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Statistics of time delay in quantum chaotic transport
We study the statistical properties of the time delay matrix in the
context of quantum transport through a chaotic cavity, in the absence of
time-reversal invariance. First, we approach the problem from the point of view
of random matrix theory, and obtain exact results that provide the average
value of any polynomial function of . We then consider the problem from the
point of view of the semiclassical approximation, obtaining the entire
perturbation series for some energy-dependent correlation functions. Using
these correlation functions, we show agreement between the random matrix and
the semiclassical approaches for several statistical properties.Comment: 20 pages, 3 figures. This paper has been split in two parts upon
publication, each part containing different results, in order to make the
presentation more consistent. First part is arXiv:1507.05524, second part is
arXiv:1507.0552
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