MAT280-001, Winter 2003: Quantum Statistical Mechanics. (CRN 70033)

General Information

This class meets MWF, 11:00-11:50am, in 27 Wellman. For the final exam, students have a choice between an in-depth study project or a traditional final exam.

Course Outline

The focus of this class will be on Non-equilibrium Statistical Mechanics. The following topics will be covered:
- Thermodynamics of equilibrium states
- Non-equilibrium thermodynamics
- Quantum dynamical systems
- Quantum statistical mechanics
- Connection between microscopic and macroscopic descriptions

References and Notes

1. Thermodynamics:

T.C. Dorlas, Statistical Mechanics. Fundamentals and Model Solutions, IOP, Bristol, 1999.
An elementary but mathematically sound introduction to equilibrium thermodynamics and statistical mechanics.

H.B. Callen, Thermodynamics, Wiley, 1960.
Good physics text on equilibrium some non-equilibrium thermodynamics.

E.H. Lieb and J. Yngvason, The physiscs and mathematics of the second law of thermodynamics, Physics Reports, 310, 2-96, 1999.
The title says it! Rigorous and complete axiomatics of the Second Law. Lots of good references, too.

G. Gallavotti, Nonequilibrium Thermodynamics?, preprint mp_arc 03-11.
Twentyseven comments on the Second Law and nonequilibrium systems.

Lech Wolowski's notes for lectures 1-6: ps-file.

2. Quantum Dynamical Systems:

R. Alicki and M. Fannes, Quantum Dynamical Systems, Oxford University Press, Oxford, New York, 2001.

O. Bratteli and D. Robinson, Operator Algebras and Quantum Statistical Mechanics, volume 1 & 2, Springer Verlag, Berlin-Heidelberg-New York, second edition, 1987, 1997.

W. Thirring, Quantum Mathematical Physics, Springer Verlag, Berlin-Heidelberg-New York, 2nd edition, 2002.

T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, Berlin-Heidelberg-New York, second, corrected edition, 1980.

M. Reed and B. Simon, Methods of Modern Mathematical Physics. Volumes I-IV, Academic Press, San Diego, 1980.

3. Quantum Statistical Mechanics:

D. Ruelle, Statistical Mechanics, W.A. Benjamin Inc, Reading, Massachusetts, 1969.

R. Israel, Convexity in the Theory of Lattice Gases, Princeton University Press, Princeton, NJ, 1979.

B. Simon, The statistical mechanics of lattice gases, volume 1, Princeton University Press, Princeton, NJ, 1993.

4. Connecting micro- and macroscopic dynamics:

G. Sewell, Quantum Mechanics and its Emergent Macrophysics, Princeton University Press, Princeton, NJ, 2002.

To be continued.

Schedule for Term Paper Presentations

Monday 03/10, 11am, 27 Wellman, Max McCoskey
Tuesday 03/11, 12:10pm, 693 Kerr, Justin Abbott
Wednesday 03/12, 11am, 27 Wellman, Ben-Shan Liao
Friday 03/14, 11am, 27 Wellman, Jeremy Clark
Talks are 50 minutes. Titles to be announced.

Instructor Contact Information

Bruno Nachtergaele (669 Kerr): office hours for MAT280 are by appointment. You can also just walk in and check whether I am available.

Office: Department of Mathematics, 669 Kerr Hall.
E-mail: bxn@math.ucdavis.edu. E-mail is my preferred medium for messages. Please use the phone numbers below only for emergencies.
Phone:    + (530) 750-1962 (home)
                + (530) 752-8061 (office)
                + (530) 752-6635 (fax)
Homepage: http://www.math.ucdavis.edu/~bxn/