The Kramers problem in 2D-coupled periodic potentials

The Kramers problem in non-separable periodic potentials is studied solving the 2D Fokker-Planck equation (FPE), by the matrix-continued-fraction method, directly obtaining the dynamic structure factor S-s. S-s is numerically evaluated, in a wide friction and coupling range, for the egg-carton potential depending on two parameters g(0) and g(1) which give the amplitude of the decoupled and coupled part respectively. By means of a quasi-discrete jump model it is shown that the quasi-elastic peak of S-s is well described by the decay function f(q) when the conditions for a good definition of the jump rate are satisfied. By Fourier analysing f(q), the jump rate and the jump probabilities are calculated both in the high- and in the low-friction regime. The FPE results are compared with those obtained in the framework of the 1D diffusion-path approximation, showing that the jump rate and the multiple-jump probability are lowered by the coupling. The 2D extension of the high-friction Kramers formula is also compared with the FPE jump rate. (C) 1998 Elsevier Science B.V. All rights reserved.