Abrikosov’s Vortices in the Critical Coupling

“…That is, Ω represents a lattice cell hosting periodically distributed Abrikosov vortices [1], where periodicity is realized by the 't Hooft boundary condition [42,47].…”

Section: Vortex Equations In Presence Of σ(X)-source Termsmentioning

confidence: 99%

Magnetic impurity inspired Abelian Higgs vortices

Han

Yang

2016

J. High Energ. Phys.

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“…The above problem has already been completely solved: when S = R 2 , the problem always has a unique solution [38,70]; when S is a compact surface with total surface area |S|, the problem has a solution (which is unique if exists) if and only if [16,31,56,74] …”

Section: Abelian Higgs Vorticesmentioning

confidence: 99%

“…and the equality is saturated if and only if (u, A) satisfies the self-dual or antiself-dual equations [13,16,38,56,74] …”

Section: Abelian Higgs Vorticesmentioning

confidence: 99%

Geometry, Topology, and Gravitation Synthesized by Cosmic Strings

Yang¹

2007

Pure and Applied Mathematics Quarterly

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In the context of static cosmic strings, the Einstein equations coupled to the Abelian Higgs model and the gauged σ-model reduce into a single equation, which directly relates the Gauss curvature of a Riemann surface hosting nontrivial geometry and gravitation to the energy density of the coupled matter-gauge sector. This equation gives rise to an equivalence relation between the topology of the Riemann surface and the topology of the complex line bundle which hosts and is determined by the physical interactions of the matter-gauge sector. The existence of solutions realizing a prescribed distribution of cosmic strings resembles the classical prescribed Gauss curvature problem.

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“…The vortex-type critical points for the energy associated with E δ , namely, the solutions of (1.1)-(1.2), have received considerable attention in recent years, in view of both their physical and geometrical interest; see, e.g., García-Prada [8], Hong, Jost, and Struwe [10], Stuart [17], Taubes [19], Wang and Yang [20], and the references therein. In particular, Hong, Jost, and Struwe [10] consider (1.1)-(1.2) on a compact Riemannian surface and perform a detailed analysis of the asymptotics as δ → 0 + .…”

Section: Introductionmentioning

confidence: 99%

Asymptotics for Selfdual Vortices on the Torus and on the Plane: A Gluing Technique

Macrì¹,

Nolasco²,

Ricciardi³

2005

SIAM J. Math. Anal.

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Abstract. We consider multivortex solutions for the selfdual Abelian Higgs model, as the ratio of the vortex core size to the separation distance between vortex points (the scaling parameter) tends to zero. To this end, we use a gluing technique (a shadowing lemma) for solutions to the corresponding semilinear elliptic equation on the plane, allowing any number (finite or countable) of arbitrarily prescribed singular sources. Our approach is particularly convenient and natural for the study of the asymptotics. In particular, in the physically relevant cases where the vortex points are either finite or periodically arranged in the plane, we prove that a frequently used factorization ansatz for multivortex solutions is rigorously satisfied, up to an error which is exponentially small.

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Abrikosov’s Vortices in the Critical Coupling

Cited by 76 publications

References 20 publications

Magnetic impurity inspired Abelian Higgs vortices

Magnetic impurity inspired Abelian Higgs vortices

Geometry, Topology, and Gravitation Synthesized by Cosmic Strings

Asymptotics for Selfdual Vortices on the Torus and on the Plane: A Gluing Technique

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