  Applying the non-adiabatic Aharonov-Anandan phase approach to a mesoscopic
ring with non-interacting many electrons in the presence of the spin-orbit
interaction, Zeeman coupling and magnetic flux, we show that the time-reversal
symmetry breaking due to Zeeman coupling is intrinsically different from that
due to magnetic flux. We find that the direction of the persistent currents
induced by the Zeeman coupling changes periodically with the particle number,
while the magnetic flux determines the direction of the induced currents by its
sign alone.
