Overdamped diffusion in coupled potentials

An analytical "quasi-2D" approximation (Q2DA) for the diffusion coefficient of an adatom migrating in a rectangular lattice, in the presence of a high damping and of a general 2D-coupled potential, is derived. The validity of the Q2DA lies on the assumption that all the most relevant diffusion paths can be treated as straight lines. That is the case of the square 2D-coupled egg-carton potential, where the Q2DA is applied. Comparison with the exact numerical results (2D Smoluchowski equation) shows that the Q2DA provides a very good approximation of the diffusion constant even in the strongest coupling situations.