AI 中文总结
本文针对具有弱相关基态的薛定谔算子，利用经典势理论刻画弱相关正则态，证明了非相互作用系统在拉普拉斯形式有界势极大类中的 Hohenberg-Kohn 定理及 Kohn-Sham 势的唯一性，揭示其基本机制是密度的（拟）唯一延拓。
AI 中文摘要
在本文中，我们表明对于具有弱相关基态的薛定谔算子，当且仅当单粒子密度几乎处处为正时，Hohenberg-Kohn 定理在形式有界外部势的极大类中成立。此外，我们证明了具有离散基态能量的非相互作用薛定谔算子的基态满足这些条件。因此，我们在拉普拉斯形式有界势的极大类中建立了非相互作用系统的 Hohenberg-Kohn 定理以及 Kohn-Sham 势的唯一性。建立这些结果的关键要素是对弱相关正则态的刻画，其证明依赖于经典势理论。而且，我们的证明揭示，在连续统设定下，Hohenberg-Kohn 定理的基本机制是密度的（拟）唯一延拓而非多体波函数的。
英文摘要
We show that for Schrödinger operators in a connected domain, the Hohenberg-Kohn theorem holds within the class of Laplace form-bounded external potentials if and only if the single-particle density is strictly positive quasi-everywhere. Furthermore, we show that this condition is satisfied for non-interacting Schrödinger operators whenever a ground-state exists. Consequently, we establish the Hohenberg-Kohn theorem for non-interacting systems, and thereby the uniqueness of the Kohn-Sham potential, within the maximal class of Laplace form-bounded distributions. The main ingredient to establish these results is a characterization of regular states, whose proof relies on tools from classical potential theory. Moreover, this characterization reveals that, in the continuum setting, the fundamental mechanism underlying the Hohenberg-Kohn theorem is the (quasi)-unique continuation of the density rather than of the many-body wavefunction.
CommentsRemoved the finite rank restriction on the characterization of regular states, reformulated the main results, some definitions, and proofs, and fixed some typos
