This paper is a rather informal survey on some recent results, presented at SIMAI 2010, on the asymptotic behavior of Ginzburg-Landau energies describing 3-D superconductivity and Bose-Einstein condensation in critical regimes where vortex nucleation occurs. As an application we rigorously derive an asymptotic expression for the relevant thresholds (respectively, the first critical magnetic field for type II superconductivity and the critical angular velocity for rotating Bose-Einstein condensates) and the curvature equation for vortices. The analysis rely on Gamma-convergence techniques. A complete description of the theory sketched here, together with the proofs, is given in forthcoming papers.
Asymptotics for Ginzburg-Landau energies in 3-D condensed matter physics
BALDO, Sisto;ORLANDI, Giandomenico;
2011-01-01
Abstract
This paper is a rather informal survey on some recent results, presented at SIMAI 2010, on the asymptotic behavior of Ginzburg-Landau energies describing 3-D superconductivity and Bose-Einstein condensation in critical regimes where vortex nucleation occurs. As an application we rigorously derive an asymptotic expression for the relevant thresholds (respectively, the first critical magnetic field for type II superconductivity and the critical angular velocity for rotating Bose-Einstein condensates) and the curvature equation for vortices. The analysis rely on Gamma-convergence techniques. A complete description of the theory sketched here, together with the proofs, is given in forthcoming papers.
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