A new approach to strongly correlated disorder

TL;DR

This paper introduces the average trace approximation to analyze systems with correlated disorder, revealing how such correlations influence the density of states, exemplified by harmonic oscillators, with results supported by simulations.

Contribution

The paper proposes a novel approximation method for disordered systems with correlated disorder, extending analysis beyond traditional random disorder models.

Findings

Correlation in disorder causes a peak in low frequency density of states

The approximation results align with computer simulations

The method provides insights into the effects of correlated disorder

Abstract

Problems involving disordered systems are usually analyzed for systems with random disorder. However, there are many systems in which the main disorder involves clusters with correlated differences between their properties and those of the average system. A new approximation, the average trace approximation, is proposed for calculating the diagonal elements of the Green function, and hence the density of states, in such systems. As an example, application of the method to a simple cubic array of harmonic oscillators shows that correlation in the disorder leads to a peak in the low frequency density of states, a result confirmed by computer simulations.