Dynamical properties of superconducting arrays

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Abstract
We calculate the current-voltage characteristics of arrays of resistively shunted Josephson junctions (RSJ’s), with and without a transverse magnetic field. In zero field, finite-temperature effects are included via an effective temperature-dependent current noise in each shunt resistance. In an ordered array at zero field, the calculated correlation length and order-parameter susceptibility are consistent with a Kosterlitz-Thouless transition, and the zero-temperature time-dependent voltage V(t) above the critical current resembles that of a single RSJ. For finite transverse magnetic fields at T=0 the calculated critical currents depend on sample size, and differ somewhat from those predicted by purely static calculations. At fields smaller than about one flux quantum per lattice, the critical current decreases quadratically with field. We find no evidence for vanishing critical current in an irrational field, at least for the small finite samples we consider. When the applied current is larger than its critical value, there are regions of both periodic and aperiodic V(t), with discrete and quasicontinuous power spectra, respectively. Under some conditions, we also see hysteretic behavior in the IV characteristics. When the applied field is very small, V(t) sometimes shows a regular sequence of spikes of equal amplitude, interrupted occasionally by aperiodic bursts.