Spectra of random matrices close to unitary and scattering theory for discretetime systems
Abstract
We analyze the statistical properties of complex eigenvalues of random matrices which are close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. The deviation from unitarity is characterized by the rank M and eigenvalues T_{i}, i=1,…,M of the matrix T̂=1̂ ^{†} . For the case M=1 the problem is solved completely by deriving the joint probability density of the eigenvalues and calculating all npoint correlation functions. For the general case the correlation function of secular determinants is presented.
 Publication:

Disordered and Complex Systems
 Pub Date:
 February 2001
 DOI:
 10.1063/1.1358183
 arXiv:
 arXiv:nlin/0002034
 Bibcode:
 2001AIPC..553..191F
 Keywords:

 03.65.Nk;
 05.45.Mt;
 Scattering theory;
 Quantum chaos;
 semiclassical methods;
 Nonlinear Sciences  Chaotic Dynamics;
 Condensed Matter;
 Mathematical Physics
 EPrint:
 4 pages, latex, no figures, a few misprints are corrected