Supersymmetry in disordered and chaotic systems - Lecture 01
The course of the lectures will serve as an introduction into supersymmetry method for studying disordered systems. I will start presenting basic information about Anderson localization and random matrices. Then, I will introduce Grassmann anticommuting variables and integrals over them. This will be followed by introducing supervectors, supermatrices and other “superobjects”. This knowledge will allow one to write correlation functions of interest in terms of integrals over supervectors. Finally, a non-linear sigma-model will be derived. Goldstone modes described by this model can be treated within this model non-perturbatively. The main structure of Q-matrices entering the sigma-model will be explained and the main difference with respect to conventional sigma-models will be emphasized. It will be shown how to study Anderson localization, level statistics and other problems of interest using the developed method.