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Josephson Junction Arrays with Long-Range Interactions

#### 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