Statistical properties of chaotic microcavities in small and large opening cases

TL;DR

This paper investigates how the statistical properties of eigenvalues in chaotic microcavities change with varying refractive indices and opening strengths, revealing a transition from Wigner to Poisson distributions and proposing a new non-Hermitian matrix model.

Contribution

It introduces a non-Hermitian matrix model to describe the spectral crossover behaviors in chaotic microcavities with different opening strengths.

Findings

Eigenvalue level spacing distributions shift from Wigner to Poisson with decreasing refractive index.

The proposed model captures the spectral crossover as opening strength increases.

The study provides insights into the spectral statistics of open chaotic microcavities.

Abstract

We study the crossover behavior of statistical properties of eigenvalues in a chaotic microcavity with different refractive indices. The level spacing distributions change from Wigner to Poisson distributions as the refractive index of a microcavity decreases. We propose a non-hermitian matrix model with random elements describing the spectral properties of the chaotic microcavity, which exhibits the crossover behaviors as the opening strength increases.