Selfdual Maxwell-Chern-Simons Vortices

Tarantello, Gabriella

doi:10.1007/s00032-004-0030-9

Cited by 10 publications

(5 citation statements)

References 114 publications

(154 reference statements)

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“…In this article, one of main goals is to improve the (CS) limit analysis for (MCS) model without any restriction on either a particular class of solutions, the number of vortex points, or the Chern-Simons parameter. Moreover, in view of our first result, we could also obtain the affirmative answers for the open problems raised by Ricciardi and Tarantello in [49], and Tarantello in [55].…”

supporting

confidence: 65%

“…In view of Theorem 1.1, we note that the blow up phenomena implies the concentration of density for the nonlinear terms in the first equation in (1.9). We emphasize that this observation provides the affirmative answer for the open problem raised in [55]. In other words, we would like to show the existence of blow up solutions with the concentrating property at the vortex points.…”

supporting

confidence: 58%

“…The most important step for this purpose is to derive the relation between the Higgs field and the neutral scalar field. Our (CS) limit result also provides the critical clue to answer the open problems raised by [Ricciardi,Tarantello (2000)] and [Tarantello (2004)], and we succeed to establish the existence of periodic Maxwell-Chern-Simons vortices satisfying the concentrating property of the density of superconductive electron pairs. Furthermore, we expect that the (CS) limit analysis in this paper would help to study the stability, multiplicity, and bubbling phenomena for solutions of the (MCS) model.…”

mentioning

confidence: 61%

“…Motivated by Theorem 1.1 and Theorem 1.2, we also could solve the open problem raised in [55], and show the existence of blow up solutions with the concentrating property at the vortex point.…”

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confidence: 99%

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Periodic Maxwell-Chern-Simons vortices with concentrating property

Ao¹,

Lee²,

Kwon³

2019

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In order to study electrically and magnetically charged vortices in fractional quantum Hall effect and anyonic superconductivity, the Maxwell-Chern-Simons (MCS) model was introduced by [Lee, Lee, Min (1990)] as a unified system of the classical Abelian-Higgs model (AH) and the Chern-Simons (CS) model. In this article, the first goal is to obtain the uniform (CS) limit result of (MCS) model with respect to the Chern-Simons parameter without any restriction on either a particular class of solutions or the number of vortex points. The most important step for this purpose is to derive the relation between the Higgs field and the neutral scalar field. Our (CS) limit result also provides the critical clue to answer the open problems raised by [Ricciardi,Tarantello (2000)] and [Tarantello (2004)], and we succeed to establish the existence of periodic Maxwell-Chern-Simons vortices satisfying the concentrating property of the density of superconductive electron pairs. Furthermore, we expect that the (CS) limit analysis in this paper would help to study the stability, multiplicity, and bubbling phenomena for solutions of the (MCS) model. INTRODUCTIONAs the pioneering work by Ginzburg and Landau, the classical Abelian-Higgs (AH) model (or, Maxwell-Higgs) was proposed in order to describe the superconductivity phenomena at low temperature (see [4,35,39,47]). This model has been studied in [6,35,56,59] for various domains. However, (AH) model can only describes electrically neutral vortices, which are static solutions of the corresponding Euler-Lagrange equation. In order to study the fractional quantum Hall effect and high temperature superconductivity, we should investigate electrically and magnetically "charged" vortices. For this purpose, one might attempt to include Chern-Simons (CS) term into (AH) model. However, just adding (CS) term into (AH) model loses the self-dual structure, which is characterized by a special class of static solution corresponding to a constrained energy minimizer. The self-dual equation has a benefit in the gauge field theory since it is a reduced first-order equation, so called "Bogomol'nyi equation", for the more complicated second order equation of motion (see [5,43]). In order to obtain a self-dual Chern-Simons theory, Hong-Kim-Pac in [33] and Jackiw-Weinberg in [34] independently proposed a model for charged vortices with electrodynamics governed only by the (CS) term without Maxwell term, which was included in the (AH) model. This pure (CS) model was suggested from the observation such that the (CS) term is dominant over the Maxwell term in the large scale. During the last few decades, the (CS) model has been extensively studied in [

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confidence: 65%

supporting

confidence: 58%

mentioning

confidence: 61%

mentioning

confidence: 99%

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Periodic Maxwell-Chern-Simons vortices with concentrating property

Ao¹,

Lee²,

Kwon³

2019

Preprint

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“…By choosing a suitable Higgs potential in gauge models, we can obtain minimum energy static vortices satisfying a first order equation, which is called the self duality equation. Self-dual vortices in various models have been studied extensively (see [3,4,5,6,7,14,18,20,26,27,28,29,33] and reference there in).…”

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confidence: 99%