Introduction to the Supersymmetry Method for the Gaussian Random-Matrix Ensembles

This article is intended to provide a pedagogical introduction to the supersymmetry method for performing ensemble-averaging in Gaussian random-matrix theory. The method is illustrated by a detailed calculation of the simplest non-trivial physical quantity, namely, the second-order correlation in the density of states for two different energies within the spectrum (commonly known as the density-density correlator) for a system described by a random Hamiltonian matrix belonging to the Gaussian unitary ensemble. PACS numbers: 05.40.+j, 71.20.−b, 05.50.+q, 24.60.−k Current address: Aeronautical Research Laboratory, Air Operations Division, P.O. Box 4331, Melbourne, Australia. (E-mail: [email protected]) CONTENTS