{
  "id": "1404.0825",
  "version": "v1",
  "published": "2014-04-03T10:10:41.000Z",
  "updated": "2014-04-03T10:10:41.000Z",
  "title": "Density Functionals in the Presence of Magnetic Field",
  "authors": [
    "Andre Laestadius"
  ],
  "comment": "26 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "physics.chem-ph",
    "quant-ph"
  ],
  "abstract": "In this paper density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density, $\\rho$, and paramagnetic current density, $j^p$. This approach is motivated by an adapted version of the Vignale and Rasolt formulation of Current Density Functional Theory (CDFT), which establishes a one-to-one correspondence between the non-degenerate ground-state and the particle and paramagnetic current density. Definition of $N$-representable density pairs $(\\rho,j^p)$ is given and it is proven that the set of $v$-representable densities constitutes a proper subset of the set of $N$-representable densities. For a Levy-Lieb type functional $Q(\\rho,j^p)$, it is demonstrated that (i) it is a proper extension of the universal Hohenberg-Kohn functional, $F_{HK}(\\rho,j^p)$, to $N$-representable densities, (ii) there exists a wavefunction $\\psi_0$ such that $Q(\\rho,j^p)=(\\psi_0,H_0\\psi_0)_{L^2}$, where $H_0$ is the Hamiltonian without external potential terms, and (iii) it is not convex. Furthermore, a convex and universal functional $F(\\rho,j^p)$ is studied and proven to be equal the convex envelope of $Q(\\rho,j^p)$. For both $Q$ and $F$, we give upper and lower bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-03T10:10:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic field",
      "representable density",
      "paramagnetic current density",
      "current density functional theory",
      "density functionals depend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0825L"
    }
  }
}