The decrease of bulk-superconductivity close to the second critical field in the ginzburg-landau model

Etienne Sandier; Sylvia Serfaty

doi:10.1137/S0036141002406084

The decrease of bulk-superconductivity close to the second critical field in the ginzburg-landau model

Etienne Sandier, Sylvia Serfaty

Mathematics

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

Abstract

We study solutions of the Ginzburg-Landau equations describing superconductors in a magnetic field, just below the "second critical field" H_c2. We thus bridge the gap between the situations described in [E. Sandier and S. Serfaty, Rev. Math. Phys., 12 (2000), pp. 1219-1257] and [X. B. Pan, Comm. Math. Phys., 228 (2002), pp. 327-370]. We prove estimates on the energy, among them one by an algebraic trick inspired by the Bogomoln'yi trick for self-duality. We thus show how, for energy-minimizers, superconductivity decreases in average in the bulk of the sample when the applied field increases to H_c2.

Original language	English (US)
Pages (from-to)	939-956
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	34
Issue number	4
DOIs	https://doi.org/10.1137/S0036141002406084
State	Published - 2003

Keywords

Asymptotic analysis
Phase transitions
Second critical field
Superconductivity

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036141002406084

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AB - We study solutions of the Ginzburg-Landau equations describing superconductors in a magnetic field, just below the "second critical field" Hc2. We thus bridge the gap between the situations described in [E. Sandier and S. Serfaty, Rev. Math. Phys., 12 (2000), pp. 1219-1257] and [X. B. Pan, Comm. Math. Phys., 228 (2002), pp. 327-370]. We prove estimates on the energy, among them one by an algebraic trick inspired by the Bogomoln'yi trick for self-duality. We thus show how, for energy-minimizers, superconductivity decreases in average in the bulk of the sample when the applied field increases to Hc2.

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The decrease of bulk-superconductivity close to the second critical field in the ginzburg-landau model

Abstract

Keywords

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