高密度极限对称多面体上电子气体交换能的两期渐近线

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2024-09-16 DOI:10.1007/s11040-024-09485-w

Thiago Carvalho Corso

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引用次数: 0

摘要

我们推导出了热力学极限下严格细分多面体和晶格基本域上自由电子气体交换能的双项渐近展开。该扩展包括一个体项（与体积有关）、著名的狄拉克交换能以及源于边界层和有限尺寸效应的新型表面修正。此外，我们还推导出半局部密度函数的类似两项渐近展开。通过匹配这些渐近展开的系数，我们得到了密度泛函理论中使用的交换能半局部近似的积分约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit

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Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit

We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.