  Dynamics of a discrete polymer in time-dependent external potentials is
studied with the master equation approach. We consider both stochastic and
deterministic switching mechanisms for the potential states and give the
essential equations for computing the stationary state properties of molecules
with internal structure in time-dependent periodic potentials on a lattice. As
an example, we consider standard and modified Rubinstein-Duke polymers and
calculate their mean drift and effective diffusion coefficient in the two-state
non-symmetric flashing potential and symmetric traveling potential. Rich
non-linear behavior of these observables is found. By varying the polymer
length, we find current inversions caused by the rebound effect that is only
present for molecules with internal structure. These results depend strongly on
the polymer type. We also notice increased transport coherence for longer
polymers.

Statistical Mechanics