标题： copula 方法在密度泛函理论中建模配对密度的应用 显示英文标题

标题： Copula methods for modeling pair densities in density functional theory

摘要： 我们提出了一种基于统计学中copula理论的新方法，用于近似密度到二密度映射。我们将copula理论扩展到多维边缘分布，并推导出可以用单粒子密度和copula描述任意（精确或近似）二密度。我们给出了尺度极限下精确copula的解析公式，在一维具有两到四个粒子的解离系统中数值计算了copula，并提出了两粒子系统的平衡态与解离态之间copula的准确近似。 显示英文摘要

摘要： We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate) pair density by the single-particle density and a copula. We present analytical formulas for the exact copula in scaling limits, numerically compute the copula for dissociating systems with two to four particles in one dimension, and propose accurate approximations of the copula between equilibrium and dissociation for two-particle systems.