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Title: Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas
Authors: Fyodorov, YV
Savin, DV
Issue Date: 2015
Publisher: IOP Publishing
Citation: EPL, 110, (4), (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 χ<inf>M</inf><sup>2</sup> 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that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.
Appears in Collections:Dept of Mathematics Research Papers

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