局域密度近似对光滑短程相互作用势的有效性
The Validity of the Local Density Approximation for Smooth Short Range Interaction Potentials
摘要：
在全量子理论中，具有给定单体密度的多体量子系统的能量由Levy-Lieb泛函描述。它是精确的，但计算起来很复杂。在实际计算中，引入局域密度近似是很有用的，它是基于定常密度的局域能量。本文的目的是在Levy-Lieb泛函理论和局域密度近似之间建立一个严格的联系。我们的理由是有效的费米子系统的一般类光滑的短程相互作用势，在制度的缓慢变化的密度。我们遵循Lewin，Lieb和Seiringer发展的库仑势的一般方法，但避免使用势的任何特殊性质，包括标度性质和屏蔽效应来确定能量的局部化。
英文摘要：
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.
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