A modified Ginzburg-Landau model for Josephson junctions in a ring

Hill, E.; Rubinstein, J.; Sternberg, P.

doi:10.1090/qam/1914438

Authors: E. Hill, J. Rubinstein and P. Sternberg
Journal: Quart. Appl. Math. 60 (2002), 485-503
MSC: Primary 35Q60; Secondary 35B27, 35J20, 82D55
DOI: https://doi.org/10.1090/qam/1914438
MathSciNet review: MR1914438
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Abstract: We consider the Ginzburg-Landau functional to analyze SNS junctions in a one-dimensional ring. We compare several canonical scalings. The linearized problem is solved to obtain the phase transition curves. We compute the $\Gamma$-limit of the functional in the different scalings. The interaction of several junctions is analyzed. We study the zero set of the order parameter for distinguished values of the flux. Finally, we compute the currents in the weakly nonlinear regime.

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