Course Description: Following a review of thermodynamics, we study the fundamentals of classical and quantum statistical mechanics including ensembles, identical particles, Bose and Fermi statistics, phase-transitions and critical phenomena, renormalization group, irreversible processes and fluctuations. Prerequisites: PHYS 265 or equivalent.
Section Description: This graduate level course builds on undergraduate training in thermodynamics and statistical me- chanics and will utilize and expand upon foundational concepts including phase space and state variables. We will focus on the theoretical description of the phases of matter and the transitions between them, paying special attention to the universal physics that arises at continuous sec- ond order phase transitions. Modern computational techniques will be employed including Monte Carlo methods for studying models of magnetism. An outline of topics that will be covered includes: 1. Review: thermodynamics, statistical physics, the partition function and Liouville’s theorem. 2. Phases and Models: solids, liquids and gases, magnetism and the Ising model, and symmetry breaking. 3. Exact Solutions: Ising model in 1 and 2 spatial dimensions. 4. Approximation Methods: mean field theory, low and high temperature expansions. 5. Critical Phenomena in Fluids: phase coexistence, the van der Waals equation and critical exponents. 6. Landau Theory: order parameters, continuous phase transitions and correlation functions. 7. Fluctuations: breakdown of Landau theory and the Gaussian approximation. 8. Anomalous Dimensions: the failure of simple dimensional analysis 9. The Renormalization Group: real space block spins, fixed points and scaling. 10. Extra Topics: continuous symmetry and the Kosterlitz-Thouless transitions, quantum phase transitions, advanced numerical methods.
|TR||14:50 - 16:05||VOTEY BLDG 223|
Instructor(s): Adrian Del Maestro
Meeting Dates: 26 Aug 2019 - 06 Dec 2019