Discrete velocity random motion in an external field

Abstract

We consider the effects of an external constant force on the one-dimensional transport of a particle whose velocity stochastically fluctuates between two fixed values, +/-v. Transport in the presence of a single trap is analyzed in detail. It is found that in the long time limit the trapping probability is decreased compared to that for the overdamped diffusion by the factor 1/(1 + v(d)/v) where v(d) is the average drift velocity.