Cunden FD. Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015;
91:060102. [PMID:
26172641 DOI:
10.1103/physreve.91.060102]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Indexed: 06/04/2023]
Abstract
We derive the joint distribution of the moments TrQ(κ) (κ≥1) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels n. This distribution turns out to be asymptotically Gaussian, and we compute explicitly averages and covariances. The results are in a compact form and have been verified numerically. The general methodology of proof and computations has a wide range of applications.
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