  The average current of an overdamped Brownian particle moving along the axis
of a three-dimensional periodic tube is investigated in the presence of a
symmetric potential and a temporally symmetric unbiased external force.
Reduction of the spatial dimensionality from two or three physical dimensions
to an effective one dimensional system entails the appearance of not only an
entropic barrier but also an effective diffusion coefficient. We find that the
phase shift between the tube shape and the potential can break the symmetry of
the effective potential and can induce net currents. Under optimal condition,
the current as a function of temperature and the phase shift possesses many
extrema of alternating signs. The current may reverse its direction several
times when temperature or the phase shift is changed. Our model is to describe
the movement of molecular motors along microtubule.
