{
  "id": "2106.15370",
  "version": "v1",
  "published": "2021-06-29T12:55:54.000Z",
  "updated": "2021-06-29T12:55:54.000Z",
  "title": "Density-Functional Theory on Graphs",
  "authors": [
    "Markus Penz",
    "Robert van Leeuwen"
  ],
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "physics.chem-ph"
  ],
  "abstract": "The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of the density-potential mapping can be won. We give precise conditions for a ground state to be uniquely v-representable and are able to prove that this property holds for almost all densities. A set of examples illustrates the theory and demonstrates the non-convexity of the pure-state constrained-search functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-29T12:55:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density-functional theory",
      "finite lattice systems",
      "fundamental hohenberg-kohn theorem",
      "pure-state constrained-search functional",
      "precise conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}