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

Mezzadri, F and Simm, N J (2011) Moments of the transmission eigenvalues, proper delay times, and random matrix theory I. Journal of Mathematical Physics, 52 (10). p. 103511. ISSN 0022-2488

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Abstract

We develop a method to compute the moments of the eigenvalue densities of matrices in the Gaussian, Laguerre and Jacobi ensembles for all the symmetry classes beta = 1,2, 4 and finite matrix dimension n. The moments of the Jacobi ensembles have a physical interpretation as the moments of the transmission eigenvalues of an electron through a quantum dot with chaotic dynamics. For the Laguerre ensemble we also evaluate the finite n negative moments. Physically, they correspond to the moments of the proper delay times, which are the eigenvalues of the Wigner-Smith matrix. Our formulae are well suited to an asymptotic analysis as n -> infinity.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Mathematical Physics Group
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Nicholas Simm
Date Deposited: 05 Feb 2018 09:27
Last Modified: 06 Apr 2018 14:39
URI: http://sro.sussex.ac.uk/id/eprint/73303

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