Josef A. Zuk | Searcharxiv

arXiv1996

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.

cond-mat↗

arXiv1996

Applications of the Dotsenko-Fateev Integral in Random-Matrix Models

The characteristic multi-dimensional integrals that represent physical quantities in random-matrix models, when calculated within the supersymmetry method, can be related to a class of integrals introduced in the context of two-dimensional conformal field theories by Dotsenko & Fateev. Known results on these Dotsenko-Fateev integrals provide a means by which to perform explicit calculations (otherwise difficult) in random-matrix theory. We illustrate this by (i) an evaluation of the mean squared S-matrix elements for the Gaussian orthogonal ensemble coupled with M external channels, and (ii) a direct derivation of the asymptotic behaviour of the dynamical density-density correlator in the limit of large spatial and temporal separation for the Calogero-Sutherland model which, at certain couplings, is known to map onto the parameter-dependent random matrix ensembles.

cond-mat↗