Solution of the v-representability problem on a one-dimensional torus

Fuente: arXiv
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Autori principali: Sutter, Sarina M., Penz, Markus, Ruggenthaler, Michael, van Leeuwen, Robert, Giesbertz, Klaas J. H.
Natura: Preprint
Pubblicazione: 2023
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author Sutter, Sarina M.
Penz, Markus
Ruggenthaler, Michael
van Leeuwen, Robert
Giesbertz, Klaas J. H.
author_facet Sutter, Sarina M.
Penz, Markus
Ruggenthaler, Michael
van Leeuwen, Robert
Giesbertz, Klaas J. H.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2312_07225
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Solution of the v-representability problem on a one-dimensional torus
Sutter, Sarina M.
Penz, Markus
Ruggenthaler, Michael
van Leeuwen, Robert
Giesbertz, Klaas J. H.
Mathematical Physics
Chemical Physics
Quantum Physics
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.
title Solution of the v-representability problem on a one-dimensional torus
topic Mathematical Physics
Chemical Physics
Quantum Physics
url https://arxiv.org/abs/2312.07225