The density functional theory (DFT) is a remarkably successful theory of electronic structure of matter. At the foundation of this theory lies the Kohn–Sham (KS) equation. In this paper, we describe the long-time behaviour of the time-dependent KS equation. Assuming weak self-interactions, we prove global existence and scattering in (almost) the full “short-range” regime. This is achieved with new and simple techniques, naturally compatible with the structure of the DFT and involving commutator vector fields and non-abelian versions of Sobolev–Klainerman-type spaces and inequalities.

中文翻译：

---

时变密度泛函理论的长期行为

密度泛函理论（DFT）是物质电子结构的非常成功的理论。该理论的基础是Kohn-Sham（KS）方程。在本文中，我们描述了时变KS方程的长时间行为。假设微弱的自我互动，我们证明了（几乎）完整的“短程”机制的整体存在和分散性。这是通过新的简单技术实现的，该技术与DFT的结构自然兼容，并且涉及换向器矢量场以及Sobolev–Klainerman型空间和不等式的非阿贝尔版本。