Existence of Minimizers for the Dirac-Fock Model of Crystals

被引：1

作者：

Catto, Isabelle ^{[1
]}

Meng, Long ^{[2
]}

Paturel, Eric ^{[3
]}

Sere, Eric ^{[1
]}

机构：

[1] Univ PSL, Univ Paris Dauphine, CEREMADE, CNRS, F-75016 Paris, France

[2] Ecole Ponts ParisTech, CERMICS, 6 & 8 Ave Pascal, F-77455 Marne La Vallee, France

[3] Univ Nantes, Lab Math J Leray, UMR CNRS 6629, F-44322 Nantes, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2024年 / 248卷 / 04期

基金：

欧洲研究理事会;

关键词：

FIELD THEORY; EQUATIONS; ATOMS; ENERGY; LIMIT;

D O I：

10.1007/s00205-024-01988-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：63