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

Abstract

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}.

4 pages

References in corpus (5)

• Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
• Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
• Quantum Disordered Systems with a Direction
• Random matrix triality at nonzero chemical potential
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Cited by in corpus (7)

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• Time Delay Correlations and Resonances in 1D Disordered Systems
• Localization-delocalization transition in disordered systems with a direction
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance