Universal spectral correlations in ensembles of random normal matrices

TL;DR

This paper studies non-Gaussian ensembles of random normal matrices, revealing universal spectral correlations and a disk-to-ring eigenvalue transition, confirmed through Monte Carlo simulations and applications to quantum systems.

Contribution

It demonstrates the universality of eigenvalue correlations in non-Gaussian normal matrix ensembles and identifies a spectral transition in the complex plane.

Findings

Eigenvalue density transitions from disk to ring

Eigenvalue correlations match those of Ginibre ensemble

Universality confirmed in quantum dissipative systems

Abstract

We consider non-gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk to ring transition in the complex plane. We also show that the n-eigenvalue correlation and the spacing distribution are universal and identical to that of complex (Gaussian) Ginibre ensemble. Our results are confirmed by Monte Carlo calculations. We verify the universality for dissipative quantum kicked rotor system.