Morphological changes of a superconducting phase in a mixed state with a normal current: a multiple scale analysis

The mixed state of superconducting (SC) and normal (N) phases in one dimensional systems are characterized by several phase slips and localization of the order parameter of the SC phase. The phenomenon is explained on the basis of a complex Ginzburg Landau (CGL) model. We present a simple analysis of the system on multiple scales to capture localization and phase slips when phases coexist.