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

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

2011-03-31

arxiv.org/abs/1103.6203v3

J. Math. Phys., Vol. 52 (2011), 103511

Physics

Mathematical Physics

33 pages, typos corrected

Scientific paper

10.1063/1.3644378

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.

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