Parametric correlations of scattering phase shifts and fluctuations of delay times in few-channel chaotic scattering

By using a supersymmetric method we derive an explicit expression for the parametric correlation function of densities of eigenphases theta(a) of the S matrix in a chaotic quantum system with broken time-reversal symmetry coupled to the continuum via M equivalent open channels; a = 1,...,M. We use it to find the distribution of derivatives of these eigenphases over the energy (''phase-shift times'') as well as over an arbitrary external parameter. We also find the parametric correlations of Wigner-Smith delay times.