Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances

TL;DR

This paper derives the distribution of resonance widths in chaotic quantum systems with multiple open channels, revealing a transition from isolated to overlapping resonances and confirming the Moldauer-Simonius relation.

Contribution

It provides an explicit formula for the resonance width distribution across different resonance regimes, bridging isolated and overlapping resonances in chaotic scattering.

Findings

Distribution transitions from chi-squared to power-law

First moment matches Moldauer-Simonius relation

Highlights spectral and ensemble averaging equivalence

Abstract

We derive the explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the $\chi^2$ distribution (regime of isolated resonances) to a broad power-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer-Simonius relation between the mean resonance width and the transmission coefficient. This fact may serve as another manifestation of equivalence between the spectral and the ensemble averaging.