Homepage of course 77802: Statistical Mechanics A - Winter 2009/10

General info
Course hours: Lectures: Tue 08-10, Wed 10-12, Shprintzak 117.
Lecturer: Omri Gat
Lecture notes: Will be published here as soon as a presentable version is ready
Homework: Student will have to solve three problem sheets, one for each chapter of the course, and each will count as 8% of the final grade. Homework problems must be solved indivdually
Exam will account for 76% of the final grade
Announcements
Syllabus
  1. Fundamentals of statistical mechanics, (weeks 1-4). The density matrix. The equlibrium state of closed systems: Extensivity, the microcanonical disrtibution, entropy. The Gibbs ditribution: Systems in contact with a heat bath, systems subject to external forces, systems in contact with a particle reservoir.
  2. Physical gases and phase transitions, (weeks 5-7). The equation of state of an interacting gas: The equipartition and virial theorems, the cluster expansion, the van-der-Waals equation of state. Phase transitions and critical phenomena (1): The condensation of a van-der-Waals gas, phase equilibrium, scaling and universality at the critical point.
  3. Magnetic systems, (weeks 8-10). Introduction to magnetism: Magnetic thermodynamics, molecular magnetism, The exchange interaction. Interacting spin systems: the Heisenberg model, the Ising model in one dimension, the Peierls argument, the mean field approximation, the Ising model on the Bethe lattice. The Landau theory of continuous phase transition.
  4. Fluctuations and linear response, (weeks 11-12).
  5. Irreversible processes, (weeks 13-14). This chapter will be skipped if the teaching pace is slower than estimated.
Textbooks
There are many standard textbooks at the level of the course, and choice between them is largely a matter of taste. All the books cited below are found in the Harman Library reserved textbooks sections, but any appropriate textbook, whether on the list or not, can be used for self-study. My personal favorite is Landau & Lifshitz, and the course will follow this book whenever possible.
General references
  1. LD Landau and EM Lifshitz, Statistical Physics, Part 1
  2. K Huang, Statistical Mechanics
  3. R Kubo, Statistical Mechanics
  4. R Kubo et al. Statistical Physics II
  5. RK Pathria, Statistcial Mechanics
  6. LE Reichl, A modern course in Statistical Physics
  7. F Reif, Statistical Physics
  8. HS Robertson, Statistcial Thermophysics
  9. M Toda et al. Statistical Physics I
References on critical phenomena
  1. HE Stanley, Introduction to phase transitions and critical phenomena
  2. LP Kadanoff et al. Rev. Mod. Phys. 39, 395 (1967)
Homework projects

General instructions:

Problem sheet number 1 consists of 8 questions. Submission deadline: Thursday 26/11/09. download problem sheet , student grades .

Problem sheet number 2 consists of 7 questions. Submission deadline: Thursday 24/12/09. download problem sheet , student grades .

Problem sheet number 3 consists of 6 questions. Submission deadline: Thursday 21/01/10. download problem sheet , student grades .

Problem sheet number 4 consists of 4 questions. Not for submission. download problem sheet .

Auxiliary material
Thermodynamics of a Lennard-Jones gas in the leading virial approximation
  1. Virial coefficient
  2. Entropy difference with respect to ideal gas
  3. Energy difference with respect to ideal gas
Thermodynamics of 1D Ising chain
  1. Magnetization as a function of external field for exchnage coefficients 0 (blue), 1 (violet), 2 (yellow), and 3 (green). Zoomed version
Mean field theory of the Ising model
  1. Magnetization as a function of temperature without external field
  2. Magnetization as a function of temperature with external field 0.05
  3. Magnetization as a function of temperature with external field 0.0001. Zoomed version. Zoomed version compared with the field-less magnetization.
Brownian motion
  1. Realization number 1 and 2 of a 10,000 step random walk in the plane
Written by Omri Gat. Last update: see announcements section