ON THE SPAN OF BROWNIAN-MOTION IN A FIELD IN ONE-DIMENSION

We study the effect of a field on the span of a particle diffusing on a line, i.e., the length covered by a Brownian particle which moves on a line for time t in the presence of a constant field. This is the on e-dimensional analog of the Wiener sausage volume, Exact expressions a re found for the probability density for the span together with the fi rst two moments, Our results indicate that at very short times the dom inant effect is diffusion while at very long times the field plays the dominant role.