THE KRAMERS PROBLEM IN 2D-COUPLED PERIODIC POTENTIALS

The Kramers problem in non-separable periodic potentials is studied so lving the 2D Fokker-Planck equation (FPE), by the matrix-continued-fra ction 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) whi ch give the amplitude of the decoupled and coupled part respectively. By means of a quasi-discrete jump model it is shown that the quasi-ela stic 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 F ourier analysing f(q), the jump rate and the jump probabilities are ca lculated both in the high- and in the low-friction regime. The FPE res ults are compared with those obtained in the framework of the 1D diffu sion-path approximation, showing that the jump rate and the multiple-j ump probability are lowered by the coupling. The 2D extension of the h igh-friction Kramers formula is also compared with the FPE jump rate. (C) 1998 Elsevier Science B.V. All rights reserved.