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.
Categories: cond-mat.mes-hall cond-mat.stat-mech math-ph math.MP nlin.CD