The magnetic D-to-N ground state energy obeys λ = α̂ b^{1/2} − α̂² + (1/3) max κ + o(1) in 2D, with a 3D limit given by the boundary infimum of λ^DN(ϑ(x)) |B(x)|^{1/2}.
On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--
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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 on the disk tends to $+\infty$ as the magnetic field tends to $+\infty$. This is an important step towards the analysis of the curvature effect in the case of general domains in $\mathbb R^2$.
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Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
The magnetic D-to-N ground state energy obeys λ = α̂ b^{1/2} − α̂² + (1/3) max κ + o(1) in 2D, with a 3D limit given by the boundary infimum of λ^DN(ϑ(x)) |B(x)|^{1/2}.