Convergence of Ginzburg-Landau Functionals in Three-Dimensional Superconductivity

S. Baldo; R. L. Jerrard; G. Orlandi; H. M. Soner

doi:10.1007/s00205-012-0527-2

Convergence of Ginzburg-Landau Functionals in Three-Dimensional Superconductivity

S. Baldo, R. L. Jerrard, G. Orlandi, H. M. Soner

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

In this paper we consider the asymptotic behavior of the Ginzburg-Landau model for superconductivity in three dimensions, in various energy regimes. Through an analysis via Γ-convergence, we rigorously derive a reduced model for the vortex density and deduce a curvature equation for the vortex lines. In the companion paper (Baldo et al. Commun. Math. Phys. 2012, to appear) we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H _c1, and the critical angular velocity of rotating Bose-Einstein condensates.

Original language	English (US)
Pages (from-to)	699-752
Number of pages	54
Journal	Archive for Rational Mechanics and Analysis
Volume	205
Issue number	3
DOIs	https://doi.org/10.1007/s00205-012-0527-2
State	Published - Aug 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-012-0527-2

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AB - In this paper we consider the asymptotic behavior of the Ginzburg-Landau model for superconductivity in three dimensions, in various energy regimes. Through an analysis via Γ-convergence, we rigorously derive a reduced model for the vortex density and deduce a curvature equation for the vortex lines. In the companion paper (Baldo et al. Commun. Math. Phys. 2012, to appear) we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H c1, and the critical angular velocity of rotating Bose-Einstein condensates.

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Convergence of Ginzburg-Landau Functionals in Three-Dimensional Superconductivity

Abstract

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