Density of states for almost diagonal random matrices

Details Density of states for almost diagonal random matrices Density of states for almost diagonal random matrices

2003-09-24

arxiv.org/abs/cond-mat/0309548v1

Phys.Rev. E69 (2004) 026104

Physics

Condensed Matter

Disordered Systems and Neural Networks

submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.69.026104

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 \geq j} $ with small off-diagonal elements: $ <|H_{i \neq 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.

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