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Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0002034 (nlin)
[Submitted on 21 Feb 2000 (v1), last revised 22 Feb 2000 (this version, v2)]

Title:Spectra of Random Matrices Close to Unitary and Scattering Theory for Discrete-Time Systems

Authors:Yan V. Fyodorov
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Abstract: We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. Deviation from unitarity are characterized by rank $M$ and eigenvalues $T_i, i=1,...,M$ of the matrix $\hat{T}=\hat{\bf 1}-\hat{A}^{\dagger}\hat{A}$. For the case M=1 we solve the problem completely by deriving the joint probability density of eigenvalues and calculating all $n-$ point correlation functions. For a general case we present the correlation function of secular determinants.
Comments: 4 pages, latex, no figures, a few misprints are corrected
Subjects: Chaotic Dynamics (nlin.CD); Condensed Matter (cond-mat); Mathematical Physics (math-ph)
Cite as: arXiv:nlin/0002034 [nlin.CD]
  (or arXiv:nlin/0002034v2 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0002034
Related DOI: https://doi.org/10.1063/1.1358183

Submission history

From: Yan Fyodorov [view email]
[v1] Mon, 21 Feb 2000 15:18:02 UTC (9 KB)
[v2] Tue, 22 Feb 2000 11:59:55 UTC (9 KB)
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