论文标题
Banach空间中正规化的Kohn-Sham迭代的收敛
Convergence of the regularized Kohn-Sham iteration in Banach spaces
论文作者
论文摘要
莫罗·约西达（Moreau-Yosida）正式化的通用lieb功能和自适应阻尼步骤的Banach空间上的广义密度功能理论的Kohn-Sham迭代显示出融合到正确的地面密度。该结果要求（准）密度和电势的状态空间，这些密度和电势均匀地凸出，具有功率类型的模量。 Moreau-Yosida正则化适用于与空间的几何形状相匹配，并将某些凸分析结果扩展到这种类型的正则化。也指出了正则化和身体效应之间的可能连接。此处介绍的收敛证明（定理23）包含一个关键错误，该错误已在Arxiv：1903.09579的有限维情况下被指出和修复。然而，提出的校正并非直接推广到无限二维Banach空间的设置。这意味着在这种情况下，融合问题仍然保持开放。我们将此草案作为技术和想法的集合介绍，以改变Banach空间中Kohn-Sham迭代的融合的成功，成功地展示。
The Kohn-Sham iteration of generalized density-functional theory on Banach spaces with Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown to converge to the correct ground-state density. This result demands state spaces for (quasi)densities and potentials that are uniformly convex with modulus of convexity of power type. The Moreau-Yosida regularization is adapted to match the geometry of the spaces and some convex analysis results are extended to this type of regularization. Possible connections between regularization and physical effects are pointed out as well. The proof of convergence presented here (Theorem 23) contains a critical mistake that has been noted and fixed for the finite-dimensional case in arXiv:1903.09579. Yet, the proposed correction is not straightforwardly generalizable to a setting of infinite-dimensional Banach spaces. This means the question of convergence in such a case is still left open. We present this draft as a collection of techniques and ideas for a possible altered, successful demonstration of convergence of the Kohn--Sham iteration in Banach spaces.
