球对称体系的严格关联电子泛函
The strictly-correlated electron functional for spherically symmetric systems revisited
摘要：
强相互作用极限的Hohenberg-Kohn功能定义了一个多边际最优运输问题的库仑成本。从物理参数来看，这个极限的解预计会产生严格相关的粒子位置，通过共同运动函数（或最佳映射）相互关联，但在一般的三维情况下，这种确定性解的存在仍然是一个悬而未决的问题。在Phys.~修订版~ A { \bf 75}，042511（2007），并且后来用于构建限制在低密度量子点中的电子的近似交换相关泛函。Colombo and Stra [数学]模型方法应用~科学，{ \bf 26} 1025（2016）]最近已经表明，这些图解的地图并不总是最佳的。在这里，我们从形式和数值的角度重新审视了整个问题，发现即使约束映射并不总是最优的，它们仍然会产生一个相互作用能（成本），在数值上非常接近真正的最小值。我们还证明了建立的功能从约束映射具有预期的功能导数时，他们也不是最佳的。
英文摘要：
The strong-interaction limit of the Hohenberg-Kohn functional defines a multimarginal optimal transport problem with Coulomb cost. From physical arguments, the solution of this limit is expected to yield strictly-correlated particle positions, related to each other by co-motion functions (or optimal maps), but the existence of such a deterministic solution in the general three-dimensional case is still an open question. A conjecture for the co-motion functions for radially symmetric densities was presented in Phys.~Rev.~A {\bf 75}, 042511 (2007), and later used to build approximate exchange-correlation functionals for electrons confined in low-density quantum dots. Colombo and Stra [Math.~Models Methods Appl.~Sci., {\bf 26} 1025 (2016)] have recently shown that these conjectured maps are not always optimal. Here we revisit the whole issue both from the formal and numerical point of view, finding that even if the conjectured maps are not always optimal, they still yield an interaction energy (cost) that is numerically very close to the true minimum. We also prove that the functional built from the conjectured maps has the expected functional derivative also when they are not optimal.
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