Universality in spectral statistics of "open" quantum graphs

TL;DR

This paper demonstrates that non-unitary quantum graphs with absorption exhibit universal spectral statistics at the spectrum edges, similar to classical non-unitary random matrix ensembles, extending universality concepts to open quantum systems.

Contribution

It reveals the universality of spectral statistics at the spectrum edges in open quantum graphs with absorption, linking quantum graph behavior to classical non-unitary random matrix ensembles.

Findings

Spectral statistics at the spectrum edges are universal in open quantum graphs.

Universality observed in classical non-unitary random matrix ensembles.

Non-unitary quantum maps with absorption show similar spectral behavior to random matrices.

Abstract

The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their spectral statistics exhibit universality at the "soft" edges of the spectrum. The same spectral behavior is observed in many classical non-unitary ensembles of random matrices with rotationally invariant measures.