Time delay, resonances, Riemann zeros and chaos in a model quantum scattering system

The quantum treatment of an intrinsically chaotic model scattering system originally studied by Gutzwiller (1983) is extended to include the time delay and to make explicit the zeros of the Riemann zeta function in the mathematical expressions for the scattering matrix S and the time delay. The system consists of a particle moving on a two-dimensional surface of constant negative curvature. The scattering in this unusual system is dominated by resonances associated with poles of S in the complex momentum plane, the real parts of these poles are one-half of the imaginary parts of the Riemann zeros. The resonances have a constant width but their average spacing varies with the momentum. The focal point is the manifestation of chaotic behaviour in the time delay. Features considered in this regard include: the momentum dependence of the time delay in regions of overlapping and isolated resonances, the decomposition of the time delay into an average (dynamical) component and a fluctuating (chaotic) component, and characterisation of the fluctuating component by its autocorrelation function.