Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in {mathbb{R}^2} |
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Authors: | Yaniv Almog Bernard Helffer Xing-Bin Pan |
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Affiliation: | 1. Department of Mathematics, Louisiana State University, Baton Rouge, LA, 70803, USA 2. Laboratoire de Mathématiques, Univ. Paris-Sud et CNRS, Bat 425, 91 405, Orsay Cedex, France 3. Department of Mathematics, East China Normal University, Shanghai, 200062, P.R. China
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Abstract: | We consider the linearization of the time-dependent Ginzburg-Landau system near the normal state. We assume that an electric current is applied through the sample, which captures the whole plane, inducing thereby, a magnetic field. We show that independently of the current, the normal state is always stable. Using Fourier analysis the detailed behaviour of solutions is obtained as well. Relying on semi-group theory we then obtain the spectral properties of the steady-state elliptic operator. |
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