Title of article :
Gamma limit of the nonself-dual Chern–Simons–Higgs energy
Author/Authors :
Matthias Kurzke، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
Pages :
54
From page :
535
To page :
588
Abstract :
We consider the Gamma limit of the Abelian Chern–Simons–Higgs energy Gcsh := 1 2 U |∇Aεuε|2 + μ2 4 |curlAε − hex|2 |uε|2 + 1 ε2 |uε|2 1 − |uε|2 2 dx on a bounded, simply connected, two-dimensional domain under the ε→0 limit. As a first step we study the Gamma limit of Ecsh := 1 2 U |∇uε|2 + 1 ε2 |uε|2 1 − |uε|2 2 dx under two different scalings; Ecsh ≈ |log ε| and Ecsh ≈ |log ε|2. We apply the |log ε|2-scaling result to the full Chern–Simons–Higgs energy Gcsh, and as a consequence we are able to compute the first critical field H1 = H1(U,μ) for the nucleation of a vortex. The method entails estimating in certain weak topologies the Jacobian J(uε) = det(∇uε) in terms of the Chern–Simons–Higgs energy Ecsh. © 2008 Elsevier Inc. All rights reserved.
Keywords :
Chern–Simons–Higgs theory , gamma convergence , Jacobian compactness , Vortices , Critical field
Journal title :
Journal of Functional Analysis
Serial Year :
2008
Journal title :
Journal of Functional Analysis
Record number :
839672
Link To Document :
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