Year: 2024
Type: article
Abstract: We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a one-dimensional torus 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 Schrödinger 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.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1230266125, Solving bottlenecks in one-body reduced density matrix functional theory, A new mathematical foundation of density-functional theory, EXC 2056: CUI: Advanced Imaging of Matter, Dispersion Interactions: a new theoretical approach in a pure Density Functional Theory framework, G5631081224
OpenAlex ID: W4403628649