广义岩冢模型的边缘态：磁场在曲线上的快速跃迁
Edge States for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve
摘要：
本文研究了$\mathbb{R}^2$中一类磁拉普拉斯算子的边缘态的局域化和传播性质。我们假设磁场强度沿规则而紧凑的曲线$Γ$有一个快速过渡。我们的主要结果扩展到一般的正则曲线的局部化特征函数的研究时，$Γ$是一条直线（即岩冢模型）。此外，我们包括在我们的分析中的情况下，缓慢变化的磁场沿曲线$Γ$，我们得到了严格和明确的表征的渐近质量分布沿$Γ$的边缘状态。
英文摘要：
In this paper, we study the localization and propagation properties of the edge states associated to a class of magnetic laplacians in $\mathbb{R}^2$. We assume that the intensity of the magnetic field has a fast transition along a regular and compact curve $Γ$. Our main results extend to a general regular curve the study of the localised eigenfunction obtained when $Γ$ is a straight line (i.e. Iwatsuka models). Furthermore, we include in our analysis the case of magnetic fields that slowly change along the curve $Γ$ and we obtain a rigorous and explicit characterization of the asymptotic mass distribution of the edge state along $Γ$.
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