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RANDOM MATRICES AND SUPERSYMMETRY IN DISORDERED SYSTEMS

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Applications of Random Matrices in Physics

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 221))

Abstract

It is described how one comes to theWigner-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. Both 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.

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Author information

Authors and Affiliations

  1. Theoretische Physik III, Ruhr-Universität Bochum, Bochum, 44780, Germany

    K.B. Efetov

  2. L.D. Landau Institute for Theoretical Physics, Moscow, 117940, Russia

    K.B. Efetov

Authors
  1. K.B. Efetov
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Editor information

Editors and Affiliations

  1. Laboratoire de Physique Théorique, Ecole Normale Supérieure, Paris, France

    Édouard Brézin

  2. Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, Université Paris-VI, Paris, France

    Vladimir Kazakov

  3. Service de Physique Théorique, CEA Saclay, Gif-sur-Yvette Cedex, France

    Didina Serban

  4. James Frank Institute, University of Chicago, Chicago, IL, U.S.A.

    Paul Wiegmann

  5. Institute of Biochemical Physics, Moscow, Russia

    Anton Zabrodin

  6. ITEP, Moscow, Russia

    Anton Zabrodin

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© 2006 Springer

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Efetov, K. (2006). RANDOM MATRICES AND SUPERSYMMETRY IN DISORDERED SYSTEMS. In: Brézin, É., Kazakov, V., Serban, D., Wiegmann, P., Zabrodin, A. (eds) Applications of Random Matrices in Physics. NATO Science Series II: Mathematics, Physics and Chemistry, vol 221. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4531-X_4

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