Diffusion with drift on a line: Effect of traps

We consider the effect of a uniform drift superposed on the free diffusion of a particle on an infinite line with traps present at random. By solving for the positional probability density on a finite line with traps (absorbers) at its ends, we obtain exact results for a number of quantities that are of interest in a trap-controlled diffusion process. These include the characteristic function of the escape time distribution and the mean time of exit from a strand of finite length, and an analytic expression for the AC diffusion coefficient valid at all frequencies. The effects of the drift and the traps on the low-frequency behaviour of the diffusion coefficient is discussed. We also obtain the configuration-averaged diffusion coefficient for a random distribution of traps in the absence of drift. Finally, we consider the behaviour of the survival probability, regarding which a number of approximate results have appeared in recent literature. We present exact results for the average survival probability at all times and show how its behaviour is modified at long times when there is an ‘attraction’ between traps, and also when the distribution of traps is a hyperbolic one (i.e., the traps are clustered in a scale-invariant manner). © 1985, IOP Publishing Ltd.