Importance of individual scattering matrix elements at Fano resonances

Single particle resonances in quantum wires are generally Fano resonances. In case of Fano resonances, the scattering phase shift in some channels show sharp phase drops and that in the other channels do not. Phase shift in a particular channel can be measured and can yield information about the integrated charge localized around the scatterer. This paper tries to analyze if some channels are more informative than the others, so that an experimentalist can measure the phase shift in only those channels.