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Large-Field Eigenvalue Asymptotics of the Magnetic Dirichlet-to-Neumann Operator

How the lowest eigenvalue (ground-state energy) of the magnetic Dirichlet-to-Neumann operator on a bounded domain behaves as the applied constant magnetic field grows large. Establishes that this eigenvalue tends to infinity and derives its precise leading-order asymptotics for general smooth two-dimensional domains, extends the result to three dimensions, and connects it to the large-field eigenvalue asymptotics of the magnetic Robin Laplacian.

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ASYMPTOTICS FOR THE MAGNETIC DIRICHLET-TO-NEUMANN EIGENVALUES IN GENERAL DOMAINS BERNARD HELFFER

Studies the magnetic Dirichlet-to-Neumann operator: for the magnetic Schrodinger operator on a bounded domain, the boundary operator sending a function's prescribed boundary values to the boundary no…