Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis

TL;DR

This paper investigates the spectral properties of band random matrices relevant to interacting particle systems, revealing that their local spectral density follows a Breit-Wigner distribution with size-independent width, impacting various spectral statistics.

Contribution

It introduces the concept of a hidden Breit-Wigner distribution in the spectral density of band random matrices and explores its implications for spectral statistics and particle interactions.

Findings

Spectral density follows Breit-Wigner distribution in both regimes

Width of distribution is independent of system size

Impacts inverse participation ratio and level spacing statistics

Abstract

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized regimes with width independent on the band/system size. We analyse the implications of this distribution to the inverse participation ratio, level spacing statistics and the problem of two interacting particles in a random potential.