The distribution of 3D superconductivity near the second critical field
Ayman Kachmar, Marwa Nasrallah · Nonlinearity · 2016
Abstract We study the minimizers of the Ginzburg–Landau energy functional with a uniform magnetic field in a three dimensional bounded domain. The functional depends on two positive parameters, the Ginzburg–Landau parameter and the intensity of the applied magnetic field, and acts on complex-valued functions and vector fields. We establish a formula for the distribution of the L 2 -norm of the minimizing complex-valued function (order parameter). The formula is valid in the regime where the Ginzburg–Landau parameter is large and the applied magnetic field is close to and strictly below the second critical field—the threshold value corresponding to the transition from the superconducting to the normal phase in the bulk of the sample. Earlier results are valid in 2 D domains and for the L 4 -norm in 3 D domains.