Resonance distribution in open quantum chaotic systems

TL;DR

This paper investigates the distribution of resonance decay rates in open quantum chaotic systems with damping, revealing clustering near a typical value that exceeds classical decay rates, and discusses implications for numerical detection.

Contribution

It introduces a model of damped quantum maps to analyze resonance spectra and explains the slow clustering of decay rates in high-frequency regimes.

Findings

Decay rates cluster near a typical value higher than classical decay rates.

Clustering occurs slowly, possibly explaining previous numerical challenges.

Provides a theoretical framework for resonance distribution in damped chaotic systems.

Abstract

In order to study the resonance spectra of chaotic cavities subject to some damping (which can be due to absorption or partial reflection at the boundaries), we use a model of damped quantum maps. In the high-frequency limit, the distribution of (quantum) decay rates is shown to cluster near a ``typical'' value, which is larger than the classical decay rate of the corresponding damped ray dynamics. The speed of this clustering may be quite slow, which could explain why it has not been detected in previous numerical data.