Solution of the v-representability problem on a one-dimensional torus

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 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.

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Cited by in corpus (6)

• Geometrical Perspective on Spin-Lattice Density-Functional Theory
• v-representability and Hohenberg-Kohn theorem for non-interacting Schrödinger operators with distributional potentials in the one-dimensional torus
• A rigorous formulation of Density Functional Theory for spinless fermions in one dimension
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory
• v-Representability on a one-dimensional torus at elevated temperatures
• A non-degeneracy theorem for interacting fermions in one dimension