Solution of the v-representability problem on a one-dimensional torus
Mathematical Physics
2024-11-06 v2 math.MP
Chemical Physics
Quantum Physics
Abstract
We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain in terms of Sobolev spaces and their duals. Any one-particle density that is square-integrable, has a square-integrable weak derivative, and is gapped away from zero can be realized from the solution of a many-particle Schr\"odinger equation, with or without interactions, by choosing a corresponding external potential. This potential can contain a distributional contribution but still gives rise to a self-adjoint Hamiltonian. Importantly, this allows for a well-defined Kohn-Sham procedure but, on the other hand, invalidates the usual proof of the Hohenberg-Kohn theorem.
Keywords
Cite
@article{arxiv.2312.07225,
title = {Solution of the v-representability problem on a one-dimensional torus},
author = {Sarina M. Sutter and Markus Penz and Michael Ruggenthaler and Robert van Leeuwen and Klaas J. H. Giesbertz},
journal= {arXiv preprint arXiv:2312.07225},
year = {2024}
}