Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

Details Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

1998-02-27

arxiv.org/abs/cond-mat/9802306v1

Phys. Rev. E. v. 58 (1998) p.1195

Physics

Condensed Matter

4 pages

Scientific paper

10.1103/PhysRevE.58.R1195

In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on statistics of $Z_i$ for systems with broken time-reversal invariance and verify that it allows to reproduce statistical characteristics of Wigner time delays known from independent calculations. We analyze the ensuing two-point statistical measures as e.g. spectral form factor and the number variance. In addition we find the density of complex eigenvalues of real asymmetric matrices generalizing the recent result by Efetov\cite{Efnh}.

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