Statistical properties of random scattering matrices

Abstract

We discuss the statistical properties of eigenphases of S matrices in random models simulating quantum systems that exhibit chaotic scattering classically. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are obtained both theoretically and numerically. A simple formula describing the velocity distribution (and hence the distribution of the Wigner time delay) is derived that is capable of explaining the algebraic tail of the time delay distribution observed recently in microwave experiments. A dependence of the eigenphases on other external parameters is also discussed. We show that in the semiclassical limit (large number of channels) the curvature distribution of S-matrix eigenphases is the same as that corresponding to the curvature distribution of the underlying Hamiltonian and is given by the generalized Cauchy distribution. © 1996 The American Physical Society.