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Journal Articles Archive for Rational Mechanics and Analysis Year : 2024

Existence of minimizers for the Dirac-Fock model of crystals

Abstract

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.
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Dates and versions

hal-03871041 , version 1 (01-12-2022)
hal-03871041 , version 2 (29-08-2023)
hal-03871041 , version 3 (11-04-2024)
hal-03871041 , version 4 (24-05-2024)
hal-03871041 , version 5 (30-05-2024)

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Isabelle Catto, Long Meng, Eric Paturel, Eric Séré. Existence of minimizers for the Dirac-Fock model of crystals. Archive for Rational Mechanics and Analysis, 2024, 248 (issue 4, article 63), ⟨10.1007/s00205-024-01988-8⟩. ⟨hal-03871041v5⟩
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