ensemble. Entropy and the meaning of temperature in statistical mechanics. The Boltzmann distribution. The grand canonical ensemble and chemical potential. Fluctuations.
2. Quantum statistical mechanics of non-interacting particles. Ideal gas of bosons or fermions, indistinguishable particles and the classical limit. Photons and blackbody radiation. Electrons in metals. Phonons and the heat capacity of a solid. White dwarfs and neutron stars. Bose-Einstein condensation.
3. Phase transitions. The Ising model as a canonical example. Mean field theory. Introduction to renormalization group. Numerical methods. Fluctuations, susceptibility, and correlations close to the critical point. Landau theory.
4. Examples of systems with interacting particles. Cooperative binding in hemoglobin. The law of mass action. Binary alloys and anti-ferromagnets. The lattice gas. Universality.
5. Fluctuations and the approach to equilibrium The connection between fluctuations, response functions, and spatial correlation functions. Brownian motion, Langevin equation. Fluctuation-dissipation theorem.
Homework 25%, and either (1) midterm 25%, final exam 50%, or (2) final exam 75%, whichever gives you the best grade. The midterm will be held in class on [To be decided] (Friday Feb 19th OR Mon Mar 15th).
McGill academic integrity statement: McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (more information).
There is no required textbook for this course. Copies of the lecture notes will be made available on WebCT.
There are many books on Statistical Mechanics. Introduction to Modern Statistical Mechanics by David Chandler covers the right material at the right level, but is very concise. Introductory Statistical Mechanics by Bowley and Sanchez gives a more basic introduction than Chandler. Statistical Mechanics: Entropy, Order Parameters, and Complexity by Sethna is a relatively new book available on the web which highlights many topical applications of statistical mechanics. Also worth looking at are the final chapters of Callen's book Thermodynamics and an Introduction to Thermostatistics which you likely already have since it was used in PHYS 253 Thermal Physics.
Other books include Statistical Physics of Particles by M. Kardar, an excellent new book, but at a slightly higher level than this course. My favourite book on thermal physics is The Theory of Thermodynamics by J. R. Waldram, which introduces the ideas of thermodynamics and statistical mechanics side by side (unfortunately no longer in print). A standard classic text is Fundamentals of Statistical and Thermal Physics by Reif.