Classical Localization of an Unbound Particle in a Two-Dimensional Periodic Potential and Surface Diffusion

Abstract

In periodic, two-dimensional potentials a classical particle might be expected to escape from any finite region if it has enough energy to escape from a single cell. However, for a class of sinusoidal potentials in which the barriers between neighboring cells can be varied, numerical tridiagonalization of Liouville's equation for the evolution of functions on phase space reveals a transition from localized to delocalized motion at a total energy significantly above that needed to escape from a single cell. It is argued that this purely elastic phenomenon increases the effective barrier for diffusion of atoms on crystalline surfaces and changes its temperature dependence at low temperatures when inelastic events are rare.