Transitions In Spectral Statistics

TL;DR

This paper investigates the long-range spectral statistics of a novel unitary random matrix ensemble, revealing how its properties transition from Wigner to Poisson distributions based on a single parameter.

Contribution

It introduces and analyzes a new unitary random matrix ensemble with spectral properties that interpolate between Wigner and Poisson statistics.

Findings

Spectral statistics exhibit a transition from Wigner to Poisson as the parameter varies.

Long-range correlations differ significantly from short-range behaviors.

The ensemble models a continuous transition in spectral statistics.

Abstract

We present long range statistical properties of a recently introduced unitary random matrix ensemble, whose short range correlations were found to describe a transition from Wigner to Poisson type as a function of a single parameter.