Time delay statistics for finite number of channels in all symmetry classes

Abstract

Within a random matrix theory approach, we obtain spectral statistics of the Wigner time delay matrix $Q$, for arbitrary channels number $M$ and for all symmetry classes, in fact for general Dyson parameter $\beta$. We also put forth two conjectures: one is related to the large-$M$ expansion of joint cumulants of traces of powers of $Q$, which generalizes and implies a previous conjecture of Cunden, Mezzadri, Vivo and Simm; the other concerns the tail of the distribution of traces of powers of $Q$.

6 pages, no figures. Accepted by Europhysics Letters

References in corpus (6)

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• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Jack polynomials and free cumulants
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Cited by in corpus (2)

• Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition
• Semiclassical calculation of time delay statistics in chaotic quantum scattering