The quantitative semi-classical limit of a large Fermi system at zero temperature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909629425909760 |
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| author | Cárdenas, Esteban |
| author_facet | Cárdenas, Esteban |
| contents | In this article we consider a large system of fermions in a combined mean-field and semiclassical limit, in three dimensions. We investigate the convergence of the Wigner function of the ground state, towards the classical Thomas-Fermi theory. The main novelty of the present article is quantifying the convergence rate with respect to the semi-classical parameter. One of the main ingredients is a recent result on the validity of semi-classical commutator estimates satisfied by the Hartree theory. Singular potentials, up to the Coulomb interaction, are included. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_24706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantitative semi-classical limit of a large Fermi system at zero temperature Cárdenas, Esteban Mathematical Physics Analysis of PDEs In this article we consider a large system of fermions in a combined mean-field and semiclassical limit, in three dimensions. We investigate the convergence of the Wigner function of the ground state, towards the classical Thomas-Fermi theory. The main novelty of the present article is quantifying the convergence rate with respect to the semi-classical parameter. One of the main ingredients is a recent result on the validity of semi-classical commutator estimates satisfied by the Hartree theory. Singular potentials, up to the Coulomb interaction, are included. |
| title | The quantitative semi-classical limit of a large Fermi system at zero temperature |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2505.24706 |