Communications in Mathematical Physics

, Volume 300, Issue 1, pp 147–184

Superconductivity Near the Normal State Under the Action of Electric Currents and Induced Magnetic Fields in \({\mathbb{R}^2}\)


DOI: 10.1007/s00220-010-1111-y

Cite this article as:
Almog, Y., Helffer, B. & Pan, X. Commun. Math. Phys. (2010) 300: 147. doi:10.1007/s00220-010-1111-y


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.

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  2. 2.Laboratoire de MathématiquesUniv. Paris-Sud et CNRSOrsay CedexFrance
  3. 3.Department of MathematicsEast China Normal UniversityShanghaiP.R. China