{
  "id": "1809.01902",
  "version": "v1",
  "published": "2018-09-06T09:33:35.000Z",
  "updated": "2018-09-06T09:33:35.000Z",
  "title": "Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime",
  "authors": [
    "Niels Benedikter",
    "Phan Thành Nam",
    "Marcello Porta",
    "Benjamin Schlein",
    "Robert Seiringer"
  ],
  "comment": "47 pages, 4 figures",
  "categories": [
    "math-ph",
    "cond-mat.quant-gas",
    "cond-mat.str-el",
    "math.MP"
  ],
  "abstract": "While Hartree-Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree-Fock state given by plane waves and introduce collective particle-hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann-Brueckner-type upper bound to the ground state energy. Our result justifies the random phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-06T09:33:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "82B10",
      "81Q10",
      "35P05"
    ],
    "keywords": [
      "optimal upper bound",
      "mean-field regime",
      "correlation energy",
      "fermi gas",
      "random phase approximation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}