PROPERTIES OF TIME-DELAY AND S-MATRIX FOR CHAOTIC SCATTERING ON A LEAKY SURFACE OF CONSTANT NEGATIVE CURVATURE

Properties of a model quantum scattering system displaying hard classi cal chaos-'elastic' scattering on a leaky surface of constant negative curvature-are analysed theoretically and serve to interpret previousl y obtained numerical results. The low energy scattering behaviour is s hown to be influenced, in the usual fashion, by a bound state just bel ow the scattering continuum threshold. A connection between the widths of the infinite number of simple poles of the S-matrix and the Lyapun ov exponent for classical trajectories is analysed. At high energies, the scattering is characterized by fluctuations in the S-matrix (via i ts phase) and the time delay. Analytic expressions for the autocorrela tion function of the S-matrix and of the time delay are obtained using Montgomery's conjecture for the pair correlation function of the cele brated Riemann zeros whose values correspond to the positions of the S -matrix poles in momentum space. The autocorrelation function for the S-matrix is found to be Lorentzian asymptotically (at large energy dif ferences DELTA-E), that is, to decrease as DELTA-E-2, but that for the time delay is not. The distribution of fluctuations of S-matrix phase s is likely to be Gaussian.