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Lower and upper bounds for the magnetic lowest Dirichlet-to-Neumann eigenvalue in the strong magnetic limit

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GST - Geometric spectral theory and applications

Inspired by some questions presented in a recent arXiv preprint(version v1) by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff,we analyze their conjecture that the ground state energy of the magneticDirichlet-to-Neumann operator tends to $\infty$ as the magnetic fieldtends to $\infty$. More precisely, we explore refined conjectures forgeneral domains in $\mathbb R2$ or $ \mathbb R3$ based on theprevious analysis in the case of the half-plane and the disk. Thispart is a work in collaboration with Ayman Kachmar and Fran\c{c}oisNicoleau. In connexion with old works on the magnetic Schr\”odingeroperator with J. Nourrigat, we will also discuss, if time permits,recent results by Zhongwei Shen.

This talk is part of the Isaac Newton Institute Seminar Series series.

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