PHYS 6562 - Statistical Physics I

Spring. 4 credits.

Prerequisite: good knowledge of quantum mechanics, classical mechanics, and undergraduate-level thermodynamics or statistical mechanics class. Primarily for graduate students.

Staff.

Starts with Hamiltonian mechanics of a single degree of freedom and its extension to many body system, ultimately arguing for probabilistic description of statistical mechanical system. Derives the Boltzmann equation from time-evolution of phase space density as a probability density, and applies the formalism to near-equilibrium examples. Reviews thermodynamics. Covers equilibrium ensembles: micro-canonical, canonical, and grand-canonical ensemble. Covers quantum statistical mechanics of ideal bose and fermi gas and discusses Bose-Einstein condensation and Fermi pressure. Discusses fundamental descriptions of phases using microscopic lattice models such as Ising model at different dimensions. Monte Carlo technique and Landau-Ginzburg theory is introduced as a classical field theory, order parameters, and the homotopy classification of topological defects. Concludes with a discussion of critical phenomena, scaling, universality, and the renormalization group.