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.
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