Correlation widths in quantum-chaotic scattering

An important parameter to characterize the scattering matrix S   for quantum-chaotic scattering is the width Γcorr${\Gamma }_{\mathrm{corr}}$ of the S  -matrix autocorrelation function. We show that the “Weisskopf estimate” d/(2π)c_∑Tc$d/(2\pi ){\sum }_c{T}_c$ (where d   is the mean resonance spacing, Tc$T_c$ with 0?Tc?1$0?T_c?1$ the “transmission coefficient” in channel c   and where the sum runs over all channels) provides a good approximation to Γcorr${\Gamma }_{\mathrm{corr}}$ even when the number of channels is small. That same conclusion applies also to the cross-section correlation function.