Magneto-polarisability of mesoscopic rings

We calculate the average polarisability of two dimensional mesoscopic rings in the presence of an Aharonov-Bohm flux. The screening is taken into account self-consistently within a mean-field approximation. We investigate the effects of statistical ensemble, finite frequency and disorder. We emphasize geometrical effects which make the observation of field dependent polarisability much more favourable on rings than on disks or spheres of comparable radius. The ratio of the flux dependent to the flux independent part is estimated for typical GaAs rings.