Anderson localization and Supersymmetry

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 $\sigma$-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.

Submitted as a chapter in the book "Fifty Years of Anderson Localization"

References in corpus (6)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• Statistics of energy levels and eigenfunctions in disordered systems
• Field theory of the quantum kicked rotor
• Quantum Transport in Disordered Wires: Equivalence of One-Dimensional Sigma Model and Dorokhov-Mello-Pereyra-Kumar Equation
• Wigner-Dyson Statistics from the Keldysh Sigma-Model