It was recalled that, when in a periodic 2-dimensional potential, a classical particle could be expected to escape from any finite region if it had enough energy to escape from a single cell. However, in the case of sinusoidal potentials in which the barriers between neighboring cells could be varied, a numerical tri-diagonalization of Liouville’s equation (for the evolution of functions in phase space) revealed a transition from localized to delocalized motion at a total energy which was significantly above that needed to escape from a single cell. It was proposed that this purely elastic phenomenon increased the effective barrier to the diffusion of atoms on crystalline surfaces, and changed the temperature dependence at low temperatures where inelastic events were rare.

Classical Localization of an Unbound Particle in a Two-Dimensional Periodic Potential and Surface Diffusion. R.Haydock: Physical Review B, 2001, 63[12], 125413 (11pp)