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Pré-Publication, Document De Travail Année : 2016

Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory

Résumé

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.
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Dates et versions

hal-01283928 , version 1 (07-03-2016)
hal-01283928 , version 2 (27-06-2016)

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Søren Fournais, Jonas Lampart, Mathieu Lewin, Thomas Østergaard Sørensen. Coulomb potentials and Taylor expansions in Time-Dependent Density Functional Theory. 2016. ⟨hal-01283928v1⟩
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