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; $a=1,\dots ,M$. 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.