NOISE-ACTIVATED DIFFUSION IN THE EGG-CARTON POTENTIAL

The noise-activated diffusion of a classical particle in spatially per iodic two-dimensional (2D) systems is studied by solving the correspon ding Fokker-Planck equation. The particle is subjected to a periodic d eterministic force, to a frictional force, and to a Gaussian white noi se. The solution is obtained by extending to 2D the matrix-continued-f raction method for a quite general potential shape. The 2D diffusion c oefficient is then numerically calculated for the square egg-carton po tential; the analysis is performed over different friction and energy- barrier regimes. Several approximations are compared with the exact nu merical results. In particular, the usual 1D diffusion-path approximat ion is discussed, showing that 2D effects are always present, becoming more and more relevant with deceasing friction. At high friction, a g ood analytical approximation is shown; on the contrary, none of the av ailable approximations gives satisfactory results in intermediate- and low-damping regimes, which are typical in adatom diffusion on crystal surfaces.