  We consider the effect of an oscillating potential on the single-particle
spectrum and the time-averaged persistent current of a one-dimensional
phase-coherent mesoscopic ring with a magnetic flux. We show that in a ring
with an even number of spinless electrons the oscillating potential has a
strong effect on the persistent current when the excited side bands are close
to the eigen levels of a pure ring. Resonant enhancement of side bands of the
Floquet state generates a sign change of the persistent current.
