Chaotic Scattering on Graphs

Abstract

Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying classical chaotic dynamics. We derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. A statistical analysis of the cross sections and resonance parameters compares well with the predictions of Random Matrix Theory. Hence, this system is proposed as a convenient tool to study the generic behavior of chaotic scattering systems, and their semiclassical description.