Geometry of Degeneracy in Potential and Density Space
Penz, M., & van Leeuwen, R. (2023). Geometry of Degeneracy in Potential and Density Space. Quantum, 7, Article 918. https://doi.org/10.22331/q-2023-02-09-918
Published in
QuantumDate
2023Copyright
© Authors, 2023
In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only occurs at very peculiar and rare densities, those where density sets arising from degenerate ground states, called degeneracy regions, touch each other or the boundary of the whole density domain. Degeneracy regions are shown to generally be in the shape of the convex hull of an algebraic variety, even in the continuum setting. The geometry arising between density regions and the potentials that create them is analyzed and explained with examples that, among other shapes, feature the Roman surface.
Publisher
Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenISSN Search the Publication Forum
2521-327XKeywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/176919605
Metadata
Show full item recordCollections
Related funder(s)
Research Council of FinlandFunding program(s)
Academy Project, AoFAdditional information about funding
R. v. L. further acknowledges the Academy of Finland for support under project no. 317139.License
Related items
Showing items with similar title or keywords.
-
Theory for the stationary polariton response in the presence of vibrations
Kansanen, Kalle S. U.; Asikainen, Aili; Toppari, J. Jussi; Groenhof, Gerrit; Heikkilä, Tero T. (American Physical Society, 2019)We construct a model describing the response of a hybrid system where the electromagnetic field—in particular, surface plasmon polaritons—couples strongly with electronic excitations of atoms or molecules. Our approach is ... -
Interacting Electrons in a Flat‐Band System within the Generalized Kadanoff–Baym Ansatz
Cosco, Francesco; Tuovinen, Riku; Lo Gullo, Nicolino (Wiley-VCH Verlag, 2024)In this work, the study of the spectral properties of an open interacting system by solving the generalized Kadanoff-Baym ansatz (GKBA) master equation for the single-particle density matrix, namely the time-diagonal lesser ... -
Existence, uniqueness, and construction of the density-potential mapping in time-dependent density-functional theory
Ruggenthaler, Michael; Penz, Markus; van Leeuwen, Robert (Institute of Physics Publishing Ltd.; Institute of Physics, 2015)In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn–Sham construction. We first present detailed ... -
Experimental Realization of a Dirac Monopole through the Decay of an Isolated Monopole
Ollikainen, T.; Tiurev, K.; Blinova, A.; Lee, W.; Hall, D. S.; Möttönen, Mikko (American Physical Society, 2017)We experimentally observe the decay dynamics of deterministically created isolated monopoles in spin-1 Bose-Einstein condensates. As the condensate undergoes a change between magnetic phases, the isolated monopole gradually ... -
Colloquium : Nonequilibrium effects in superconductors with a spin-splitting field
Bergeret, F. Sebastian; Silaev, Mikhail; Virtanen, Pauli; Heikkilä, Tero (American Physical Society, 2018)This Colloquium discusses the recent progress in understanding the properties of spin-split superconductors under nonequilibrium conditions. Recent experiments and theories demonstrate a rich variety of transport phenomena ...