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. DIFFUSION: Boltzmann equation, failure of the relaxation time approximation, Lorenz model, diffusion equation, first passage problems, surface growth, other examples.

Time permitting, we will cover one of the following:

5. COARSENING: time-dependent Ginzburg-Landau and Cahn-Hilliard equations, domain wall evolution, stability, droplets, Lifshitz-Slyozov-Wagner theory of Ostwald ripening

6. SPIN DYNAMICS: voter model, correlation functions, continuum limit, Ising-Glauber model, Kawasaki dynamics, clusters

7. EXCLUSION: symmetric and asymmetric exclusion processes, hydrodynamics, vehicular traffic, shock formation, open systems

Course Text
I plan to draw upon four main texts:

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

Z. Schuss, "Theory and Applications of Stochastic Processes" (Springer, 2010)

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

S. Redner, "A Guide to First-Passage Processes" (Cambridge, 2007)

I am requesting that a copy of each of these texts be placed on reserve at the Geisel Library. The main course text is Gardiner. This is the first time I have taught this course in over 20 years, so I will be composing my own lecture notes as we go along. Since this will be a first draft, I would very much appreciate your identifying errors, typos, confusions, and in general anything you think could be improved.

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. The notes themselves are essentially complete (I am working on a final chapter on renormalization, which we will not cover anyway), but I may make some editorial changes or additions as we go along. I will indicate on the lecture notes page the date, time, and size (in pages) of the most recent upload for each chapter. If you find any errors in the notes, I would greatly appreciate it if you would alert me via the web forum pages.

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.).