Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains Article Swipe

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Eigenvalues and eigenvectors Dirichlet distribution Mathematics Dirichlet eigenvalue Pure mathematics Applied mathematics Mathematical analysis Dirichlet's principle Physics Quantum mechanics Boundary value problem

Bernard Helffer , Ayman Kachmar , François Nicoleau ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2501.00947 · OA: W4406033050

Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity as the magnetic field tends to infinity. More precisely, we prove refined conjectures for general two dimensional domains, based on the analysis in the case of the half-plane and the disk by two of us (B.H. and F.N.). We also extend our analysis to the three dimensional case, and explore a connection with the eigenvalue asymptotics of the magnetic Robin Laplacian.