Quantum Vortex Dynamics in Josephson Junction Arrays. Ballistic Motion, Dissipation, and Tunnelling

Vortices in arrays of low-capacitance Josephson junctions behave as quantum particles showing tunnelling and interference effects. Classical arguments predict a vortex mass, but simultaneously a strong damping due to the excitation of spin waves. We show that the discrete nature of the charges on the islands leads to qualitatively new results. the spin wave spectrum becomes stiffer, which substantially reduces the dissipation. Ballistic motion of vortices becomes possible in a wide range of velocities, consistent with recent experiments. The vortex properties change further near the superconductor-insulator transition found in these arrays.