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Satellite meeting "Spectral Theory of Coulomb Systems - Symposion in honor of Heinz Siedentop on the occasion of his 60th birthday"
Organizers: Volker Bach (Braunschweig), Laszlo Erdös (Munich), Rupert Frank (Princeton), Simone Warzel (Munich)


Bernard Helffer (Paris, France): "Global stability of the normal state of superconductors in the presence of a strong electric current"
Saturday 20 April 2013, 09:00 - 09:35
Amphi Hermite


Abstract: We consider the time-dependent Ginzburg-Landau model of superconductivity in the presence of an electric current flowing through a two-dimensional wire. We show that when the current is sufficiently strong the solution converges in the long-time limit to the normal state. We provide two types of upper bounds for the critical current where such global stability is achieved: by using the principal eigenvalue of the magnetic Laplacian associated with the normal magnetic field, and through the norm of the resolvent of the linearized steady-state operator. In the latter case we estimate the resolvent norm in large domains by the norms of approximate operators defined on the plane and the half-plane. We also obtain a lower bound, in large domains, for the above critical current by obtaining the current for which the normal state looses its local stability. This is joint work with Yaniv Almog.