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