Chaotic scattering on graphs

Quantized, compact graphs are excellent paradigms for quantum chaos in boun ded systems. Connecting them with leads to infinity, we show that they disp lay all the features which characterize quantum chaotic scattering. We deri ve exact expressions for the scattering matrix, and an exact trace formula for the density of resonances. in terms of classical orbits, analogous to t he semiclassical theory of chaotic scattering. A statistical analysis of th e cross sections and resonance parameters compares well with thr prediction s of random matrix theory. Hence, this system is proposed ns a convenient t ool to study the generic behavior of chaotic scattering systems and their s emiclassical description.