Fermionic semiclassical Lp estimates
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915205642977280 |
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| author | Nguyen, Ngoc Nhi |
| author_facet | Nguyen, Ngoc Nhi |
| contents | We generalize the semiclassical Lp estimates of Koch, Tataru and Zworski in the setting of Schr{ö}dinger operators with confining potentials to density matrices. This is motivated by the problem of the concentration of free fermionic particles in a trapping potential. Our proof relies on semiclassical and many-body tools. As an application, we provide bounds on spectral clusters. We also discuss the optimality of the one-body and many-body bounds through explicit examples of quasimodes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_00722 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fermionic semiclassical Lp estimates Nguyen, Ngoc Nhi Analysis of PDEs Mathematical Physics Spectral Theory We generalize the semiclassical Lp estimates of Koch, Tataru and Zworski in the setting of Schr{ö}dinger operators with confining potentials to density matrices. This is motivated by the problem of the concentration of free fermionic particles in a trapping potential. Our proof relies on semiclassical and many-body tools. As an application, we provide bounds on spectral clusters. We also discuss the optimality of the one-body and many-body bounds through explicit examples of quasimodes. |
| title | Fermionic semiclassical Lp estimates |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2205.00722 |