Bifurcation and stability of superconductivity

Abstract

In this article, we present a bifurcation and stability analysis on time-dependent Ginzburg–Landau model of superconductivity. It is proved in particular that there are two different phase transitions from the normal state to superconducting states or vice versa: one is continuous, and the other is jump. These two transitions are precisely determined by a simple nondimensional parameter, which links the superconducting behavior with the geometry of the material, the applied field and the physical parameters. The rigorous analysis is conducted using a bifurcation theory newly developed by the authors, and provides some interesting physical predictions.