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

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

1994-12-13

arxiv.org/abs/cond-mat/9412060v3

Physics

Condensed Matter

36 pages, LaTeX, No figures. New address for correspondence. Some misprints corrected and background material added.

Scientific paper

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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