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arXiv · 2508.07784

v-Representability on a one-dimensional torus at elevated temperatures

Sarina M. Sutter·Markus Penz·Michael Ruggenthaler·Robert van Leeuwen·Klaas J. H. Giesbertz
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Abstract

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, G\^ateaux 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.

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Sarina M. Sutter, Markus Penz, Michael Ruggenthaler, Robert van Leeuwen, Klaas J. H. Giesbertz. 2025-08-11. v-Representability on a one-dimensional torus at elevated temperatures. https://doi.org/10.1088/1751-8121%2Fae38a5

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