Quantum unique ergodicity for magnetic Laplacians on T^2
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911328524828672 |
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| author | Morin, Léo Rivière, Gabriel |
| author_facet | Morin, Léo Rivière, Gabriel |
| contents | Given a smooth integral two-form and a smooth potential on the flat torus of dimension 2, we study the high energy properties of the corresponding magnetic Schrödinger operator. Under a geometric condition on the magnetic field, we show that every sequence of high energy eigenfunctions satisfies the quantum unique ergodicity property even if the Liouville measure is not ergodic for the underlying classical flow (the Euclidean geodesic flow on the 2-torus). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum unique ergodicity for magnetic Laplacians on T^2 Morin, Léo Rivière, Gabriel Spectral Theory Mathematical Physics Analysis of PDEs Given a smooth integral two-form and a smooth potential on the flat torus of dimension 2, we study the high energy properties of the corresponding magnetic Schrödinger operator. Under a geometric condition on the magnetic field, we show that every sequence of high energy eigenfunctions satisfies the quantum unique ergodicity property even if the Liouville measure is not ergodic for the underlying classical flow (the Euclidean geodesic flow on the 2-torus). |
| title | Quantum unique ergodicity for magnetic Laplacians on T^2 |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2411.18449 |