Commutator Estimates and Quantitative Local Weyl's Law for Schrödinger Operators with Non-Smooth Potentials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866929725603053568 |
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| author | Cárdenas, Esteban Lafleche, Laurent |
| author_facet | Cárdenas, Esteban Lafleche, Laurent |
| contents | We analyze semi-classical Schrödinger operators with potentials of class $C^{1,1/2}$ and establish commutator estimates for the associated projection operators in Schatten norms. These are then applied to prove quantitative versions of the local and phase space Weyl laws in $L^p$ spaces. We study both non-interacting, and interacting particle systems. In particular, we are able to treat the case of the minimizers of the Hartree energy in the case of repulsive singular pair interactions such as the Coulomb potential. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Commutator Estimates and Quantitative Local Weyl's Law for Schrödinger Operators with Non-Smooth Potentials Cárdenas, Esteban Lafleche, Laurent Mathematical Physics Analysis of PDEs Spectral Theory Quantum Physics 35J10, 81S30, 47B47 (Primary) 47B15, 47B10, 35P30 (Secondary) We analyze semi-classical Schrödinger operators with potentials of class $C^{1,1/2}$ and establish commutator estimates for the associated projection operators in Schatten norms. These are then applied to prove quantitative versions of the local and phase space Weyl laws in $L^p$ spaces. We study both non-interacting, and interacting particle systems. In particular, we are able to treat the case of the minimizers of the Hartree energy in the case of repulsive singular pair interactions such as the Coulomb potential. |
| title | Commutator Estimates and Quantitative Local Weyl's Law for Schrödinger Operators with Non-Smooth Potentials |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory Quantum Physics 35J10, 81S30, 47B47 (Primary) 47B15, 47B10, 35P30 (Secondary) |
| url | https://arxiv.org/abs/2501.01381 |