Random Matrices and Supersymmetry in Disordered Systems

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It is described how one comes to the Wigner-Dyson random matrix theory (RMT) starting from a model of a disordered metal. The lectures start with a historical introduction where basic ideas of the RMT and theory of disordered metals are reviewed. This part is followed by an introduction into supermathematics (mathematics operating with both commuting and anticommuting variables). The main ideas of the supersymmetry method are given and basic formulae are derived. As an example, level-level correlations and fluctuations of amplitudes of wave functions are discussed. It is shown how one can both obtain known formulae of the RMT and go beyond. In the last part some recent progress in the further development of the method and possible perspectives are discussed.
Lectures given at the Les Houches Summer School "Applications of Random Matrices in Physics", June 2004, 45p

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Mesoscale and Nanoscale Physics, Disordered Systems and Neural Networks, High Energy Physics - Theory, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/99108

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0502322
 http://arxiv.org/abs/cond-mat/0502322
 Applications of Random Matrices in Physics, edited by E. Brezin, V. Kazakov, P. Wiegmann, and A. Zabrodin, Springer, p. 95 (2006)

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arXiv