Nearest-neighbor distances in diffusion-controlled reactions modelled by a single mobile trap

Abstract

We consider a system consisting of an infinite number of identical particles on a lattice initially uniformly distributed, which diffuese in the presence of a singke mobile trap and ask for the time-dependent behavior of the distance of the trap from the nearest particle. This quantity is a measure of the tendency of the system to self-segregate. We show, by a simulation incorporating the exact enumeration method, that in one dimension the expected distance L(t)> scales as L(t)>[approximate]t[alpha] as t-->[infinity], where the exponent [alpha] depends only on the ratio of the diffusion constant. A heuristic expression for [alpha] is suggested, analogous to a rigorous exponent found by ben-Avraham for a similar but not identical problem. The flux into the trap is found to vary as t-1/2 independent of the diffusion constants.