Solution of the <i>v</i>-representability problem on a one-dimensional torus
Abstract We provide a solution to the v -representability problem for a non-relativistic quantum many-particle system on a one-dimensional torus 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.
Authors
- Robert van Leeuwen (ORCID: https://orcid.org/0000-0002-2499-9125)
- Klaas J. H. Giesbertz (ORCID: https://orcid.org/0000-0001-6380-5015)
- Michael Ruggenthaler (ORCID: https://orcid.org/0000-0002-0728-8372)
- Markus Penz (ORCID: https://orcid.org/0000-0001-8363-1980)
- Sarina Mirjam Sutter
Institutions
- Universität Hamburg (DE)
- OsloMet – Oslo Metropolitan University (NO)
- Exact Sciences (United States) (US)
- Center for Free-Electron Laser Science (DE)
- Max Planck Institute for the Structure and Dynamics of Matter (DE)
- University of Jyväskylä (FI)
Publication Details
- Journal
- Journal of Physics A Mathematical and Theoretical
- Published
- 2024-10-22
- DOI
- https://doi.org/10.1088/1751-8121/ad8a2a
- Citations
- 4
- Primary Topic
- Graph Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 1.00
Funders
- Deutsche Forschungsgemeinschaft
- Academy of Finland
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Mathematisches Forschungsinstitut Oberwolfach