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Edge states for magnetic Schrödinger operators in domains with compact boundary

Arianna Giunti (Imperial College London)
Tuesday 4 May 2021 16:15 Zoom
Mathematics Seminar

In this talk we consider a magnetic Schrödinger operator H in a domain $\Omega \subset {\mathbb R}^2$ with compact boundary. We impose Dirichlet boundary conditions on $\partial \Omega$. For a constant magnetic field having large intensity, we focus on the existence and the description of the edge states, namely eigenfunctions for H whose mass is localized along the boundary $\partial \Omega$. We show that such edge states exist and we give a detailed description of the localization and distribution of their mass along $\partial \Omega$. From this result, we also infer asymptotic formulas for the eigenvalues of H. If time allows, we briefly discuss how the previous localization results generalise to a class of Iwatsuka models, namely when the presence of a boundary $\partial \Omega$ is replaced by a fast oscillation of the magnetic field along an interface.

This talk is based on joint works with J.J. L. Velazquez (IAM Bonn).

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Organised by: SQM
Revised: 24.11.2021