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

TL;DR

This paper derives spectral statistics of the Wigner time delay matrix for any number of channels and symmetry class using random matrix theory, and proposes two conjectures related to cumulants and distribution tails.

Contribution

It provides a general framework for spectral statistics of the Wigner time delay matrix across all symmetry classes and channels, extending previous conjectures.

Findings

Spectral statistics for arbitrary channels and symmetry classes derived.

Two conjectures proposed: one on large-$M$ cumulants, another on distribution tails.

Generalizes previous results and conjectures in the field.

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 $Q$.