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, $D_N(\rho )$, 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 $F_N(\rho )=N((1-\mathring{)}-[D_N(\rho )/D_N(0)])/(\rho (1-\rho ))$ 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 $N\ge 20$.

24 pages, in TeX, 1 figure, e-mail addresses: [email protected], [email protected], [email protected]

References in corpus (2)

• Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
• Generalized Boltzmann Equation for Lattice Gas Automata

Cited by in corpus (1)

• Adsorption and desorption in confined geometries: a discrete hopping model