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  Solution of the v-representability problem on a ring domain

Sutter, S. M., Penz, M., Ruggenthaler, M., van Leeuwen, R., & Giesbertz, K. J. H. (2023). Solution of the v-representability problem on a ring domain.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000E-17E1-A Version Permalink: https://hdl.handle.net/21.11116/0000-000E-17E2-9
Genre: Preprint

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2312.07225.pdf (Preprint), 533KB
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https://arxiv.org/abs/2312.07225 (Preprint)
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 Creators:
Sutter, Sarina M.1, Author
Penz, M.2, 3, 4, Author           
Ruggenthaler, M.2, 3, 5, Author           
van Leeuwen, R.6, Author
Giesbertz, K. J. H.1, Author
Affiliations:
1Theoretical Chemistry, Faculty of Exact Sciences, VU University, Amsterdam, ou_persistent22              
2Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
3Center for Free-Electron Laser Science, ou_persistent22              
4Department of Computer Science, Oslo Metropolitan University, ou_persistent22              
5The Hamburg Center for Ultrafast Imaging, ou_persistent22              
6Department of Physics, Nanoscience Center, University of Jyväskylä, ou_persistent22              

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 Abstract: We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain in terms of Sobolev spaces and their duals. Any one-particle density that is square-integrable, has a square-integrable weak derivative, and is gapped away from zero can be realized from the solution of a many-particle Schrödinger equation, with or without interactions, by choosing a corresponding external potential. This potential can contain a distributional contribution but still gives rise to a self-adjoint Hamiltonian. Importantly, this allows for a well-defined Kohn-Sham procedure but, on the other hand, invalidates the usual proof of the Hohenberg-Kohn theorem.

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Language(s): eng - English
 Dates: 2023-12-12
 Publication Status: Published online
 Pages: 15
 Publishing info: -
 Table of Contents: -
 Rev. Type: No review
 Identifiers: arXiv: 2312.07225
 Degree: -

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