Coulomb potentials and Taylor expansions in time-dependent density-functional theory
Fournais, Søren; Lampart, Jonas; Lewin, Mathieu; Sørensen, Thomas Østergaard (2016), Coulomb potentials and Taylor expansions in time-dependent density-functional theory, Physical Review A, 93, 6, p. n°062510. 10.1103/PhysRevA.93.062510
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1603.02219v2
Journal namePhysical Review A
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Abstract (EN)We investigate when Taylor expansions can be used to prove the Runge-Gross theorem, which is at the foundation of time-dependent density-functional theory (TDDFT). We start with a general analysis of the conditions for the Runge-Gross argument, especially the time differentiability of the density. The latter should be questioned in the presence of singular (e.g., Coulomb) potentials. Then we show that a singular potential in a one-body operator considerably decreases the class of time-dependent external potentials to which the original argument can be applied. A two-body singularity has an even stronger impact and an external potential is essentially incompatible with it. For the Coulomb interaction and all reasonable initial many-body states, the Taylor expansion only exists to a finite order, except for constant external potentials. Therefore, high-order Taylor expansions are not the right tool to study atoms and molecules in TDDFT.
Subjects / KeywordsTDDFT
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