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

F Mezzadri, NJ Simm

Research output: Contribution to journalArticle (Academic Journal)peer-review

35 Citations (Scopus)

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 β ∈ {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 → ∞.
Translated title of the contributionMoments of the transmission eigenvalues, proper delay times and random matrix theory
Original languageEnglish
Article number103511
Number of pages29
JournalJournal of Mathematical Physics
Volume52
Issue number10
DOIs
Publication statusPublished - Oct 2011

Bibliographical note

Publisher: American Institute of Physics

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