  We consider the motion of electrons through a mesoscopic ring in the presence
of spin-orbit interaction, Zeeman coupling, and magnetic flux. The coupling
between the spin and the orbital degrees of freedom results in the geometric
and the dynamical phases associated with a cyclic evolution of spin state.
Using a non-adiabatic Aharonov-Anandan phase approach, we obtain the exact
solution of the system and identify the geometric and the dynamical phases for
the energy eigenstates. Spin precession of electrons encircling the ring can
lead to various interference phenomena such as oscillating persistent current
and conductance. We investigate the transport properties of the ring connected
to current leads to explore the roles of the time-reversal symmetry and its
breaking therein with the spin degree of freedom being fully taken into
account. We derive an exact expression for the transmission probability through
the ring. We point out that the time-reversal symmetry breaking due to Zeeman
coupling can totally invalidate the picture that spin precession results in
effective, spin-dependent Aharonov-Bohm flux for interfering electrons.
Actually, such a picture is only valid in the Aharonov-Casher effect induced by
spin-orbit interaction only. Unfortunately, this point has not been realized in
prior works on the transmission probability in the presence of both SO
interaction and Zeeman coupling. We carry out numerical computation to
illustrate the joint effects of spin-orbit interaction, Zeeman coupling and
magnetic flux. By examining the resonant tunneling of electrons in the weak
coupling limit, we establish a connection between the observable time-reversal
symmetry breaking effects manifested by the persistent current and by the
transmission probability. For a ring formed by two-dimensional electron gas, we
