Self-Diffusion in Simple Models: Systems with Long-Range Jumps

Abstract

We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self diffusion coefficient, $D_N(ρ)$, in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set of $N$ neighboring sites. We obtain positive upper and lower bounds on $F_N(ρ)=N((1-\r)-[D_N(ρ)/D_N(0)])/(ρ(1-ρ))$ for $ρ\in [0,1]$. Computer simulations for the square, triangular and one dimensional lattice suggest that $F_N$ becomes effectively independent of $N$ for $N\ge 20$.