Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas

TL;DR

This paper revises the understanding of resonance width distributions in quantum chaotic systems with weak coupling, introducing corrections to the Porter-Thomas distribution using random matrix theory beyond first-order perturbation.

Contribution

It provides a corrected distribution formula for resonance widths in RMT, valid beyond the weak coupling limit and not assuming small widths relative to level spacing.

Findings

Corrects the Porter-Thomas distribution with a spectral determinant factor.

Derives a simple expression valid at large resonance overlap.

Shows the corrected distribution aligns with numerical simulations.

Abstract

We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the standard first-order perturbation theory treatment we do not a priory assume the resonance widths being small compared to the mean level spacing. We show that to the leading order in weak coupling the perturbative $\chi^2_M$ distribution of the resonance widths (in particular, the Porter-Thomas distribution at M=1) should be corrected by a factor related to a certain average of the ratio of square roots of the characteristic polynomial ("spectral determinant") of the underlying RMT Hamiltonian. A simple single-channel expression is obtained that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.