Éric Cancès, Théo Duez, Jari van Gog, Asbjørn Bækgaard Lauritsen, Mathieu Lewin, Julien Toulouse
We provide a new formulation of time-dependent density functional theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation involving a new density-to-current functional map. In the corresponding Kohn-Sham equation, the density is reproduced using a nonlocal operator. Finally, we present numerical simulations for one-dimensional soft-Coulomb systems.