Escape times in interacting biased random walks

Abstract

The dynamics ofN 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 theN sites of the lattice closest to the wall. ForN=1 the leading behavior of the first passage timeT _FP to a distant sitel is known to follow the Kramers escape time formulaT _FP∼λ ^l whereλ is the ratio of hopping rates toward and away from the wall. ForN > 1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes toT _FR∼λ ^IN. First passage times for the other particles are studied as well. A second question that is studied pertains to survival timesT _s in the presence of an absorbing barrier placed at sitel. In contrast to the first passage time, it is found thatT _s follows the leading behaviorλ′ independent ofN.