关于一维均质材料的密度泛函理论模型

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-08-14 DOI:10.1063/5.0194944
Bouchra Bensiali, Salma Lahbabi, Abdallah Maichine, Othmane Mirinioui
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引用次数: 0

摘要

本文研究三维空间中均质一维材料的密度泛函理论(DFT)模型。它沿袭了之前关于三维空间中均质二维材料的密度泛函理论模型的研究成果[Gontier 等人,Commun. Math. Phys. 388, 1475-1505 (2021)]。我们展示了如何将问题从三维能量函数简化为二维能量函数。动能的处理与二维材料的情况一样,通过对可容许态进行对角处理,并将动能写成还原态上修正动能函数的下确值。此外,我们还处理了二维情况下的哈特里(Hartree)相互作用项,并展示了如何通过里兹(Riesz)势来正确定义均场势能。然后,我们展示了还原模型的良好假设性,并给出了一些数值说明。
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On density functional theory models for one-dimensional homogeneous materials
This paper studies Density Functional Theory (DFT) models for homogeneous 1D materials in the 3D space. It follows the previous work [Gontier et al., Commun. Math. Phys. 388, 1475–1505 (2021)] about DFT models for homogeneous 2D materials in 3D. We show how to reduce the problem from a 3D energy functional to a 2D energy functional. The kinetic energy is treated as in the 2D material case by diagonalizing admissible states, and writing the kinetic energy as the infimum of a modified kinetic energy functional on reduced states. Besides, we treat here the Hartree interaction term in 2D, and show how to properly define the mean-field potential, through Riesz potential. We then show the well-posedness of the reduced model and present some numerical illustrations.
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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