2019/07/08 by Weiwei Ao, Ao, Weiwei, Youngae Lee +3
Mathematics · Physics and Astronomy · #35J47 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Quantum and electron transport phenomena #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1907.03559
openalex publication_date 2019/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.