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Algebra i Analiz, 2004, Volume 16, Issue 1, Pages 239–268 (Mi aa595)  

This article is cited in 10 scientific papers (total in 10 papers)

Research Papers

Pinning of magnetic vortices by an external potential

I. M. Sigala, F. Tingbc

a Department of Mathematics, University of Toronto, Toronto, ON, Canada
b Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, Canada
c Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA
References:
Abstract: The existence and uniqueness of vortex solutions is proved for the Ginzburg–Landau equations with external potentials in $\mathbb R^2$. These equations describe the equilibrium states of superconductors and the stationary states of the $U(1)$-Higgs model of particle physics. In the former case, the external potentials are due to impurities and defects. Without the external potentials, the equations are translationally (as well as gauge) invariant, and they have gauge equivalent families of vortex (equivariant) solutions called magnetic or Abrikosov vortices, centered at arbitrary points of $\mathbb R^2$. For smooth and sufficiently small external potentials, it is shown that for each critical point $z_0$ of the potential, there exists a perturbed vortex solution centered near $z_0$, and that there are no other single vortex solutions. This result confirms the “pinning” phenomena observed and described in physics, whereby magnetic vortices are pinned down to impurities or defects in the superconductor.
Keywords: superconductivity, Ginzburg–Landau equations, pinning, magnetic vortices, external potential, existence.
Received: 20.11.2003
English version:
St. Petersburg Mathematical Journal, 2005, Volume 16, Issue 1, Pages 211–236
DOI: https://doi.org/10.1090/S1061-0022-04-00848-9
Bibliographic databases:
Document Type: Article
Language: English
Citation: I. M. Sigal, F. Ting, “Pinning of magnetic vortices by an external potential”, Algebra i Analiz, 16:1 (2004), 239–268; St. Petersburg Math. J., 16:1 (2005), 211–236
Citation in format AMSBIB
\Bibitem{SigTin04}
\by I.~M.~Sigal, F.~Ting
\paper Pinning of magnetic vortices by an external potential
\jour Algebra i Analiz
\yr 2004
\vol 16
\issue 1
\pages 239--268
\mathnet{http://mi.mathnet.ru/aa595}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2069485}
\zmath{https://zbmath.org/?q=an:1067.58015}
\transl
\jour St. Petersburg Math. J.
\yr 2005
\vol 16
\issue 1
\pages 211--236
\crossref{https://doi.org/10.1090/S1061-0022-04-00848-9}
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  • https://www.mathnet.ru/eng/aa/v16/i1/p239
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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