NEAREST-NEIGHBOR DISTANCES IN DIFFUSION-CONTROLLED REACTIONS MODELED BY A SINGLE MOBILE TRAP

We consider a system consisting of an infinite number of identical particles on a lattice initially uniformly distributed, which diffuse in the presence of a single 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)] approximately t-alpha as t --> infinity, where the exponent alpha depends only on the ratio of the diffusion constants. 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.