密度泛函理论中的局域密度近似
The Local Density Approximation in Density Functional Theory
摘要：
本文首次给出了密度泛函理论中局域密度近似的严格数学证明。我们提供了一个定量的估计之间的差异的巨正则Levy-Lieb能量的一个给定的密度（所有量子态具有这种密度的最低可能的能量）和积分的均匀电子气能量的这种密度。误差涉及梯度项，并证明在空间中足够大的区域上密度非常平坦的情况下使用局部密度近似是合理的。
英文摘要：
We give the first mathematically rigorous justification of the Local Density Approximation in Density Functional Theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum states having this density) and the integral over the Uniform Electron Gas energy of this density. The error involves gradient terms and justifies the use of the Local Density Approximation in the situation where the density is very flat on sufficiently large regions in space.
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