Advanced Statistical Physics
Course outline: (Brock 2012-13 Graduate Calendar Description:
Statistical ensembles; mean field and Landau theory, critical phenomena, and the renormalization group; quantum fluids; superfluidity; selected topics on disordered systems.)
Major topics and subtopics:
Review of microcanonical, canonical and grand canonical formalism, Density operator and density matrix formulation.
Quantum gases and fluids, Superfluidity of liquid He II, Landau criterion of superfluidity, Bogoliubov and Brueckner-Sawada theories, Feynman variational treatment.
Topics from theory of liquids and disordered systems, structure factor and pair correlation function, n-body distribution function, deriving inter-atomic potentials from n-body correlation functions.
Phase transitions and critical phenomena:
critical exponents, exponent equalities and inequalities, transfer matrix method,Mean Field methods: Weiss Molecular field, Landau and Landau-Ginzburg theories, improvements over mean field: Bethe and higher order cluster methods,
Finite size scaling, universality hypothesis and classes, introduction to renormalization group method. localization in random media, scaling theory of localization.
There is no required textbook for the course. The library has many textbooks on this subject and students can choose any book
they find suitable. Some suggested books are:
The last two books are suggested for making up for any background deficiency in the subject
- Statistical Mechanics by R.K. Pathria, QC175 P37
- Equlibrium Statistical Physics by M. Plischke and B. Bergersen, QC174.8 P55 1998
- Introduction to Phase Transitions and Critical Phenomena by H. Eugene Stanley, QC 307 S7
- A modern course in Statistical Physics by L.E. Reichl, QC174.8 R44, QC174.8 R44 1998
- Statistical mechanics by Kerson Huang, QC 175 H83, QC 174.8 H83 1987
- Fundamentals of Statistical and Thermal Physics by F. Reif, QC 175 R43
- Elementary Statistical Physics by C. Kittel, QC 175 K58
assignments (40%), 1 midterm test (25%), final exam (35%)
late assignments will not be accepted unless approved by the instructor