Physics 210B : Course Description

Subject Matter
The subject matter of Physics 210B is nonequilibrium statistical physics. The tentative outline is as follows:

1. PROBABILITY: fundamental axioms, random variables, discrete vs. continuous, Bayesian statistics, univariate and multivariate, maximum entropy construction, central limit theorem, moments and cumulants.

2. MARKOV PROCESSES: conditional probabilities, Markov processes, Chapman-Kolmogorov equation, master equation, Fokker-Planck equation, examples

3. STOCHASTIC DIFFERENTIAL EQUATIONS: Langevin equation, stochastic integration, Ito calculus, Stratonovich integral, examples.

4. BOLTZMANN EQUATION: Local equilibrium, scattering processes, detailed balance, H-theorem, weakly inhomogeneous gas, relaxation time approximation, transport coefficients, diffusion and the Lorentz model, linearized Boltzmann equation, Chapman-Enskog method, hydrodynamics, nonequilibrium quantum transport.

5. APPLICATIONS: Selections from the following topics: first passage problems, surface growth, time-dependent Ginzburg-Landau and Cahn-Hilliard equations, domain wall evolution, stability, droplets, Lifshitz-Slyozov-Wagner theory of Ostwald ripening, symmetric and asymmetric exclusion processes, hydrodynamics, vehicular traffic, shock formation, open systems, etc.

Course Texts
I plan to follow my own lecture notes. There is no single text which covers all our material, but I recommend each of the following:

C. Gardiner, "Stochastic Methods" (4th edition, Springer, 2009)

N. Pottier, "Nonequilibrium Statistical Physics" (Oxford, 2010)

P. L. Krapivsky, S. Redner, E. Ben-Naim, "A Kinetic View of Statistical Physics" (Cambridge, 2010)

Course Web Site
Lecture notes and reading assignments, important announcements, homework assignments and solutions will all be available through the course web site. Please check it before each lecture to see if there is new material.

On the course home page, I have included a number of links to potentially useful resources.

Problem Sets
I will try to assign one problem set every other week. Problem sets will not be printed out for you, but rather will be available through the course website. You are encouraged to discuss the problem sets with your fellow students. I suggest that you initially try to do the problems by yourselves, so that you can more accurately identify your confusions and honestly assess your weaknesses. Then, before you write up your assignment, get together with some of your fellow students to talk over the problems and hammer out the details. Solutions to problem sets will be posted on the course website. Hopefully the solutions and your graded assignments will be made available in a timely manner, but invariably there are lags from time to time.

Office hours
My office hours are by appointment.

Final project
Rather than there being a final examination, this course will involve a final project. You have the option of collaborating with another student on this project. A sign-up sheet for final project topics will be posted sometime around the fifth week of classes.

Course grade
The magic formula: 40% problem sets, 50% final project, 10% intangibles (e.g. personal hygiene, taste in music, sense of humor [= laughing at my jokes], etc.).