Temperature-dependent effective mass of a self-trapped electron on the surface of a liquid-helium film

We have used the Feynman path-integral formulation of the polaron problem to compute the temperature-dependent effective mass of a two-dimensional electron on a film of liquid helium for values of the coupling constant from weak to strong. Because of the nature of the ripplon spectrum (very low velocities) we find that the self-trapped structure (found at $T=0\mathrm{}$) "melts" for rather small $\frac{\mathrm{kT}}{E_B}$. Here $E_B$ is the zero-temperature binding of the localized state.