Stochastic versus semiclassical approach to quantum chaotic scattering

The authors explore the universal features of quantum scattering system for which the classical scattering is chaotic. They do so by comparing the semiclassical approach and the stochastic approach, exhibiting their mutual overlap and their individual limits of applicability. They investigate in particular predictions of both approaches for the average cross section, for the autocorrelation function of a pair of S-matrix elements, its Fourier transform, the Wigner time delay, and the distribution of the poles of the S-matrix in the complex energy plane. The relationship of both approaches with Dyson's circular ensemble of S-matrices is also exhibited