The Correlation Energy of the Electron Gas in the Mean-Field Regime
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911671259234304 |
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| author | Christiansen, Martin Ravn Hainzl, Christian Nam, Phan Thành |
| author_facet | Christiansen, Martin Ravn Hainzl, Christian Nam, Phan Thành |
| contents | We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in \cite{ChrHaiNam-23b}, our result establishes an analogue of the Gell-Mann--Brueckner formula $c_{1}ρ\log\left(ρ\right)+c_{2}ρ$ for the correlation energy of the electron gas in the high-density limit. Moreover, our analysis allows us to go beyond mean-field scaling while still covering the same class of potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01386 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Correlation Energy of the Electron Gas in the Mean-Field Regime Christiansen, Martin Ravn Hainzl, Christian Nam, Phan Thành Mathematical Physics We prove a rigorous lower bound on the correlation energy of interacting fermions in the mean-field regime for a wide class of singular interactions, including the Coulomb potential. Combined with the upper bound obtained in \cite{ChrHaiNam-23b}, our result establishes an analogue of the Gell-Mann--Brueckner formula $c_{1}ρ\log\left(ρ\right)+c_{2}ρ$ for the correlation energy of the electron gas in the high-density limit. Moreover, our analysis allows us to go beyond mean-field scaling while still covering the same class of potentials. |
| title | The Correlation Energy of the Electron Gas in the Mean-Field Regime |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2405.01386 |