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

Mezzadri, F and Simm, N (2012) Moments of the transmission eigenvalues, proper delay times and random matrix theory II. Journal of Mathematical Physics, 53 (5). 053504-1-053504-42. ISSN 0022-2488

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematical Physics Group
Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QC Physics
Depositing User: Nicholas Simm
Date Deposited: 17 May 2018 09:20
Last Modified: 17 May 2018 09:20

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