Existence of Minimizers for the Dirac–Fock Model of Crystals
Whereas many different models exist in mathematics and physics for the 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...
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2024-08, Vol.248 (4), p.63, Article 63 |
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| creator | Catto, Isabelle Meng, Long Paturel, Éric Séré, Éric |
| description | Whereas many different models exist in mathematics and physics for the 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. |
| doi_str_mv | 10.1007/s00205-024-01988-8 |
| format | Article |
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| subjects | Analysis of PDEs Approximation Atoms & subatomic particles Classical Mechanics Complex Systems Crystals Digital Object Identifier Energy Fluid- and Aerodynamics Ground state Mathematical and Computational Physics Mathematical Physics Mathematics Physics Physics and Astronomy Quantum Physics Relativistic effects Theoretical |
| title | Existence of Minimizers for the Dirac–Fock Model of Crystals |
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