Noise activated diffusion in a 2D egg-crate potential
G. Caratti, R. Ferrando, R. Spadacini, G.E. Tommei
Centro di Fisica delle Superfici e delle Basse Temperature del CNR
and Unitá INFM,
Dipartimento di Fisica, via Dodecaneso 33, 16146 Genova, Italy
The Brownian motion of a classical particle in a two-dimensional coupled periodic potential (egg-crate potential) in a square is studied by numerically solving the Fokker-Planck equation (FPE) in the full phase space. The four-variable FPE is solved by an extention of Risken's matrix continued fraction method. The dynamic structure factor, from which all the relevant correlation functions can be extracted, is calculated. A very wide friction range, from the energy-controlled diffusion to the Smoluchowski limit, has been explored both at low and high potential barriers. The x-y coupling reduces the diffusion coefficient with respect to the diffusion-path approximation (exact for decoupled potential), the latter becoming increasingly inaccurate at low friction; this effect is very relevant when the diffusion takes place along flat channels (strong coupling). At high potential barriers, the total jump rate and the single and multiple jump probabilities have been calculated. The jump rate shows a turnover behaviour; the probability of long jumps is significantly reduced by the coupling. The solution of the Brownian motion problem in the egg-crate potential is interesting for adatom surface diffusion in particular at low friction where long jumps are activated.