v-Representability on a one-dimensional torus at elevated temperatures
Abstrak
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.
Topik & Kata Kunci
Penulis (5)
Sarina M. Sutter
Markus Penz
Michael Ruggenthaler
Robert van Leeuwen
Klaas J. H. Giesbertz
Akses Cepat
- Tahun Terbit
- 2025
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓