Distribution of local density of states in superstatistical random matrix theory

TL;DR

This paper links the distribution of local spectral density of states in disordered systems with superstatistics in random matrix theory, proposing a model that aligns well with numerical data for disordered wires.

Contribution

It introduces a connection between local density of states distribution and superstatistics, applying it to disordered conductors within random matrix theory.

Findings

Distribution matches numerical results for disordered wires

Supports using superstatistics to model disordered conductors

Provides a framework for estimating parameter distributions in superstatistical ensembles

Abstract

We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random matrix theory. The latter represents the matrix-element joint probability density function as an average of the corresponding quantity in the standard random-matrix theory over a distribution of level densities. We show that this distribution is in reasonable agreement with the numerical calculation for a disordered wire, which suggests to use the results of theory of disordered conductors in estimating the parameter distribution of the superstatistical random-matrix ensemble.