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Mathematical Physics

arXiv:1103.6203 (math-ph)
[Submitted on 31 Mar 2011 (v1), last revised 23 Dec 2011 (this version, v3)]

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

Authors:F. Mezzadri, N. J. Simm
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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.
Comments: 33 pages, typos corrected
Subjects: Mathematical Physics (math-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
MSC classes: 15B52, 81V65
Cite as: arXiv:1103.6203 [math-ph]
  (or arXiv:1103.6203v3 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1103.6203
Journal reference: J. Math. Phys., Vol. 52 (2011), 103511
Related DOI: https://doi.org/10.1063/1.3644378

Submission history

From: Francesco Mezzadri [view email]
[v1] Thu, 31 Mar 2011 14:52:31 UTC (31 KB)
[v2] Wed, 5 Oct 2011 09:35:33 UTC (31 KB)
[v3] Fri, 23 Dec 2011 20:59:25 UTC (31 KB)
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