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Mathematics > Analysis of PDEs

arXiv:2212.01142v5 (math)
[Submitted on 2 Dec 2022 (v1) , last revised 11 Jun 2024 (this version, v5)]

Title: Existence of minimizers for the Dirac-Fock model of crystals

Title: 晶体的Dirac-Fock模型的极小值的存在性

Authors:Isabelle Catto (CEREMADE), Long Meng (CERMICS), Eric Paturel (LMJL), Eric Séré (CEREMADE)
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.
Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Cite as: arXiv:2212.01142 [math.AP]
  (or arXiv:2212.01142v5 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2212.01142
Journal reference: Archive for Rational Mechanics and Analysis 248 (2024), issue 4, article 63
Related DOI: https://doi.org/10.1007/s00205-024-01988-8

Submission history

From: Eric Sere [view email]
[v1] Fri, 2 Dec 2022 12:44:03 UTC (42 KB)
[v2] Thu, 31 Aug 2023 09:05:36 UTC (54 KB)
[v3] Tue, 16 Apr 2024 08:19:09 UTC (59 KB)
[v4] Tue, 28 May 2024 12:23:48 UTC (59 KB)
[v5] Tue, 11 Jun 2024 06:28:26 UTC (59 KB)
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