Avoided level crossing statistics in open chaotic billiards

TL;DR

This paper develops a two-level model to analyze how open decay channels affect avoided level crossing statistics in chaotic billiards, revealing decay-induced modifications and matching experimental data.

Contribution

It introduces a new two-level model for open chaotic billiards that captures the impact of decay channels on avoided level crossing statistics, including explicit formulas for different symmetry cases.

Findings

Decay process causes attraction of resonances at small spacings.

Theoretical predictions match recent experimental results.

Open channels modify the probability distribution of avoided crossings.

Abstract

We investigate a two-level model with a large number of open decay channels in order to describe avoided level crossing statistics in open chaotic billiards. This model allows us to describe the fundamental changes of the probability distribution of the avoided level crossings compared with the closed case. Explicit expressions are derived for systems with preserved and broken Time Reversal Symmetry (TRS). We find that the decay process induces a modification at small spacings of the probability distribution of the avoided level crossings due to an attraction of the resonances. The theoretical predictions are in complete agreement with the recent experimental results of Dietz \textit{et al.} (Phys. Rev. E {\bf 73} (2006) 035201).