Spectra of random matrices close to unitary and scattering theory for discrete-time 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 Ti, 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 n-point 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
- E-Print:
- 4 pages, latex, no figures, a few misprints are corrected