PHY604A - Review of Statistical Mechanics

Problem oriented review of Statistical Mechanics. Review of thermodynamics: Laws of thermodynamics; thermodynamics of phase transitions and phase diagram. Review of Ensembles and rules of calculation: Micro canonical, canonical, grand canonical and other ensembles; applications to models of ideal classical and quantum gases. Models of classical interacting systems : Ising model in 1dimension: exact solution by transfer matrix ; Peierls Griffiths argument for Ising model in 2dimensions; Mean field approximation for magnets and fluids, Landau Theory, critical exponents, upper and lower critical dimensions. Models of quantum interacting systems : Density matrix, Transverse Ising model, exact solution by Jordan Wigner transformation, Heisenberg model magnons; Mermin Wagner theorem; general theory of quantum phase transitions. Brief overview of Non equilibrium statistical mechanics: Random walk and diffusion, Markov processes and master equation; Systems near equilibrium Linear Response Theory, Fluctuation. Dissipation Theorem; Escape over a barrier relaxation phenomena; critical dynamics. Supplementary reading materials for term papers: Momentum space Renormalization Group, Real space Renormalization Group, Duality in Statistical mechanics, Various types of series expansions, Boltz mann equation, Molecular hydro dynamics, BBGKY hierarchy; Random and glassy systems, Linear and branched Polymers, Percolation; XY model and vortices super fluidity.