标题： 传输本征值的矩、适当延迟时间和随机矩阵理论 II 显示英文标题

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

摘要： 我们系统地研究了当输运通道数量n在引线中趋于无穷大时，传输本征值和适当延迟时间的矩的渐近展开式的前三个项。 计算基于这样一个假设，即混沌弹道腔的Landauer-Bütticker散射矩阵可以用随机矩阵理论(RMT)的圆型系综来建模。 起点是我们最近发现的有限n公式（Mezzadri和Simm，J. Math. Phys. 52 (2011), 103511）。 我们的分析包括所有对称性类beta=1,2,4；此外，它适用于Andreev双球的传输本征值，其对称性类由Zirnbauer（J. Math. Phys. 37 (1996), 4986-5018）和Altland和Zirnbauer（Phys. Rev. B. 55 (1997), 1142-1161）分类。 在适用的情况下，我们的结果与Berkolaiko等人（J. Phys. A.: Math. Theor. 41 (2008), 365102）开发的介观系统的半经典理论完全一致，以及Berkolaiko和Kuipers（J. Phys. A: Math. Theor. 43 (2010), 035101和New J. Phys. 13 (2011), 063020）。 我们的方法也适用于类似Selberg的积分。 我们显式地计算了它们渐近展开式的前两项。 显示英文摘要

摘要： 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-B\"utticker 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 (Mezzadri and Simm, J. Math. Phys. 52 (2011), 103511). Our analysis includes all the symmetry classes beta=1,2,4; in addition, it applies to the transmission eigenvalues of Andreev billiards, whose symmetry classes were classified by Zirnbauer (J. Math. Phys. 37 (1996), 4986-5018) and Altland and Zirnbauer (Phys. Rev. B. 55 (1997), 1142-1161). Where applicable, our results are in complete agreement with the semiclassical theory of mesoscopic systems developed by Berkolaiko et al. (J. Phys. A.: Math. Theor. 41 (2008), 365102) and Berkolaiko and Kuipers (J. Phys. A: Math. Theor. 43 (2010), 035101 and New J. Phys. 13 (2011), 063020). Our approach also applies to the Selberg-like integrals. We calculate the first two terms in their asymptotic expansion explicitly.