The structure of the density-potential mapping. Part II: Including magnetic fields
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910657454014464 |
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| author | Penz, Markus Tellgren, Erik I. Csirik, Mihály A. Ruggenthaler, Michael Laestadius, Andre |
| author_facet | Penz, Markus Tellgren, Erik I. Csirik, Mihály A. Ruggenthaler, Michael Laestadius, Andre |
| contents | The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. In this Part~II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some non-standard alternatives. For the former, it is known that the Hohenberg-Kohn theorem is no longer valid due to counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework closest to standard DFT and, just like in standard DFT, non-differentiability of the density functional can be mitigated through Moreau-Yosida regularization. Interesting insights can be drawn from both Maxwell-Schrödinger DFT and quantum-electrodynamical DFT, which are also discussed here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01357 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The structure of the density-potential mapping. Part II: Including magnetic fields Penz, Markus Tellgren, Erik I. Csirik, Mihály A. Ruggenthaler, Michael Laestadius, Andre Chemical Physics Quantum Physics The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. In this Part~II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some non-standard alternatives. For the former, it is known that the Hohenberg-Kohn theorem is no longer valid due to counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework closest to standard DFT and, just like in standard DFT, non-differentiability of the density functional can be mitigated through Moreau-Yosida regularization. Interesting insights can be drawn from both Maxwell-Schrödinger DFT and quantum-electrodynamical DFT, which are also discussed here. |
| title | The structure of the density-potential mapping. Part II: Including magnetic fields |
| topic | Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2303.01357 |