We show how the partition function of a network of parallel superconducting wires weakly coupled together by the proximity effect, subjected a vector potential along the wires can be mapped onto N-distinguishable two dimensional quantum-mechanics problem with a perpendicular imaginary magnetic field. Then, we show, using a mean field approximation, that, for a given coupling, there is a critical temperature for onset of inter-wire phase coherence. The transition temperature Tc is plotted on both cases for non-magnetic and a magnetic field perpendicular to the wires.
@article{arxiv.0806.3551,
title = {Theory of Fluctuations in a Network of Parallel Superconducting Wires},
author = {Kohjiro Kobayashi and David Stroud},
journal= {arXiv preprint arXiv:0806.3551},
year = {2008}
}