Random-matrix description of chaotic scattering: Semiclassical approach

Abstract

We present a semiclassical theory for the two-point correlation function of the eigenphases of the S matrix for chaotic scattering. It is expressed as a sum of contributions from unstable periodic orbits of the classical scatttering mapping. Backed by numerical results and for correlation ranges ${r}^{\mathrm{*}}$(\ensuremath{\sim}1/\ensuremath{\Elzxh}) we obtain a universal function which is consistent with the result for Dyson's circular ensemble. This result adds to the conjecture that universal fluctuations governed by random matrix theory are the quantum manifestation of classical chaos.