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Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems

Yan V. Fyodorov·H. -J. Sommmers
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Abstract

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex eigenvalues of generic $N\times N$ random matrices $\hat{A}$ of such a type, corresponding to systems with broken time-reversal invariance. Deviations from unitarity are characterized by rank $M\le N$ and a set of eigenvalues $0 >M,n$ the correlation functions acquire the universal form found earlier for weakly non-Hermitian random matrices.

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Yan V. Fyodorov, H. -J. Sommmers. 2000-05-29. Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems. https://doi.org/10.1134/1.1335121

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