Aharonov-Anandan phase and persistent currents in a mesoscopic ring

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Abstract
The exact solution for a mesoscopic ring in the presence of a classical, static, inhomogeneous magnetic field is found and used to derive the formulas for persistent currents. From the derivation, we can see the close relation of the Aharonov-Anandan phase to the persistent currents. In the adiabatic limit, our results are shown to be identical with those of Loss et al., who explored the connection between the persistent currents and the Berry phase.