  The damping of quantum effects in the transport properties of electrons
deposited on a surface of liquid helium is studied. It is found that due to
vertical motion of the helium vapour atoms the interference of paths of
duration $t$ is damped by a factor $\exp - (t/\tau_v)^3$. An expression is
derived for the weak-localization lineshape in the case that damping occurs by
a combination of processes with this type of cubic exponential damping and
processes with a simple exponential damping factor.

Mesoscale and Nanoscale Physics