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

¹ Queen Mary University of London, School of Mathematical Sciences - London E1 4NS, UK
² Department of Mathematics, Brunel University London - Uxbridge, UB8 3PH, UK
³ Max Planck Institute for the Physics of Complex Systems - 01187 Dresden, Germany

Received: 24 March 2015
Accepted: 20 May 2015

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 priori assume the resonance widths being small compared to the mean level spacing. We show that to the leading order in weak coupling the perturbative 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that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.