Quantum Mechanical Time-Delay Matrix in Chaotic Scattering

We calculate the probability distribution of the matrix Q0ex{0ex}=0ex{0ex}-iS^-1/ for a chaotic system with scattering matrix S at energy E. The eigenvalues ₉ of Q are the so-called proper delay times, introduced by Wigner and Smith to describe the time dependence of a scattering process. The distribution of the inverse delay times turns out to be given by the Laguerre ensemble from random-matrix theory.