Surface transport and diffusion at low damping reveals a number of unexplained or at least not systematically explained behaviors. Here we present two problems that require further study for a full understanding. One involves motion on a random surface, the unresolved issue being the parameter regimes leading to subdiffusive, diffusive, and superdiffusive motions at intermediate times. The other involves the temperature dependence of maximal diffusion on a periodic surface in the presence of a constant external force

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