Long-Time Behaviour of Time-Dependent Density Functional Theory

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