Geometric Time-Dependent Density Functional Theory
\'Eric Canc\`es, Th\'eo Duez, Jari van Gog, Asbj{\o}rn B{\ae}kgaard Lauritsen, Mathieu Lewin, Julien Toulouse
TL;DR
This paper introduces a novel geometric formulation of Time-Dependent Density Functional Theory (TDDFT), utilizing a hydrodynamics approach and non-local operators, with numerical validation on 1D systems.
Contribution
It presents a new geometric and orbital-free formulation of TDDFT, incorporating a density-to-current map and non-local operators for improved modeling.
Findings
Successful numerical simulations on one-dimensional soft-Coulomb systems.
New density-to-current functional map enhances TDDFT modeling.
Non-local operators effectively reproduce density in Kohn-Sham equations.
Abstract
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 non-local operator. Finally, we present numerical simulations for one-dimensional soft-Coulomb systems.
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