Trajectories and transport characteristics of a Brownian particle in a 1D potential subject to bias.

We investigate one-dimensional driven, diffusive motion of a single Brownian particle moving through a periodic lattice potential and subject to a constant, uniform bias using a Langevin equation of motion. The model yields explicit trajectories with bias-dependent trapping, hopping, and linear response regimes at sufficiently low temperatures and the statistical behavior generated by an ensemble of trajectories are essentially those of an asymmetric simple exclusion process. Moreover, we find that, at low bias, the system exhibits a negative differential mobility, decreasing with applied bias, to a distinct local minimum in the hopping transport regime. In the context of the dynamical model, we argue the non-monotonic behavior of the transport coefficient can be explained by the role of friction as the particle passes through the minima in each well. Such a model may be employed to describe a wide variety of intriguing transport behaviors. As an example, we show that experimental data on the transition from static to kinetic friction through a plastic regime can be described by such a model.