Dynamics of Interacting Brownian Particles in a Two-Dimensional Periodic Potential

Abstract
The static structure factor and diffusion mechanism of N interacting Brownian particles immersed in a two-dimensional periodic potential are discussed, in relation with superionic conductors, premelting surfaces and adsorbed monolayers. For the static structure factor we report Brownian dynamics results assuming a repulsive Yukawa pair potential. For some values of the concentration, the system can be decomposed in two equivalent or in two different subsystems along the two directions of space. To get information about the diffusion mechanism, we have computed the full width at half maximum (f.w.h.m.) (q), of the quasi-elastic line of the dynamical structure factor up large values of q covering several Brillouin zones. The entire analysis of (q) with different physical parameters shows that the most probable diffusion process in good superionic conductors (concentration of mobile ions c=2/3) consists of a competition between a back correlated hopping in one direction and forward correlated hopping in addition to liquid-like motions in the other spatial direction. The analytical treatment of this investigation is done by using different approximations such as the homogeneous approximation and the time dependent mean field approximation within the lattice gas model.