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

Instituto de Física, Universidade Federal de Uberlândia - Uberlândia, 38408-100, Brazil

^(a) marcel.novaes@gmail.com (corresponding author)

Received: 2 April 2022
Accepted: 12 July 2022

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 the general Dyson parameter β. 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.