Title: Density-potential inversion from Moreau-Yosida regularization Show Chinese title

Title: 从Moreau-Yosida正则化进行密度-势能反演

Abstract: For a quantum-mechanical many-electron system, given a density, the Zhao-Morrison-Parr method allows to compute the effective potential that yields precisely that density. In this work, we demonstrate how this and similar inversion procedures mathematically relate to the Moreau-Yosida regularization of density functionals on Banach spaces. It is shown that these inversion procedures can in fact be understood as a limit process as the regularization parameter approaches zero. This sheds new insight on the role of Moreau-Yosida regularization in density-functional theory and allows to systematically improve density-potential inversion. Our results apply to the Kohn-Sham setting with fractional occupation that determines an effective one-body potential that in turn reproduces an interacting density. Show Chinese abstract

Abstract: 对于一个量子力学的多电子系统，给定一个密度，Zhao-Morrison-Parr方法允许计算出产生该密度的有效势。在本工作中，我们展示了这种方法以及类似的反演过程如何在数学上与Banach空间上密度泛函的Moreau-Yosida正则化相关联。结果表明，这些反演过程实际上可以被理解为当正则化参数趋近于零时的极限过程。这为Moreau-Yosida正则化在密度泛函理论中的作用提供了新的见解，并允许系统地改进密度-势反演。我们的结果适用于具有分数占据的Kohn-Sham设置，该设置确定了一个有效的单体势，该势又再现了相互作用的密度。