论文标题
存在最小化晶体模型的最小化器
Existence of minimizers for the Dirac-Fock model of crystals
论文作者
论文摘要
尽管在数学和物理文献中存在许多不同模型的非权威主义晶体基础状态，但相对论的病例的研究少得多，我们不知道对晶体的完全相对论治疗的任何数学结果。在本文中，我们在周期性密度矩阵方面引入了晶体的平均相对论能量。由于我们中的一个以及晶体的非相关性Hartree-fock模型，该模型的最新定义是对原子和分子的狄拉克孔基态的最新定义的启发。当每个单元的电子数量不大时，我们证明了基态的存在。
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.
