Escape times in interacting biased random walks

Abstract

The dynamics of N particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on the N sites of the lattice closest to the wall. For N=1 the leading behavior of the first passage time T_FP to a distant site l is known to follow the Kramers escape time formula T _FP~λ¹ where λ is the ratio of hopping rates toward and away from the wall. For N >1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes to T_FR~ λ ^IN. First passage times for the other particles are studied as well. A second question that is studied pertains to survival times T _s in the presence of an absorbing barrier placed at site l. In contrast to the first passage time, it is found that T _s follows the leading behavior λ ¹independent of N.