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

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

1998-09-11

arxiv.org/abs/cond-mat/9809175v1

Journal of Statistical Physics 87 (1997) 1131--1144

Physics

Condensed Matter

Statistical Mechanics

24 pages, in TeX, 1 figure, e-mail addresses: asselah@math.ethz.ch, brito@seneca.fis.ucm.es, lebowitz@math.rutgers.edu

Scientific paper

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, $D_N(\rho)$, 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 $F_N(\rho)=N((1-\r)-[D_N(\rho)/D_N(0)])/(\rho(1-\rho))$ for $\rho\in [0,1]$. 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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