Moments of the transmission eigenvalues, proper delay times and random matrix theory II

We systematically study the first three terms in the asymptotic expansions of the moments of the transmission eigenvalues and proper delay times as the number of quantum channels n in the leads goes to infinity. The computations are based on the assumption that the Landauer-Buttiker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of random matrix theory. The starting points are the finite-n formulae that we recently discovered [F. Mezzadri and N. J. Simm, Moments of the transmission eigenvalues, proper delay times and random matrix theory, J. Math. Phys. 52, 103511 (2011)]. Our analysis includes all the symmetry classes beta is an element of {1, 2, 4}; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer [Riemannian symmetric superspaces and their origin in random-matrix theory, J. Math. Phys. 37(10), 4986 (1996)] and Altland and Zirnbauer [Random matrix theory of a chaotic Andreev quantum dot, Phys. Rev. Lett. 76(18), 3420 (1996); Nonstandard symmetry classes inmesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55(2), 1142 (1997)]. Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. [Full counting statistics of chaotic cavities from classical action correlations, J. Phys. A: Math. Theor. 41(36), 365102 (2008)] and Berkolaiko and Kuipers [Moments of the Wigner delay times, J. Phys. A: Math. Theor. 43(3), 035101 (2010); Transport moments beyond the leading order, New J. Phys. 13(6), 063020 (2011)]. Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion explicitly. (C) 2012 American Institute of Physics. [http://dx. doi.org/10.1063/1.4708623]