Resonance width distribution in RMT: Weak-coupling regime beyond Porter-Thomas
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^2M 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that properly approximates the width distribution also at large resonance overlap, where the Porter-Thomas result is no longer applicable.
- Publication:
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EPL (Europhysics Letters)
- Pub Date:
- May 2015
- DOI:
- 10.1209/0295-5075/110/40006
- arXiv:
- arXiv:1503.06787
- Bibcode:
- 2015EL....11040006F
- Keywords:
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- Condensed Matter - Mesoscale and Nanoscale Physics;
- Mathematical Physics;
- Nonlinear Sciences - Chaotic Dynamics;
- Nuclear Theory
- E-Print:
- 6 pages, 1 figure (minor corrections, typos fixed)