TL;DR
This paper reviews the supersymmetry method for disordered systems, deriving the nonlinear supermatrix sigma-model and applying it to problems like level statistics, localization, and the Anderson transition.
Contribution
It introduces the supersymmetry approach and derives the sigma-model, providing new analytical tools for studying disordered electronic systems.
Findings
Solution of level statistics in small metal grains
Analysis of localization in wires and films
Insights into the Anderson metal-insulator transition
Abstract
The supersymmetry method for study of disordered systems is shortly reviewed. The discussion starts with a historical introduction followed by an explanation of the idea of using Grassmann anticommuting variables for investigating disordered metals. After that the nonlinear supermatrix -model is derived. Solution of several problems obtained with the help of the -model is presented. This includes the problem of the level statistics in small metal grains, localization in wires and films, and Anderson metal-insulator transition. Calculational schemes developed for studying these problems form the basis of subsequent applications of the supersymmetry approach.
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