Semi-Classical Localization of the Schrödinger Resolvent on Closed Riemann Surfaces
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917184873168896 |
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| author | Campagne, Sébastien |
| author_facet | Campagne, Sébastien |
| contents | This paper investigates the localization properties of solutions to the semi-classical Schrödinger equation on closed Riemann surfaces. Unlike classical studies that assume a smooth potential, our work addresses the challenges arising from irregular potentials, specifically those that are merely bounded. We employ a regularization technique to manage the potential's lack of smoothness and establish a local-to-global estimate. This result provides a quantitative measure of how the local regularity of the potential influences the global concentration of the solution, thereby bridging the gap between smooth and non-continuous regimes in semi-classical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02274 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semi-Classical Localization of the Schrödinger Resolvent on Closed Riemann Surfaces Campagne, Sébastien Analysis of PDEs This paper investigates the localization properties of solutions to the semi-classical Schrödinger equation on closed Riemann surfaces. Unlike classical studies that assume a smooth potential, our work addresses the challenges arising from irregular potentials, specifically those that are merely bounded. We employ a regularization technique to manage the potential's lack of smoothness and establish a local-to-global estimate. This result provides a quantitative measure of how the local regularity of the potential influences the global concentration of the solution, thereby bridging the gap between smooth and non-continuous regimes in semi-classical analysis. |
| title | Semi-Classical Localization of the Schrödinger Resolvent on Closed Riemann Surfaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.02274 |