Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation

We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S dagger(E - epsilon)S(E + epsilon)](n), for general positive integer n. Our result is an infinite series in epsilon, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = -i (h) over barS dagger dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys. 56, 062110 (2015)]. (C) 2015 AIP Publishing LLC.