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arXiv · 1507.05524

Statistics of time delay and scattering correlation functions in chaotic systems I. Random Matrix Theory

Marcel Novaes
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Abstract

We consider the statistics of time delay in a chaotic cavity having $M$ open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix $Q=-i\hbar S^†dS/dE$, where $S$ is the scattering matrix. Our results do not assume $M$ to be large. In a companion paper, we develop a semiclassical approximation to $S$-matrix correlation functions, from which the statistics of $Q$ can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.

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Marcel Novaes. 2015-07-20. Statistics of time delay and scattering correlation functions in chaotic systems I. Random Matrix Theory. https://doi.org/10.1063/1.4922746

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