Physics 704: (Advanced) Statistical Mechanics

Spring 2011 3 credits

Instructor: Prof. Ted Einstein, x56147, einstein@umd.edu

Class meeting times: T, Th 11-12:15; Physics Building, Rm. 0405

Office hours: After class and whenever office door open, or by appointment.

Course Text:  M. Plischke and B. Bergerson, Equilibrium Statistical Physics, 3rd ed., World Scientific, 2006; pb [ 9812561552]

I used the second edition in 2001 and found it to be an excellent book, treating material of contemporary interest at an appropriate level without excessive verbiage or detail. However, its coverage was incomplete. The 3rd edition remedies this.

Other highly recommended texts: (See also the extensive Reference list.)

Michel Le Bellac, Fabrice Mortessagne, and G. George Batrouni, Equilibrium and Non-Equilibrium Statistical Thermodynamics, Cambridge, 2004; [0521821436].  Used as the text in 2006, but not enough orientation toward condensed matter.

Paul M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge, 2000; pb [0521794501]. About half the text is germane to this course. Specifically, we will cover much of (but not all of) chaps. 3–5, 7, 9, 10, with a few sections for other chapters. We will not study liquid crystals or hydrodynamics, except for a few basic ideas. In some cases C&L is more detailed than ideal but, compensatingly, it is quite thorough. Excerpts from other books will be provided as appropriate.

Mehran Kardar, Statistical Physics of Fields, Cambridge, 2007; [978-0-521-87341-3]

L. P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization, World Scientific, 2000; pb [9810237642]; unique perspective and many important reprints.

http://www.physics.cornell.edu/sethna/StatMech/EntropyOrderParametersComplexity.pdf

J.M. Thijssen, Computational Physics, Cambridge, 1999; pb [052157588]: lots of physics, presented in a format useful for computations, but over 1/3 on electronic aspects.

This course is most suitable for students who have taken Physics 603 and/or passed the classical part of the physics qualifier, though neither is required. Topics will include

Brief review and notations

Correlation functions

Mean field and Landau theory

Aspects of dense gases and fluids

Critical phenomena (scaling, simple models, renormalization group, roughening)

Numerical simulations (Monte Carlo, molecular dynamics, transfer matrix methods)

Disordered systems

Statistical mechanical aspects surfaces

Intro. to non-equilibrium stat. mech. (esp. Langevin and Fokker-Planck equations).

Other topics might include

Models of crystal growth

Polymers and membranes

Quantum fluids

Linear response theory

Conformal invariance and phase transitions in 2 dimensions

Since the enrollment of this course is expected to be relatively small, the choice of topics can be flexibly tailored to students' interests and planned research areas.

There will be regular homework assignments and a final exam, possibly oral. To share special interests, students may be asked to prepare 1/2-hour class presentations.