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

[img] PDF - Published Version
Download (508kB)

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-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
URI: http://srodev.sussex.ac.uk/id/eprint/75903

View download statistics for this item

📧 Request an update