  Time periodic perturbations of an electron system on a ring are examined. For
small frequencies periodic small amplitude perturbations give rise to side band
currents which in leading order are inversely proportional to the frequency.
These side band currents compensate the current of the central band such that
to leading order no net pumped current is generated. In the non-adiabatic
limit, larger pump frequencies can lead to resonant excitations: as a
consequence a net pumped current arises. We illustrate our results for a one
channel ring with a quantum dot whose barriers are modulated parametrically.
