MOMENTS OF THE TRANSMISSION EIGENVALUES, PROPER DELAY TIMES AND RANDOM MATRIX THEORY II

Abstract. 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-Büttiker scattering matrix for chaotic ballistic cavities can be modelled by the circular ensembles of Random Matrix Theory (RMT). The starting points are the finite-n formulae that we recently discovered.53 Our analysis includes all the symmetry classes β ∈ {1, 2, 4}; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer74 and Altland and Zirnbauer.3 Where applicable, our results are in complete agreement with the semi-classical theory of mesoscopic systems developed. by Berkolaiko et al.9 and Berkolaiko and Kuipers.10;11 Our approach also applies to the Selberg-like integrals. We calculat