严格关联密度泛函理论的凸松弛方法
Convex relaxation approaches for strictly correlated density functional theory
摘要：
在本文中，我们介绍了凸优化的方法来解决多边际运输型问题的背景下出现的密度泛函理论。凸松弛被用来提供外部近似的一组$N$ -可表示的2-边缘和3-边缘，这反过来又提供下界的能量。我们进一步提出舍入方案，以获得上界的能量。数值实验表明，在上界和下界之间存在$10^{-3}$到$10^{-2}$数量级的间隙。Kantorovich潜在的多边际运输问题也近似具有类似的精度。
英文摘要：
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of $N$-representable 2-marginals and 3-marginals, which in turn provide lower bounds to the energy. We further propose rounding schemes to obtain upper bound to the energy. Numerical experiments demonstrate a gap of the order of $10^{-3}$ to $10^{-2}$ between the upper and lower bounds. The Kantorovich potential of the multi-marginal transport problem is also approximated with a similar accuracy.
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