On the Behavior of a Superconducting Wire Subjected to a Constant Voltage Difference

We investigate a version of the time-dependent Ginzburg-Landau system that models a thin superconducting wire subjected to an applied voltage. Using a mixture of rigorous analysis, formal asymptotics and numerics, we analyze the behavior of solutions as the physical parameters of wire length, voltage and temperature are varied. Stable periodic solutions are shown to exist exhibiting phase slip centers (zeros of the order parameter), with period-doubling, period-tripling and chaotic behavior emerging in certain length/voltage regimes.