Density of states for almost-diagonal random matrices.

Abstract

We study the density of states (DOS) for disordered systems whose spectral statistics can be described by a Gaussian ensemble of almost-diagonal Hermitian random matrices. The matrices have independent random entries H(i > or =j) with small off-diagonal elements: <|H(i not equal to j)|2> << <|H(ii)|2> approximately 1. Using the recently suggested method of a virial expansion in the number of interacting energy levels [J. Phys. A 36, 8265 (2003)], we calculate the leading correction to the Poissonian DOS in the cases of the Gaussian orthogonal and unitary ensembles. We apply the general formula to the critical power-law banded random matrices and the unitary Moshe-Neuberger-Shapiro model and compare the DOS's of these models.