Noise-activated diffusion in the egg-carton potential

The noise-activated diffusion of a classical particle in spatially periodic two-dimensional (2D) systems is studied by solving the corresponding Fokker-Planck equation. The particle is subjected to a periodic deterministic force, to a frictional force, and to a Gaussian white noise. The solution is obtained by extending to 2D the matrix-continued-fraction method for a quite general potential shape. The 2D diffusion coefficient is then numerically calculated for the square egg-carton potential; the analysis is performed over different friction and energy-barrier regimes. Several approximations are compared with the exact numerical results. In particular, the usual 1D diffusion-path approximation is discussed, showing that 2D effects are always present, becoming more and more relevant with deceasing friction. At high friction, a good analytical approximation is shown; on the contrary, none of the available approximations gives satisfactory results in intermediate- and low-damping regimes, which are typical in adatom diffusion on crystal surfaces.