S-matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices: from isolated to overlapping resonances

1998/07/09 by H. -J. Sommers, Yan V. Fyodorov, M. Titov · 1 citation
Physics and Astronomy · #chao-dyn #cond-mat #nlin.CD

paper · pdf · doi:10.1088/0305-4470/32/5/003

published as J. Phys. A 32, L77 (1999) · 8 pages+2 eps figures

arxiv created 1998/07/09 · arxiv updated 2010/03/01

Abstract

We study complex eigenvalues of large N× N symmetric random matrices of the form \cal H=H-iΓ, where both H and Γ are real symmetric, H is random Gaussian and Γ is such that NTr Γ²₂∼ Tr H₁² when N→ ∞. When Γ≥ 0 the model can be used to describe the universal statistics of S-matrix poles (resonances) in the complex energy plane. We derive the ensuing distribution of the resonance widths which generalizes the well-known χ² distribution to the case of overlapping resonances. We also consider a different class of "almost real" matrices when Γ is random and uncorrelated with H.

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• Random Matrix Theory for Chaotic Wave Scattering and Transport