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The inverse problem of time-dependent density functional theory on the torus

  • Asbjørn Bækgaard Lauritsen
  • Mathieu Lewin
  • Jakob Oldenburg
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Abstract

We prove that, for any given sufficiently regular one-particle density, there exists a unique external potential for which the solution to the many-body Schrödinger equation has this prescribed density. This implies in particular that one can exactly reproduce the time-dependent density of an interacting system using non-interacting electrons, which is at the heart of time-dependent density functional theory. Our result covers the Coulomb interaction and densities arising from extended nuclei.

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Cite

BibTeXRIS
BibTeX
@misc{lauritsen2026inverse,
  title = {{The inverse problem of time-dependent density functional theory on the torus}},
  author = {Asbjørn Bækgaard Lauritsen and Mathieu Lewin and Jakob Oldenburg},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08984},
  eprint = {2609.08984},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05744835v1},
}
RIS
TY  - UNPB
TI  - The inverse problem of time-dependent density functional theory on the torus
AU  - Asbjørn Bækgaard Lauritsen
AU  - Mathieu Lewin
AU  - Jakob Oldenburg
PY  - 2026
DA  - 2026/09/08
PB  - HAL
DO  - 10.48550/arxiv.2609.08984
UR  - https://hal.science/hal-05744835v1
AB  - We prove that, for any given sufficiently regular one-particle density, there exists a unique external potential for which the solution to the many-body Schrödinger equation has this prescribed density. This implies in particular that one can exactly reproduce the time-dependent density of an interacting system using non-interacting electrons, which is at the heart of time-dependent density functional theory. Our result covers the Coulomb interaction and densities arising from extended nuclei.
ER  -