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 ${\rm Tr}[S^†(E-ε)S(E+ε)]^n$, for general positive integer $n$. Our result is an infinite series in $ε$, whose coefficients are rational functions of $M$. From this we extract moments of the time delay matrix $Q=-i\hbar S^†dS/dE$, and check that the first 8 of them agree with the random matrix theory prediction from our previous paper.

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