  We present a study on the dynamics of a system consisting of a pair of
hardcore particles diffusing with different rates. We solved the
drift-diffusion equation for this model in the case when one particle, labeled
F, drifts and diffuses slowly towards the second particle, labeled M. The
displacements of particle M exhibits a crossover from diffusion to drift at a
characteristic time which depends on the rate constants. We show that the
positional fluctuation of M exhibits an intermediate crossover regime of
subdiffusion separating initial and asymptotic diffusive behavior; this is in
agreement with the complete set of Master Equations that describe the
stochastic evolution of the model. The intermediate crossover regime can be
considerably large depending on the hopping probabilities of the two particles.
This is in contrast to the known crossover from diffusive to subdiffusive
behavior of a tagged particle that is in the interior of a large single-file
system on an unbound real line. We discuss our model with respect to the
biological phenomena of membrane protrusions where polymerizing actin filaments
(F) push the cell membrane (M).
