论文标题
潜力和密度空间中的变性几何形状
Geometry of Degeneracy in Potential and Density Space
论文作者
论文摘要
在先前的工作中[J。化学物理。 155，244111（2021）]，我们发现了由图表代表的有限晶格系统中密度功能理论的基本霍恩伯格 - 科恩定理的反例。在这里，我们证明这仅发生在非常奇特和罕见的密度下，而密度集的密度是由退化基态（称为退化区域），相互接触或整个密度域的边界的。即使在连续性环境中，变性区域通常处于代数品种的凸壳的形状。对密度区域和创造它们的电势之间产生的几何形状进行了分析和解释，其中包括罗马表面的其他示例。
In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only occurs at very peculiar and rare densities, those where density sets arising from degenerate ground states, called degeneracy regions, touch each other or the boundary of the whole density domain. Degeneracy regions are shown to generally be in the shape of the convex hull of an algebraic variety, even in the continuum setting. The geometry arising between density regions and the potentials that create them is analyzed and explained with examples that, among other shapes, feature the Roman surface.
