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 $H_{i\ge j}$ with small off-diagonal elements: $<|H_{i\ne j}{|}^2>\ll <|H_{ii}{|}^2>\sim 1$. Using the recently suggested method of a {\it virial expansion in the number of interacting energy levels} (Journ.Phys.A {\bf 36}, 8265), 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 DOS of these models.

submitted to Phys. Rev. E

References in corpus (2)

• Virial expansion for almost diagonal random matrices
• Energy level statistics of a critical random matrix ensemble

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