Advanced Statistical Physics: February - July, 2021
TIFR graduate school 2021
Updated, July 14, 2021
Instructor: Tridib Sadhu
Teaching assistant: Aman Kumar
Class timings: Wednesday 16h and Friday 17h45. Each class 1h 30min long. Total around 56 hours of lectures.
Master equation, Langevin and Fokker Planck description, Path integral for stochastic processes. Few important results for Brownian motion, Levy flight, Anomalous diffusion. Extreme events and Large deviations.
Concepts of equilibrium and non-equilibrium, Time reversibility, Stochastic trajectories.
Revision of basic equilibrium concepts, Phase transitions, Lee-Yang theory.
Question of order, Peierls argument, Graphical expansion and duality, Mermin-Wagner theorem, Entropic forces.
Exact solution of lattice models: Ising on 1d and Bethe lattice. Ising on 2d by transfer matrix and graphical methods, Potts model, Dimer covering, Heisenberg model (Bethe ansatz).
Renormalization group: Idea and phenomenology, Real-space RG, Epsilon expansion.
Dynamics: Phase ordering kinetics, Model A and B dynamics.
Out of equilibrium:
Fluctuation theorems (Jarzynski relation, Gallavotti-Cohen symmetry), Linear response outside equilibrium, Onsager-Machlup theory .
Non-equilibrium processes: Interface growth (EW and KPZ), Disordered medium, Exactly solvable models (zero range process, exclusion process using Matrix algebra and Bethe ansatz), Transport phenomena, Active matter, Non-equilibrium phase transitions.
Hydrodynamic approach for non-equilibrium systems.
M. Kardar: Statistical Physics of Fields.
G. Mussardo: Statistical Field Theory
N. Goldenfeld: Lectures on phase transitions and the renormalization group.
Lecture note of Abhishek Dhar (ICTS). These are basic concepts of probability theory. I expect that these concepts
are known to all of you from Stat Phys I course, and they will not be covered. If you have difficulty, please let me
know and I can help.