SELF-DIFFUSION IN SIMPLE-MODELS - SYSTEMS WITH LONG-RANGE JUMPS

We review some exact results for the morion of a tagged particle in si mple models. Then, we study the density dependence of the sill-diffusi on coefficient D-N(rho) in lattice systems with simple symmetric exclu sion in which the particles can jump, with equal rates, to a set of N neighboring sites. We obtain positive upper and lower bounds on F-N(rh o) = N{(1 - rho) - [D-N(rho)/D-N(0)]}/[rho(1 - rho)] for rho is an ele ment of [0, 1]. Computer simulations For the square, triangular, and o ne-dimensional lattices suggest that F-N becomes effectively independe nt of N for N greater than or equal to 20.