Spectra of random contractions and scattering theory for discrete-time systems
| Autor: | H. J. Sommers, Yan V. Fyodorov |
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| Rok vydání: | 2000 |
| Předmět: |
Pure mathematics
Physics and Astronomy (miscellaneous) Unitarity Rank (linear algebra) Condensed Matter (cond-mat) FOS: Physical sciences Condensed Matter Nonlinear Sciences - Chaotic Dynamics Matrix (mathematics) Discrete time and continuous time Joint probability distribution Scattering theory Chaotic Dynamics (nlin.CD) Random matrix Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Experimental and Theoretical Physics Letters. 72:422-426 |
| ISSN: | 1090-6487 0021-3640 |
| DOI: | 10.1134/1.1335121 |
| Popis: | 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. Comment: Complete solution of the problem discussed in earlier e-preprint nlin.CD/0002034 |
| Databáze: | OpenAIRE |
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