Nearest level spacing statistics in open chaotic systems: a generalization of the Wigner Surmise

TL;DR

This paper derives generalized nearest level spacing distributions for open chaotic systems, explaining environmental coupling effects, and validates the formulas with simulations and experiments.

Contribution

It introduces a generalized surmise for level spacing statistics in open systems, extending the classical Wigner Surmise to multi-channel cases with a free parameter.

Findings

Derived analytical expressions for spacing distributions in open chaotic systems.

Validated the formulas with numerical simulations of non-Hermitian matrices.

Confirmed the model's accuracy with experimental data from electromagnetic cavities.

Abstract

We investigate the nearest level spacing statistics of open chaotic wave systems. To this end we derive the spacing distributions for the three Wigner ensembles in the one-channel case. The theoretical results give a clear physical meaning of the modifications on the spacing distributions produced by the coupling to the environment. Based on the analytical expressions obtained, we then propose general expressions of the spacing distributions for any number of channels, valid from weak to strong coupling. The latter expressions contain one free parameter. The surmise is successfully compared with numerical simulations of non-Hermitian random matrices and with experimental data obtained with a lossy electromagnetic chaotic cavity.