Statistics of Resonances in a Semi-infinite Disordered Chain

Abstract

We study the average density of resonances (DOR) for a semi-infinite disordered chain, coupled to the outside world by a (semi-infinite) perfect lead. A set of equations is derived, which provides the general framework for calculating the average DOR, for an arbitrary disorder and coupling strength. These general equations are applied to the case of weak coupling and an asymptotically exact expression for the averaged DOR is derived, in the limit of small resonance width. This expression is universal, in the sense that it holds for any degree of disorder and everywhere in the (unperturbed) energy band.

12 pages, 1 figure

References in corpus (7)

• Probing Anderson localization of light via decay rate statistics
• Universality of the Wigner time delay distribution for one-dimensional random potentials
• Statistics of Resonances and Delay Times in Random Media: Beyond Random Matrix Theory
• Time Delay Correlations and Resonances in 1D Disordered Systems
• Distribution of resonance widths in localized tight-binding models
• Resonance width distribution for high-dimensional random media
• Resonances in one-dimensional Disordered Chain

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