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Vortices and pinning effects for the Ginzburg‐Landau model in multiply connected domains
Author(s) -
Alama Stan,
Bronsard Lia
Publication year - 2006
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20086
Subject(s) - vortex , mathematics , statistical physics , condensed matter physics , physics , mechanics
We consider the two‐dimensional Ginzburg‐Landau model with magnetic field for a superconductor with a multiply connected cross section. We study energy minimizers in the London limit as the Ginzburg‐Landau parameter κ = 1/ϵ → ∞ to determine the number and asymptotic location of vortices. We show that the holes act as pinning sites, acquiring nonzero winding for bounded fields and attracting all vortices away from the interior for fields up to a critical value h ex = O (|1nϵ|). At the critical level the pinning effect breaks down, and vortices appear in the interior of the superconductor at locations that we identify explicitly in terms of the solutions of an elliptic boundary value problem. The method involves sharp upper and lower energy estimates, and a careful analysis of the limiting problem that captures the interaction between the vortices and the holes. © 2005 Wiley Periodicals, Inc.

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