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We systematically study the first three terms in the asymptotic expansions ofthe moments of the transmission eigenvalues and proper delay times as thenumber of quantum channels n in the leads goes to infinity. The computationsare based on the assumption that the Landauer-B\"utticker scattering matrix forchaotic ballistic cavities can be modelled by the circular ensembles of RandomMatrix Theory (RMT). The starting points are the finite-n formulae that werecently discovered (Mezzadri and Simm, J. Math. Phys. 52 (2011), 103511). Ouranalysis includes all the symmetry classes beta=1,2,4; in addition, it appliesto the transmission eigenvalues of Andreev billiards, whose symmetry classeswere classified by Zirnbauer (J. Math. Phys. 37 (1996), 4986-5018) and Altlandand Zirnbauer (Phys. Rev. B. 55 (1997), 1142-1161). Where applicable, ourresults are in complete agreement with the semiclassical theory of mesoscopicsystems developed by Berkolaiko et al. (J. Phys. A.: Math. Theor. 41 (2008),365102) and Berkolaiko and Kuipers (J. Phys. A: Math. Theor. 43 (2010), 035101and New J. Phys. 13 (2011), 063020). Our approach also applies to theSelberg-like integrals. We calculate the first two terms in their asymptoticexpansion explicitly.

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