Statistical distribution of the Wigner-Smith time-delay matrix moments for chaotic cavities

TL;DR

This paper derives the joint distribution of the moments of the Wigner-Smith time-delay matrix in chaotic cavities, showing it is asymptotically Gaussian and providing explicit averages and covariances, with broad applicability.

Contribution

It provides the first explicit derivation of the joint distribution of Wigner-Smith matrix moments for large chaotic cavities, including asymptotic Gaussianity and explicit statistical measures.

Findings

Distribution is asymptotically Gaussian

Explicit formulas for averages and covariances

Numerical verification confirms theoretical results

Abstract

We derive the joint distribution of the moments $\mathrm{Tr}\, Q^{\kappa}$ ($\kappa\geq0$) 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.