K. B. Efetov
Published 2010-02-12Version 1
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 $\sigma$-model is derived. Solution of several problems obtained with the help of the $\sigma$-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.
Comments: Submitted as a chapter in the book "Fifty Years of Anderson Localization"
Journal: Int.J.Mod.Phys.B24:1756-1788,2010
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