Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers

Germán Miranda

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arXiv · 2308.14680

Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers

Germán Miranda

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Abstract

The magnetic Laplacian with a step magnetic field has been intensively studied during the last years. We adapt the construction introduced by Bonnaillie-No\"el, Fournais, Kachmar and Raymond to prove the existence of bound states of a new effective operator involving a magnetic step field on a domain with an almost flat magnetic barrier. This result emphasizes the fact that even a small non-smoothness of the discontinuity region can cause the appearance of eigenvalues below the essential spectrum. We also give an example where this effective operator arises.

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Germán Miranda. 2023-08-28. Discrete spectrum of the magnetic Laplacian on almost flat magnetic barriers. https://arxiv.org/abs/2308.14680

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