Quantum Mechanical Time-Delay Matrix in Chaotic Scattering

We calculate the probability distribution of the matrix Q0ex0ex=0ex0ex-iS^-1∂S/∂E for a chaotic system with scattering matrix S at energy E. The eigenvalues τⱼ 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.