For the unit disk with a constant magnetic field of strength 2b, the ground state energy of the magnetic Dirichlet-to-Neumann operator satisfies λ_DN(b)=α√b-(α²+2)/6+O(b^{-1/2}) with α=0.76495..., the unique negative zero of the parabolic cylinder function D_{1/2}.
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On the magnetic Dirichlet to Neumann operator on the disk -- strong diamagnetism and strong magnetic field limit--
For the unit disk with a constant magnetic field of strength 2b, the ground state energy of the magnetic Dirichlet-to-Neumann operator satisfies λ_DN(b)=α√b-(α²+2)/6+O(b^{-1/2}) with α=0.76495..., the unique negative zero of the parabolic cylinder function D_{1/2}.