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Spectra of Random Contractions and Scattering Theory for Discrete-Time Systems | | Yan V. Fyodorov
; H.-J.Sommmers
; | | Date: |
29 May 2000 | | Journal: | JETP Lett. 72, 422--426 (2000) | | Subject: | Chaotic Dynamics | nlin.CD cond-mat | | 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 $N imes N$ random matrices $hat{A}$ of such a type, corresponding to systems with broken time-reversal invariance. Deviations from unitarity are characterized by rank $Mle N$ and a set of eigenvalues $0>M,n$ the correlation functions acquire the universal form found earlier for weakly non-Hermitian random matrices. | | Source: | arXiv, nlin.CD/0005061 | | Services: | Forum | Review | PDF | Favorites | |
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