Teaching
Teaching
Statistical Mechanics @TIFR (Feb - May, 2025)
Review of thermodynamics
Foundations of Statistical Physics: macroscopic vs. microscopic variables, phase space, Liouville's theorem, ergodic approach
Ensembles (Microcanonical, Canonical, and Grand canonical) and their equivalence, relationship to thermodynamic potentials
Non-interacting Classical Systems: Classical Ideal gas
Noninteracting Quantum Systems: Ideal quantum gases, Indistinguishability, Bose, Fermi and
Boltzmann statistics, Bose-Einstein condensation
Phases and phase transitions, first and second order transitions
Kinetic theory: BBGKY hierarchy, Boltzmann equation, Boltzmann H theorem
Phase transitions in and out of equilibrium: Phenomena and Techniques @TIFR (Jan - May, 2023)
Basic introduction to phase transitions: first order and continuous
Phase transitions in equilibrium
Critical phenomena: critical exponents and scaling hypothesis
Ising model: exact solution in one dimension, discussion of the model in two dimensions
Two-dimensional XY model and the Kosterlitz-Thouless transition
Mean-field approximation and calculation of critical exponents
Landau theory of phase transitions
Renormalization group (preliminary ideas)
Phase transitions out of equilibrium
Review of probability theory: Law of large numbers and the central limit theorem, Large deviations (introductory ideas)
Stochastic processes: Markovian approximation, Master equation, Fokker-Planck equation, Langevin description, concept of steady states, detailed balance and equilibrium vs. nonequilibrium
Random walk, Brownian motion, Langevin and Fokker-Planck descriptions, Fluctuation-Dissipation theorem
Phase transitions in the asymmetric simple exclusion process and the zero-range process