A master equation was derived for phonon-mediated hopping and friction, by using the Wannier representation, on the basis of a microscopic Hamiltonian for a particle on the corrugated surface of a solid. In the case of a sinusoidal corrugation (in addition to a Morse surface potential), an investigation was made of the role of interband transitions and numerical calculations were made of the transition probabilities. It was found that that long hops beyond nearest-neighbor sites were significant; especially in weakly coupled systems.

Long Jumps in Surface Diffusion: a Microscopic Derivation of the Jump Frequencies M.Azzouz, H.J.Kreuzer, M.R.A.Shegelski: Physical Review Letters, 1998, 80[7], 1477-80