Metastable currents in loops with Josephson junctions

The problem of persistent currents in loops interrupted by Josephson junctions is considered. We prove that persistent currents are related to local minimizers of the Ginzburg Landau energy functional. Although the order parameter is discontinuous at the junction, we show that the local minimizers are related to the homotopy types of the domain. Therefore, persistent currents will occur in any multiply connected domain if the junction strength is weak enough.