RESPONSE OF JOSEPHSON-JUNCTION ARRAYS NEAR THE QUANTUM PHASE-TRANSITION

We study the superconductor-insulator transition of a two-dimensional Bose-Hubbard model, considering as a specific example, an array of Jos ephson junctions. Within a coarse-graining approach we derive an effec tive free-energy functional from which we determine the phase diagram. At zero temperature it consists of a superconducting phase and Mott-i nsulating lobes. The phase boundaries of some of these lobes display r eentrant behavior as a function of temperature. Next, we evaluate the electromagnetic-response functions of the system. The real part of the longitudinal conductivity is characterized by an excitation gap, wher eas the imaginary part describes a capacitor. In an ideal system, unde r certain conditions a universal conductance is found at the transitio n. If we add low frequency dissipation to the model a different value of the universal conductance is found, but still it is independent of the strength of the dissipation. Qualitatively differing results are o btained for frustrated and unfrustrated systems. We also discuss the H all conductance of the system.