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Moments of the transmission eigenvalues, proper delay times, and random matrix theory I
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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Publication status
- Published
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- Published version
Journal
Journal of Mathematical PhysicsISSN
0022-2488Publisher
American Institute of PhysicsExternal DOI
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10Volume
52Page range
103511Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Mathematical Physics Group Publications
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- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-02-05First Open Access (FOA) Date
2018-02-05First Compliant Deposit (FCD) Date
2018-02-05Usage metrics
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