Correlation widths in quantum-chaotic scattering

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