Distribution of the quantum mechanical time-delay matrix for a chaotic cavity

P. W. Brouwer, K. M. Frahm, C. W. J. Beenakker

We calculate the joint probability distribution of the Wigner-Smith time-delay matrix $Q=-i\hslash S^{-1}\partial S/\partial \epsilon$ and the scattering matrix $S$ for scattering from a c…