Quantum vortex dynamics in Josephson arrays and optical lattices

In Josephson junction arrays, vortices form stable topological excitations. A key step towards the understanding of their properties was the observation made by Eckern and Schmid that in low-capacitance junction arrays a vortex behaves as a massive particle moving in a periodic potential and subject to dissipation. The mass is low and quantum effects become observable. The present contribution provides a review of these properties together with a discussion of similar scenarios realized in optical lattices.