Solution of the v-representability problem on a one-dimensional torus
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917828373774336 |
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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 |