Nonuniversal Diffusion Exponent for a Soft Percolation Process
in Three Dimensions

Abstract

The diffusion property of a soft percolation process in three dimensions is studied. The jump rate w of a random walker between two sites distributed randomly in space is assumed to fall off with the distance r as w ∼ [1-(r/r₀)]^α, where r₀ is a cutoff length. The diffusion exponent d_w is determined by a new computational approach using the exact expression for mean-square displacement, < r²(t) >, of a random walker on a single percolation cluster. The diffusion exponent d_w is shown to depend on α, deviating gradually from the value for α=0.