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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.24049 |
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| _version_ | 1866915373151944704 |
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| author | Balc'h, Kévin Le Niu, Jingrui Sun, Chenmin |
| author_facet | Balc'h, Kévin Le Niu, Jingrui Sun, Chenmin |
| contents | In this article we revisit the observability of the Schrödinger equation on the two-dimensional torus. In contrast to the Schrödinger operator with a purely electric potential, for which any non-empty open set guarantees observability, the presence of a magnetic potential introduces an additional obstruction. We establish a sufficient and almost necessary geometric condition for the observability of electromagnetic Schrödinger operators. This condition incorporates the magnetic potential, which can also be characterized by a geometric control condition for the corresponding magnetic field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric condition for the observability of electromagnetic Schrödinger operators on $\mathbb{T}^2$ Balc'h, Kévin Le Niu, Jingrui Sun, Chenmin Analysis of PDEs In this article we revisit the observability of the Schrödinger equation on the two-dimensional torus. In contrast to the Schrödinger operator with a purely electric potential, for which any non-empty open set guarantees observability, the presence of a magnetic potential introduces an additional obstruction. We establish a sufficient and almost necessary geometric condition for the observability of electromagnetic Schrödinger operators. This condition incorporates the magnetic potential, which can also be characterized by a geometric control condition for the corresponding magnetic field. |
| title | Geometric condition for the observability of electromagnetic Schrödinger operators on $\mathbb{T}^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.24049 |