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

Abstract

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 $\mathrm{Tr}[S^{†}(E-\epsilon )S(E+\epsilon ){]}^n$, 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 $Q=-i\hslash S^{†}dS/dE$, and check that the first 8 of them agree with the random matrix theory prediction from our previous paper.

20 pages, 3 figures. A previous paper, arXiv:1408.1669, has been split in two parts upon publication, each part containing different results, in order to make the presentation more consistent. This is the second part

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