晶体 Dirac-Fock 模型极小化子的存在性
Existence of minimizers for the Dirac-Fock model of crystals
AI总结：
本文针对晶体完全相对论处理的研究空白，提出了一种基于周期密度矩阵的晶体平均场相对论能量模型，并证明了当每个晶胞电子数不太大时基态的存在性。
摘要：
尽管数学和物理文献中存在许多关于非相对论晶体基态的模型，但相对论情形的研究要少得多，我们尚未知晓任何关于晶体完全相对论处理的数学结果。在本文中，我们引入了一个用周期密度矩阵表示的晶体平均场相对论能量。该模型受启发于我们中一位作者近期提出的关于原子和分子的 Dirac-Fock 基态定义，以及非相对论 Hartree-Fock 晶体模型。我们证明了当每个晶胞的电子数不太大时基态的存在性。
英文摘要：
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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