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arXiv · 2109.09651

Edge States for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve

Arianna Giunti·Juan J. L. Velázquez
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Abstract

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 $\Gamma$. Our main results extend to a general regular curve the study of the localised eigenfunction obtained when $\Gamma$ 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 $\Gamma$ and we obtain a rigorous and explicit characterization of the asymptotic mass distribution of the edge state along $\Gamma$.

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Arianna Giunti, Juan J. L. Velázquez. 2021-09-20. Edge States for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve. https://arxiv.org/abs/2109.09651

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