Effects of hard-core interaction on nearest neighbor distances at a single trap for random walks and for diffusion processes

The phenomenon of self-organization of reacting systems in low dimensions has recently been discussed by a number of investigators. One characterization of the tendency to self-organize is to study the distribution of the distance of the closest among a number of diffusing particles to a centrally located trap, which is allowed to be perfect or imperfect. We study this quantity in one dimension when the particles are assumed to interact by means of a hard-core potential. Our results indicate that there is an observable difference between results obtained for the interacting and non-interacting cases for random walks on a discrete line. These differences tend to disappear at long enough times. A simple argument shows that there is no such difference for diffusing particles on a line.