Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk
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| Format: | Preprint |
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2025
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| _version_ | 1866908981460467712 |
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| author | Helffer, Bernard Kachmar, Ayman Nicoleau, François |
| author_facet | Helffer, Bernard Kachmar, Ayman Nicoleau, François |
| contents | We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field limit. This improves recent results of Helffer-Nicoleau (2025) based on special function asymptotics, and extends earlier works by Fournais-Helffer (2006), Kachmar (2006), and R. Fahs, L. Treust, N. Raymond, S. Vũ Ng\d{o}c (2024). Notably, our analysis reveals how the third term encodes the dependence on the magnetic flux. Finally, we investigate the weak magnetic field limit and establish the flux dependence in the asymptotics of Kachmar-Lotoreichik-Sundqvist (2025). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk Helffer, Bernard Kachmar, Ayman Nicoleau, François Spectral Theory Mathematical Physics 58J50, 35P20 We derive a three-term asymptotic expansion for the lowest eigenvalue of the magnetic Laplace and Steklov operators in the exterior of the unit disk in the strong magnetic field limit. This improves recent results of Helffer-Nicoleau (2025) based on special function asymptotics, and extends earlier works by Fournais-Helffer (2006), Kachmar (2006), and R. Fahs, L. Treust, N. Raymond, S. Vũ Ng\d{o}c (2024). Notably, our analysis reveals how the third term encodes the dependence on the magnetic flux. Finally, we investigate the weak magnetic field limit and establish the flux dependence in the asymptotics of Kachmar-Lotoreichik-Sundqvist (2025). |
| title | Flux effects on Magnetic Laplace and Steklov eigenvalues in the exterior of a disk |
| topic | Spectral Theory Mathematical Physics 58J50, 35P20 |
| url | https://arxiv.org/abs/2508.18119 |