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**Fournais, Søren; Lampart, Jonas; Lewin, Mathieu and Sørensen, Thomas Østergaard (2016): Coulomb potentials and Taylor expansions in time-dependent density-functional theory. In: Physical Review A, Vol. 93, No. 6, 62510**

**Full text not available from 'Open Access LMU'.**

## Abstract

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.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 2469-9926 |

Language: | English |

Item ID: | 47278 |

Date Deposited: | 27. Apr 2018, 08:12 |

Last Modified: | 04. Nov 2020, 13:24 |