Author:
Giunti Arianna,Velázquez Juan J. L.
Abstract
AbstractIn this paper, we study the localization and propagation properties of the edge states associated with a class of magnetic Laplacians in$$\mathbb {R}^2$$R2. We assume that the intensity of the magnetic field has a fast transition along a regular and compact curve$$\Gamma $$Γ. Our main results extend to a general regular curve the study of the localized eigenfunction obtained when$$\Gamma $$Γis a straight line (i.e.Iwatsuka models). Furthermore, we include in our analysis the case of magnetic fields that slowly change along the curve$$\Gamma $$Γand we obtain a rigorous and explicit characterization of the asymptotic mass distribution of the edge state along$$\Gamma $$Γ.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics
Reference20 articles.
1. Assaad, W., Kachmar, A., Persson-Sundqvist, M.: The distribution of superconductivity near a magnetic barrier. Commun. Math. Phys. 366(1), 269–332 (2019)
2. Assaad, W., Helffer, B., Kachmar, A.: Semi-classical eigenvalue estimates under magnetic steps. ArXiv Preprint (2021)
3. Avron, J., Herbst, I., Simon, B.: Schrödinger operators with magnetic fields. I. General interactions. Duke Math. J. 4, 847–883 (1978)
4. Barbaroux, J.-M., Le Treust, L., Raymond, N., Stockmeyer, E.: On the semi-classical spectrum of the Dirichlet-Pauli operator, ArXiv Preprint (2020)
5. Bernevig, B.A., Hughes, T.L.: Topological Insulators and Topological Superconductors. Princeton University Press (2013)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Effective operators on an attractive magnetic edge;Journal de l’École polytechnique — Mathématiques;2023-05-09