Role of long jumps in surface diffusion

We analyze a probability of atomic jumps for more than one lattice spacing in activated surface diffusion. First, we studied a role of coupling between the x and y degrees of freedom for the diffusion in a two-dimensional substrate potential. Simulation results show that in the underdamped limit the average jump length <lambda> scales with the damping coefficient eta as <lambda>proportional toeta(lambda)(-sigma) with 1/2less than or equal tosigma(lambda)less than or similar to2/3, so that the diffusion coefficient behaves as Dproportional toeta(-sigma) with 0less than or equal tosigmaless than or similar to1/3. Second, we introduced a realistic friction coefficient for the phonon damping mechanism and developed the technique for Langevin equation with a velocity-dependent friction coefficient. The study of diffusion in this model shows that long jumps play an essential role for diffusing atoms of small masses, especially in two limiting cases, in the case of a large Debye frequency of the substrate, when the rate of phonon damping is low, and in the case of a small Debye frequency, when the one-phonon damping mechanism is ineffective.