Role of entropy barriers for diffusion in the periodic potential

Diffusion of a particle in the N-dimensional external potential which is periodic in one dimension and unbounded in the other N-1 dimensions is investigated. We find an analytical expression for the overdamped diffusion and study numerically the cases of moderate and low damping. We show that in the underdamped limit, the multi-dimensional effects lead to reduction (comparing with the one-dimensional motion) of jump lengths between subsequent trapping of the atom in bottoms of the external periodic potential. As application we consider the diffusion of a dimer adsorbed on the crystal surface.