Non-Hermitian Euclidean random matrix theory

TL;DR

This paper develops a theoretical framework for analyzing the eigenvalue density of non-Hermitian Euclidean matrices, with applications to wave propagation, localization, and lasing in disordered media.

Contribution

It introduces a new theory for eigenvalue distributions of non-Hermitian Euclidean matrices, including closed-form equations for resolvent and eigenvector correlator.

Findings

Derived closed equations for resolvent and eigenvector correlator.

Applied theory to Green's matrix in wave scattering.

Provides insights into wave diffusion, localization, and lasing phenomena.

Abstract

We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave propagation in an ensemble of point-like scattering centers. This opens a new perspective in the study of wave diffusion, Anderson localization, and random lasing.