v-Representability on a one-dimensional torus at elevated temperatures
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arXiv
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| Format: | Preprint |
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2025
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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 extend a previous result [Sutter et al., J. Phys. A: Math. Theor. 57, 475202 (2024)] to give an explicit form of the set of $v$-representable densities on the one-dimensional torus with any fixed number of particles in contact with a heat bath at finite temperature. The particle interaction has to satisfy some mild assumptions but is kept entirely general otherwise. For densities, we consider the Sobolev space $H^1$ and exploit the convexity of the functionals. This leads to a broader set of potentials than the usual $L^p$ spaces and encompasses distributions. By including temperature and thus considering all excited states in the Gibbs ensemble, Gâteaux differentiability of the thermal universal functional is guaranteed. This yields $v$-representability and it is demonstrated that the given set of $v$-representable densities is even maximal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | v-Representability on a one-dimensional torus at elevated temperatures Sutter, Sarina M. Penz, Markus Ruggenthaler, Michael van Leeuwen, Robert Giesbertz, Klaas J. H. Mathematical Physics Chemical Physics Quantum Physics We extend a previous result [Sutter et al., J. Phys. A: Math. Theor. 57, 475202 (2024)] to give an explicit form of the set of $v$-representable densities on the one-dimensional torus with any fixed number of particles in contact with a heat bath at finite temperature. The particle interaction has to satisfy some mild assumptions but is kept entirely general otherwise. For densities, we consider the Sobolev space $H^1$ and exploit the convexity of the functionals. This leads to a broader set of potentials than the usual $L^p$ spaces and encompasses distributions. By including temperature and thus considering all excited states in the Gibbs ensemble, Gâteaux differentiability of the thermal universal functional is guaranteed. This yields $v$-representability and it is demonstrated that the given set of $v$-representable densities is even maximal. |
| title | v-Representability on a one-dimensional torus at elevated temperatures |
| topic | Mathematical Physics Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2508.07784 |