A. Asselah (asselah@math.ethz.ch), R. Brito, (brito@seneca.fis.ucm.es), J. L. Lebowitz, (lebowitz@math.rutgers.edu)
Self-Diffusion in Simple Models: Systems with Long-Range Jumps
(26K, Tex files and a ps file)
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, $D_N(\rho)$, 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 $N\ge 20$.