# Anderson localization and Supersymmetry - Condensed Matter > Disordered Systems and Neural Networks

Abstract: The supersymmetry method for study of disordered systems is shortly reviewed.The discussion starts with a historical introduction followed by an explanationof the idea of using Grassmann anticommuting variables for investigatingdisordered metals. After that the nonlinear supermatrix $\sigma$-model isderived. Solution of several problems obtained with the help of the$\sigma$-model is presented. This includes the problem of the level statisticsin small metal grains, localization in wires and films, and Andersonmetal-insulator transition. Calculational schemes developed for studying theseproblems form the basis of subsequent applications of the supersymmetryapproach.

Author: K.B. Efetov

Source: https://arxiv.org/