Anderson Localization in Euclidean Random Matrices

TL;DR

This paper investigates the spectral and localization characteristics of Euclidean random matrices, introducing a novel method to determine the density of states and localization thresholds, with applications to liquid system normal modes.

Contribution

It presents a new approach to analyze Euclidean random matrices by mapping to random graphs and solving an exact distribution equation using population dynamics.

Findings

Method effectively finds density of states.

Accurately determines localization thresholds.

Applied to liquid system normal modes.

Abstract

We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the localization threshold. We solve numerically an exact equation for the probability distribution function of the diagonal element of the the resolvent matrix, with a population dynamics algorithm, and we show how this can be used to find the localization threshold. An application of the method in the context of the Instantaneous Normal Modes of a liquid system is given.