Fermion N-representability for prescribed density and paramagnetic current density
Fermion N-representability for prescribed density and paramagnetic current density
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DOI：
10.1103/physreva.89.012515
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发表时间：
2014-01-30
影响因子：
2.9
通讯作者：
Helgaker, Trygve
中科院分区：
文献类型：
--
作者：
Tellgren, Erik I.;Kvaal, Simen;Helgaker, Trygve
N-表象问题是确定是否存在具有一定性质的N-粒子态的问题。在这里，我们报道了当密度和顺磁电流密度都给定时，费米子N-表象问题的一个肯定解。这个问题出现在电流密度泛函理论中，是密度泛函理论中研究得很好的相应问题(只给出密度)的推广。给出任何密度和顺磁电流密度满足最小正则性条件(本质上是von Weizacker类正则动能密度是局部可积的)，我们证明了存在相应的N粒子态。我们通过构造位置空间核形式的显式单粒子约化密度矩阵来证明这一点，即两个连续位置变量的函数。为了做最小的假设，我们还讨论了关于对角线的数学微妙之处，以及如何严格地从核形式的单粒子约化密度矩阵中提取顺磁电流密度。
The N-representability problem is the problem of determining whether there exists N-particle states with some prescribed property. Here we report an affirmative solution to the fermion N-representability problem when both the density and the paramagnetic current density are prescribed. This problem arises in current-density functional theory and is a generalization of the well-studied corresponding problem (only the density prescribed) in density functional theory. Given any density and paramagnetic current density satisfying a minimal regularity condition (essentially that a von Weizacker-like canonical kinetic energy density is locally integrable), we prove that there exists a corresponding N-particle state. We prove this by constructing an explicit one-particle reduced density matrix in the form of a position-space kernel, i.e., a function of two continuous-position variables. In order to make minimal assumptions, we also address mathematical subtleties regarding the diagonal of, and how to rigorously extract paramagnetic current densities from, one-particle reduced density matrices in kernel form.