Binary correlations in random matrix spectra

The spectrum for a Gaussian orthogonal ensemble of random matrices augmented by a pairing interaction, which has been given by Edwards and Jones (1976) and by Jones, Kosterlitz and Thouless (1978), is derived in other ways.

Abstract

The spectrum for a Gaussian orthogonal ensemble of random matrices augmented by a pairing interaction, which has been given by Edwards and Jones (1976) and by Jones, Kosterlitz and Thouless (1978), is derived in other ways. Several extensions are given and relationships to other problems of current interest discussed. Stress is laid on the importance of the dominance of binary Hamiltonian correlations in the moments which define the density and relevant correlation functions.