标题： 用于密度泛函理论中对密度对建模的Copula方法 显示英文标题

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

摘要： 我们提出了一种新的方法，基于统计学中的Copula理论来逼近密度到对密度的映射。 我们将Copula理论扩展到多维边缘分布，并推导出可以通过单粒子密度和一个Copula来描述任何（精确或近似）的对密度。 我们给出了在尺度极限下精确Copula的解析公式，数值计算了一维中具有两个到四个粒子的解离系统的Copula，并为双粒子系统在平衡与解离之间的Copula提出了精确的近似方法。 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.