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

A. Asselah·R. Brito·J. L. Lebowitz
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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 $N\ge 20$.

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A. Asselah, R. Brito, J. L. Lebowitz. 1998-09-11. Self-Diffusion in Simple Models: Systems with Long-Range Jumps. https://doi.org/10.1007/bf02181276

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