A strong periodic potential generally enhances the short wavelength fluctuations of a superfluid beyond the validity of standard continuum approaches. Here we report some recent results on hard core bosons on finite lattices. We find several interesting effects of the periodic potential on the ground state, vortex dynamics, and and Hall conductivity. For example, the Magnus field on a vortex abruptly reverses direction at half filling. A rotating Bose condensate on an optical lattice may allow an experimental test of our results. Insight may also be gained about strongly fluctuating superconductors modelled by charge 2e lattice bosons.
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