We show how the partition function of a network of parallel superconductingwires weakly coupled together by the proximity effect, subjected a vectorpotential along the wires can be mapped onto N-distinguishable two dimensionalquantum-mechanics problem with a perpendicular imaginary magnetic field. Then,we show, using a mean field approximation, that, for a given coupling, there isa critical temperature for onset of inter-wire phase coherence. The transitiontemperature $T_c$ is plotted on both cases for non-magnetic and a magneticfield perpendicular to the wires.
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