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

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

2000-05-29

arxiv.org/abs/nlin/0005061v1

JETP Lett. 72, 422--426 (2000)

Nonlinear Sciences

Chaotic Dynamics

Complete solution of the problem discussed in earlier e-preprint nlin.CD/0002034

Scientific paper

10.1134/1.1335121

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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