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Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis

Ph. Jacquod·D. L. Shepelyansky
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Abstract

We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized regimes with width independent on the band/system size. We analyse the implications of this distribution to the inverse participation ratio, level spacing statistics and the problem of two interacting particles in a random potential.

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Ph. Jacquod, D. L. Shepelyansky. 1995-09-18. Hidden Breit-Wigner distribution and other properties of random matrices with preferential basis. https://doi.org/10.1103/physrevlett.75.3501

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