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.

中文翻译：

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具有集中性质的周期性麦克斯韦-陈-西蒙斯涡旋

为了研究分数量子霍尔效应和任意子超导中的带电涡流和带磁电涡流，麦克斯韦-陈-西蒙斯 (MCS) 模型由 [Lee, Lee, Min (1990)] 引入，作为经典阿贝尔-希格斯模型 (AH) 和陈-西蒙斯 (CS) 模型。在本文中，第一个目标是获得 (MCS) 模型关于 Chern-Simons 参数的均匀 (CS) 极限结果，对特定的解类或涡点数量没有任何限制。为此目的最重要的步骤是推导出希格斯场和中性标量场之间的关系。我们的 (CS) 极限结果也为回答 [Ricciardi,Tarantello (2000)] 和 [Tarantello (2004)] 提出的开放问题提供了关键线索，我们成功地建立了满足超导电子对密度集中特性的周期性麦克斯韦-陈-西蒙斯涡旋的存在性。此外，我们希望本文中的（CS）极限分析有助于研究（MCS）模型解的稳定性、多重性和冒泡现象。