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

1994/12/13 by Josef Zuk, Zuk, Josef A.
Mathematics · Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum optics and atomic interactions #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.cond-mat/9412060

openalex publication_date 1994/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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