Classical Diffusion on a Random Chain

Abstract

A simple model of classical diffusion on a random chain is studied. The velocities to the right and to the left are calculated. When one changes continuously the probability distribution $\ensuremath{\rho}$ of the hopping rates, a whole region is found where these two velocities vanish. In this region, the distance $R$ covered by a particle during the time $t$ behaves like $R\ensuremath{\sim}{t}^{x}$, where $x$ depends continuously on $\ensuremath{\rho}$. The exponent $x$ is calculated for a simple example.