Berry’s phase, motive forces, and mesoscopic conductivity

A ring in a magnetic field whose direction varies in space is considered. It is shown that the Berry phase accumulated by the spins of electrons encircling the ring affects the conductance of the ring in a way similar to the Aharonov-Bohm effect. A time-dependent Berry phase is shown to induce a motive force in the ring. This motive force couples to the electron’s spin, similar to the way Faraday’s law couples an electromotive force to the electric charge.