EFFECTS OF GEOMETRIC PHASES IN JOSEPHSON-JUNCTION ARRAYS

We show that the sn route vortex velocity dependent part of the Magnus force in a Josephson junction array is effectively zero, and predict zero Hall effect ill the classical limit. However, geometric phases du e to the finite superfluid density at superconductor grains have a pro found influence on the quantum dynamics of vortices. Subsequently we f md rich and complex Hall behaviors analogous to the Thouless-Kohmoto-N ightingale-den Nijs effect in the quantum regime.