Existence of minimizers for the Dirac-Fock model of crystals
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911932652453888 |
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| author | Catto, Isabelle Meng, Long Paturel, Eric Séré, Eric |
| author_facet | Catto, Isabelle Meng, Long Paturel, Eric Séré, Eric |
| contents | Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and we are not aware of any mathematical result on a fully relativistic treatment of crystals. In this paper, we introduce a mean-field relativistic energy for crystals in terms of periodic density matrices. This model is inspired both from a recent definition of the Dirac-Fock ground state for atoms and molecules, due to one of us, and from the non-relativistic Hartree-Fock model for crystals. We prove the existence of a ground state when the number of electrons per cell is not too large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_01142 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence of minimizers for the Dirac-Fock model of crystals Catto, Isabelle Meng, Long Paturel, Eric Séré, Eric Analysis of PDEs Mathematical Physics Quantum Physics Whereas many different models exist in the mathematical and physics literature for ground states of non-relativistic crystals, the relativistic case has been much less studied and we are not aware of any mathematical result on a fully relativistic treatment of crystals. In this paper, we introduce a mean-field relativistic energy for crystals in terms of periodic density matrices. This model is inspired both from a recent definition of the Dirac-Fock ground state for atoms and molecules, due to one of us, and from the non-relativistic Hartree-Fock model for crystals. We prove the existence of a ground state when the number of electrons per cell is not too large. |
| title | Existence of minimizers for the Dirac-Fock model of crystals |
| topic | Analysis of PDEs Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2212.01142 |