论文标题
局部密度近似的有效性对于平滑短距离相互作用势
The Validity of the Local Density Approximation for Smooth Short Range Interaction Potentials
论文作者
论文摘要
在完整的量子理论中，Levy-lieb函数描述了具有给定单体密度的多体量子系统的能量。这是准确的，但是计算非常复杂。对于实际计算，引入基于恒定密度的局部能量的局部密度近似是有用的。本文的目的是建立征费-LIEB功能理论与局部密度近似之间的严格联系。我们的理由对于在缓慢变化的密度缓慢的状态下具有一般平滑短距离相互作用电位的费米子系统有效。我们遵循Lewin，Lieb和Seiringer开发的一般方法，以寻求库仑电位，但避免使用电位的任何特殊特性，包括缩放特性和筛选效果来定位能量。
In the full quantum theory, the energy of a many-body quantum system with a given one-body density is described by the Levy-Lieb functional. It is exact, but very complicated to compute. For practical computations, it is useful to introduce the Local Density Approximation which is based on the local energy of constant densities. The aim of this paper is to make a rigorous connection between the Levy-Lieb functional theory and the Local Density Approximation. Our justification is valid for fermionic systems with a general class of smooth short range interaction potentials, in the regime of slowly varying densities. We follow a general approach developed by Lewin, Lieb and Seiringer for Coulomb potential, but avoid using any special properties of the potential including the scaling property and screening effects for the localization of the energy.
