Advanced Statistical Physics
Instructor: S.K. Bose
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.
Textbook:

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:

  • 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
The last two books are suggested for making up for any background deficiency in the subject

Marking scheme:

assignments (40%), 1 midterm test (25%), final exam (35%)

late assignments will not be accepted unless approved by the instructor