Physics 352: Graduate Statistical Mechanics

as of March 28, 1995. under construction

General Information

• Instructor: Tom Witten, Research Institutes L104, t-witten@uchicago.edu
• Grader: Julie Blum, julie@yukawa
• Class times: The class meets Tuesdays and Thursdays from 11:30 to 12:50 in Kersten 105
• Aim of course:} To bring your knowledge and abilities with statistical mechanics to the level of a professional physicist.
• Prerequisites: a working knowledge of undergraduate physics
• Coursework:

  • Homework

    A problem set will be assigned each week, to be turned in the following week. The problems are the main learning activity of the course. I will be available the hour following Monday classes or by appointment to discuss problems. Don't hesitate to consult me about problems; it is inevitable that I will assign some that are confusingly worded or ill-posed. I encourage collaboration on problems. But you should report the solution as you personally understand it.
  • The homework will include small monte-carlo simulations that can be done on a personal computer or programmable calculator.

  • Midterm

    A midterm exam will be given in class on Tuesday April 25, covering the the work up to that point.

  • Final exam

    Probably a two-hour final at the scheduled time.
• Textbooks:

  Main text

  David Chandler, Introduction to modern statistical mechanics (New York : Oxford University Press, 1987)

  • Supplementary texts

    • Shang-Keng Ma Statistical mechanics (Philadelphia : World Scientific, c1985.)
    • R. K. Pathria Statistical mechanics (NewYork, Pergamon Press 1972)
    • L. D. Landau and E. M. Lifshitz. Statistical physics, 3d revised edition, two volumes (Oxford; New York : Pergamon Press, 1980)
    • Amnon Katz Principles of statistical mechanics; the information theory approach (San Francisco, W. H. Freeman 1967)
• Office hour: I plan to be available immediately after each class for questions on the material. Other times are available by appointment.
• Bulletin board: I plan to post course materials on the internet so that you can access them via Mosaic, Netscape, etc. You're looking at it. The location (URL) is http://rainbow.uchicago.edu/tten/Physics.352/readme.html You can also get to this page via the physics department web page, under my name. Announcements of revisions in problems, schedule changes, etc. will be posted there.

Plan of course

Thermodynamics

• Equilibrium, Work and heat, Laws of thermodynamics, Thermodynamic potentials Chandler, Ch. 1 (These references tell where information can be found on the topic. They may use different notation or logic than I will use.)
• Stability and phase rule; convexity; Legendre transformation and alternative potentials (free energies); correlations and response functions Chandler, Ch. 2
• Maxwell relations; interfacial free energies Chandler, Ch. 2

Statistical foundation of thermodynamics

• Microscopic variables, probability, quantum probability, ergodic hypothesis, time-reversal paradox Chandler, Ch. 3; handout; Landau, Ch. 5; Katz, Ch. 5; Ma, Ch. 26
• Entropy of a probability distribution; Adiabatically allowed changes Katz, Ch. 1
• Equilibrium with a reservoir; Boltzmann distribution; monte-carlo sampling Chandler, Ch. 3; Ch. 6, handout
• Partition function; equilibrium of few-body systems; Microscopic justification for thermodynamic laws; thermodynamic potentials Chandler, Ch. 3

Solvable many-particle systems

• noninteracting systems; photon gas; bose gas; fermi gas lattice gas; classical limit Chandler, Ch. 4
• dilute gas of molecules; chemical equilibrium Chandler, Ch. 4

Phase transitions

• Ising model and interacting lattice gas; Broken symmetry; Spatial correlations; Mean-field approximation Chandler, Ch. 5
• Limitations on phase transitions: Mermin-Wagner theorems; Yang-Lee theorem Ma, Ch. 29.4, Ch. 9

Weakly interacting systems: diagrammatic methods

• Dilute lattice gas; Diagrams for partition function; free energy; correlation functions. Pathria, Ch. 9, handout?

Time-dependent phenomena

• Relaxation to equilibrium; response functions; Fluctuation-Dissipation theorem Chandler, Ch. 8
• Steady-state flow; Onsager coefficients; Onsager relations; Pathria, Ch. 13.8; Katz, Ch. 8
• Langevin dynamics; ``activated" processes Chandler, Ch. 8
• Formalisms for nonequilibrium systems: master equations Pathria, Ch. 13.5; Katz, Ch. 9

Problem sets and handouts

• see "All materials" below

Pointers

• All materials for this course <\A>
• Text books
• viewing course handouts online. I plan to make the TeX files for course materials available on this bulletin board. This pointer points to information on viewing TeX files automatically. It's probably easier just to look at the source files or typeset them yourself. If you do try to typeset a file, you should prepend my Physics Department home page

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Tom Witten, t-witten@uchicago.edu