Quantum effects and the dissipation by quasiparticle tunneling in arrays of Josephson junctions

We investigate the influence of dissipative quasiparticle tunneling currents on quantum effects and phase transitions in d-dimensional arrays of Josephson junctions. We show how the dissipative phase transition, which is known from single junctions at zero temperature, is modified due to the multidimensional coupling. The transition depends on the strength of the dissipation but also on the ratio of Josephson coupling energy to the capacitive charging energy $e^2$/2C. It separates an ordered (superconducting) regime from a disordered (resistive) regime where fluctuations prevent phase coherence. In arrays with small capacitance junctions and weak dissipation, the disordered phase persists down to zero temperature. Finite temperatures modify the phase diagram significantly. A reentrant transition between a resistive and a superconducting state is found for weak dissipation. We also make contact with the familiar phase transitions of d-dimensional XY models and show how the charging energy and dissipation in Josephson-junction arrays influence these transitions. The results are of relevance for granular superconductors.