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Article Dans Une Revue Journal of Mathematical Physics Année : 2023

MAGNETIC PERTURBATIONS OF THE ROBIN LAPLACIAN IN THE STRONG COUPLING LIMIT

Résumé

This paper is devoted to the asymptotic analysis of the eigenvalues of the Laplace operator with a strong magnetic field and Robin boundary condition on a smooth planar domain and with a negative boundary parameter. We study the singular limit when the Robin parameter tends to infinity which is equivalent to a semi-classical limit involving a small positive semi-classical parameter. The main result is a comparison between the spectrum of the Robin Laplacian with an effective operator defined on the boundary of the domain via the Born-Oppenheimer approximation. More precisely, the low-lying eigenvalue of the Robin Laplacian is approximated by the those of the effective operator. When the curvature has a unique non-degenerate maximum, we estimate the spectral gap and find that the magnetic field does not contribute to the three-term expansion of the eigenvalues. In the case of the disc domains, the eigenvalue asymptotics displays the contribution of the magnetic field explicitly.
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Dates et versions

hal-03410740 , version 1 (01-11-2021)
hal-03410740 , version 2 (12-11-2021)
hal-03410740 , version 3 (04-02-2022)
hal-03410740 , version 4 (01-05-2023)

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Rayan Fahs. MAGNETIC PERTURBATIONS OF THE ROBIN LAPLACIAN IN THE STRONG COUPLING LIMIT. Journal of Mathematical Physics, 2023, 64 (4), ⟨10.1063/5.0101330⟩. ⟨hal-03410740v4⟩
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