AN ANALYTICAL APPROXIMATION TO THE DIFFUSION-COEFFICIENT IN OVERDAMPED MULTIDIMENSIONAL SYSTEMS

An analytical approximation for the mobility of an overdamped particle in a periodic multidimensional system is presented. Attention is focu sed, on two dimensions (quasi-2D approximation) in the most generic ca se of a 2D-coupled periodic potential in a rectangular lattice and of a position-dependent friction. The approximation is derived in the fra mework of the Linear Response Theory by fixing the value of one coordi nate ant solving the problem of diffusion along the other coordinate a s strictly 1D. This is expected to be essentially correct if all the m ost relevant diffusion paths are straight lines. Two different specifi c applications have been considered: diffusion in a square egg-carton potential and diffusion in absence of potential in a 2D channel with u nsurmountable periodic walls. Exact results are available in literatur e in the latter case and are obtained in the first case by solving the Smoluchowski equation (matrix continued fraction method). Comparisons with the quasi-2D approximation show that the agreement is excellent for the egg-carton potential but far less satisfying fbr migration in the 2D periodically shaped channel, characterized by important diffusi on paths not being straight lines.