COURSE INFORMATION, PHYSICS 715, STATISTICAL MECHANICS

COURSE INFORMATION

PHYSICS 715, STATISTICAL MECHANICS

Instructor:

Loyal Durand
Office: 4209 Chamberlin.
Email address: ldurand@hep.wisc.edu
Web site: http://hep.wisc.edu/~ldurand/
Telephone: 262--3996.

Office hours:

Usually available after class, but flexible---check after class for a good time to come by my office. But please do not come the hours before class!

Meets:

9:55 MWF, B231 Van Vleck

Goal and theme of the course:

The objective of the course is to help you learn how to apply statistical ideas to the solution of real physical problems. Before you can do so, you will have to learn to recognize when statistical ideas will be useful, what the most promising approach is likely to be, and what methods are available to solve the problem. All are probably best learned by seeing how statistical ideas have been used in past research. This will be the general theme of the course. The lectures will develop the methods of statistical mechanics systematically, and illustrate their application with numerous examples and applications to real problems. The homework will continue this theme, with a large fraction of the problems dealing with real, rather than practice, problems, many quite important in the development of statistical mechanics or in current research, as the names attached to the problems will indicate.

A very interesting discussion of historical developments in statistical mechanics is given in a talk by C.N. Yang, one of the modern masters of the subject. We will see many of the things he discusses during the semester.

Text:

Landau and Lifshitz, Statistical Physics, 3rd edition, Part I (Pergamon). The early printings of the 3rd edition give the authors as Lifshitz and Pitaevskii because Pitaevskii helped with the revision of the original Landau and Lifshitz. The text is the same. The text has good, physical, explanations of most of the material, includes modern applications of statistical mechanics, and has many worked examples. The text by Huang (see below) fills in many of the mathematical details, but is considerably more formal than Landau and Lifshitz.

Lectures:

The lectures will cover and supplement the material in Landau and Lifshitz. The order of presentation will be slightly different, with an emphasis in the first part of the course on classical statistical mechanics, followed by quantum statistical mechanics.

Homework:

There will be problem sets most weeks. These will be posted on the web in two versions at the link above, a pdf for printing, and an html version with comments and hints.

The problems are intended to give you practice in using statistical mechanics in a various physical situations. The problems are not always simple - the icons on the html version indicate the difficulty of the problems for most students - but are designed to illustrate a variety of techniques, some perhaps not familiar. Some of the problems require numerical work, in part to get you familiar with typical numbers in applications, and in part to get you connect the outcome with theory. Nothing more than a scientific calculator, graph paper, and a table of integrals is actually needed, but you will probably want to use Mathematica, Maple, Matlab, Fortran, or some other computer program for a few problems. Another useful tool is The Integrator for calculating integrals analytically. However, beware: the results you get with any of these programs may not be transparent. Your emphasis should be on developing an understanding of the results. We will introduce a number of approximation methods which will simplify the results in many cases and help you develop that understanding. Learn to use them when appropriate!

Problem solutions will be put on reserve in the library after the due date. No late homeworks are accepted without prior arrangement.

Students in the class are strongly encouraged to discuss the problems with other students, and to work together on their solution. I am happy to discuss the problems and give hints, but you may learn more from your fellow students! Most physics is done in collaborations, and this will give you practice in working in a collaborative setting, something expected by most potential employers of physicists.

Exams and grades:

The problem grade will count as 25% (25 points) of the final grade (free points if you do the work!). There will be two hour exams in class during the semester, probably Wednesday, February 22 and Wednesday, April 12. Each will count 25 points in the final grade. The final exam (another hour exam, 25 points) will be Monday, May 8, at 12:25 pm, location to be announced.

My grading scale is normally 87-100 for A, 70-86 B, 60-69 C, with AB used in the area approaching the B to A transition. I don't raise the cutoffs, but may dip below the levels stated if an exam turns out to be too hard, if a person started poorly but demonstrated real improvement during the semester, or in other exceptional circumstances.

References on reserve in the Physics Library, 4220 Chamberlin

Landau and Lifshitz, Statistical Physics, 3rd edition, Part I: Has a wide range of applications. Derivations tend to be heuristic and somewhat sketchy mathematically, but are very physical in the Landau style. There are many examples worked out or set up. Study these to learn how to approach problems in statistical physics, of which Landau was a master (Nobel Prize, 1962). Good text.
K. Huang, Statistical Mechanics, 2nd edition: Good on the background and formal aspects of statistical mechanics. Uses Boltzmann's approach. The derivations are more complete mathematically than those in Landau and Lifshitz. Lots of material on the Ising and similar models, and on modern scaling relations, but using methods somewhat beyond what we will be using. The notation in Huang is different from that used by Landau and Lifshitz.
R. Kubo et al., Statistical Mechanics: Many examples with detailed solutions, not much in the way of derivations. Good for learning how to set up problems, general reference.
D.S. Betts and R.E. Turner, Introductory Statistical Mechanics: Uses the information theory approach to introduce statistical ideas. Clear development and discussions, many good physical examples. Good supplementary reading.
Math reference: Abramowitz and Stegun, Handbook of Mathematical Functions (Dover): very useful handbook, covers almost everything we will need.