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An Isaac Newton Institute Workshop

Random Matrix Theory and Arithmetic Aspects of Quantum Chaos

Granular bosonization (or Fyodorov meets SUSY)

18th May 2004

Author: Zirnbauer, M.R. (Uni Koeln)

Abstract

Random matrix methods can be roughly divided into two categories: methods which rely on having the joint probability density of the eigenvalues in closed form, and others which don't. Supersymmetry methods belong to the latter category.

The supersymmetry method used in the theory of disordered metals goes back to Schaefer and Wegner (1980). Quite recently, Fyodorov has proposed a related but different method, which computes averages of inverse characteristic polynomials for granular systems or random matrices with a hierarchical structure.

In this talk Fyodorov's method is reviewed, and it is shown how to generalize it to the case of characteristic polynomials (where it amounts to a form of bosonization) and to the case of ratios of such polynomials (the supersymmetric variant). Some applications to granular systems are presented.