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

• Published in: Europhysics letters Vol. 110; no. 4; pp. 40006 - p1-40006-p6
• Main Authors: Fyodorov, Yan V., Savin, Dmitry V.
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences, IOP Publishing and Società Italiana di Fisica 01.05.2015; IOP Publishing
• Subjects: 03.65.Nk; 05.45.Mt; 05.60.Gg; Approximation; Channels; Coupling; Joining; Mathematical analysis; Matrix theory; Open channels; Perturbation theory; Polynomials; Resonance; Spectra; Texts
• ISSN: 0295-5075; 1286-4854
• DOI: 10.1209/0295-5075/110/40006

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that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.