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

2015/03/31 by Yan V. Fyodorov, Dmitry V. Savin · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.mes-hall #math-ph #math.MP #nlin.CD #nucl-th

paper · pdf · doi:10.1209/0295-5075/110/40006

published as EPL (Europhys. Lett.) 110, 40006 (2015) · 6 pages, 1 figure (minor corrections, typos fixed)

arxiv created 2015/06/09 · arxiv updated 2015/06/10

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 χ²_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that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.

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• Random Matrix Theory for Chaotic Wave Scattering and Transport