A semiclassical Birkhoff normal form for constant-rank magnetic fields
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866914848288276480 |
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| author | Morin, Léo |
| author_facet | Morin, Léo |
| contents | We consider the semiclassical magnetic Laplacian $\mathcal{L}_h$ on a Riemannian manifold, with a constant-rank and non-vanishing magnetic field $B$. Under the localization assumption that $B$ admits a unique and non-degenerate well, we construct three successive Birkhoff normal forms to describe the spectrum of $\mathcal{L}_h$ in the semiclassical limit $\hbar \rightarrow 0$. We deduce an expansion of all the eigenvalues under a threshold, in powers of $\hbar^{1/2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_09386 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A semiclassical Birkhoff normal form for constant-rank magnetic fields Morin, Léo Analysis of PDEs Mathematical Physics Spectral Theory We consider the semiclassical magnetic Laplacian $\mathcal{L}_h$ on a Riemannian manifold, with a constant-rank and non-vanishing magnetic field $B$. Under the localization assumption that $B$ admits a unique and non-degenerate well, we construct three successive Birkhoff normal forms to describe the spectrum of $\mathcal{L}_h$ in the semiclassical limit $\hbar \rightarrow 0$. We deduce an expansion of all the eigenvalues under a threshold, in powers of $\hbar^{1/2}$. |
| title | A semiclassical Birkhoff normal form for constant-rank magnetic fields |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2005.09386 |