Quantum methods for stochastic dynamics

These lectures will take place on Feb. 3rd, 4th and 5th, 2016, from 13:30 till 15:00 and 15:30 till 17:30 in room K206 of the Yukawa Institute, Kyoto University. See here.

Lecture notes in preparation

Lecture 1
Stochastics dynamics. Master equation, Fokker-Planck, Langevin. Itô vs. Stratonovitch. Martin-Siggia-Rose-Janssen-De Dominicis path integral formulation.

Lecture 2
Reversibility, irreversibility, entropy production, Gallavotti-Cohen theorem, linear response, Fluctuation-Dissipation theorem. Supersymmetry and its uses in classical stochastics dynamics.

Lecture 3
Many-body problems and quantum spin chains, interacting fermions and interacting bosons. Kinetic Ising model.

Lecture 4
Nonequilibrium phase transitions and critical phenomena. Field theoretic methods. Doi-Peliti.


Lecture 5
Fluctuating hydrodynamics of diffusive systems. WKB method. The Simple Symmetric Exclusion Process.

Lecture 6
Dynamical large deviations in classical systems and quantum phase transitions.