Γ-limit of the Ginzburg–Landau energy in a thin domain with a large magnetic field

Extract

A one-dimensional Ginzburg–Landau model that describes a superconducting closed thin wire with an arbitrary cross-section subject to a large applied magnetic field is derived from the three-dimensional Ginzburg–Landau energy in the spirit of Γ-convergence. Our result proves the validity of the formal result of Richardson and Rubinstein, which reveals the double limit of a large field and a thin domain. An additional magnetic potential related to the applied field is found in the limiting functional, which yields a parabolic background for the oscillatory phase transition curve between the normal and superconducting states.