Long-time behaviour of time-dependent density functional theory

Abstract

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.

Minor changes

References in corpus (1)

• Time-dependent density functional theory: Past, present, and future

Cited by in corpus (6)

• Asymptotic stability of a wide class of stationary solutions for the Hartree and Schrödinger equations for infinitely many particles
• Global well-posedness of the nonlinear Hartree equation for infinitely many particles with singular interaction
• A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory
• Differential Equations of Quantum Mechanics
• Probabilistic Strichartz estimates in Schatten classes and their applications to the Hartree equation
• Stability of homogeneous equilibria of the Hartree-Fock equation, for its equivalent formulation for random fields