J. Kent Harbaugh and D. Stroud, Department of Physics, The Ohio State University, Columbus, Ohio 43210-1106

We calculate the current-voltage (IV) characteristics of a Josephson junction array with long-range interactions. The array consists of two sets of equally-spaced parallel superconducting wires placed at right angles. A Josephson junction is formed at every point wherever the wires cross. We treat each such junction as an overdamped resistively-shunted junction, and each wire segment between two junctions as a similar resistively-shunted junction with a much higher critical current. The IV characteristics are obtained by solving the coupled Josephson equations numerically. We find that, for a sufficiently large number of wires, the critical current saturates at a finite value because of the wire inductance, in excellent agreement with experiment. The calculated IV characteristics also show a striking hysteresis, even though each of the individual junctions is non-hysteretic. The hysteresis results from a global redistribution of current flow on the upper and lower voltage branches, and is also in excellent agreement with experiment.

PACS Nos.: 74.50.+r, 74.40.+k