Frequency dependent response of an electron on a liquid helium film.

The linear response of a two-dimensional electron on a liquid helium film to a time varying electric field at zero temperature is calculated. The effect of the self-trapping transition on the mobility spectrum is investigated. We find that at the localization transition 1) the small frequency mobility drops by several orders of magnitude as found recently experimentally and 2) the mobility spectrum transforms from the spectrum of a Brownian particle to a spectrum with a series of sharp peaks which reflect Franck-Condon states and collective electron- ripplon states (CERS).