QUANTUM-MECHANICAL TIME-DELAY MATRIX IN CHAOTIC SCATTERING

We calculate the probability distribution of the matrix Q = -i (h) ove r bar S(-1)partial derivative S/partial derivative E for a chaotic sys tem with scattering matrix S at energy E. The eigenvalues tau(j) of Q are the so-called proper delay times, introduced by Wigner and Smith t o describe the time dependence of a scattering process. The distributi on of the inverse delay times turns out to be given by the Laguerre en semble from random-matrix theory.