{
  "id": "2005.08933",
  "version": "v1",
  "published": "2020-05-18T17:57:48.000Z",
  "updated": "2020-05-18T17:57:48.000Z",
  "title": "Correlation Energy of a Weakly Interacting Fermi Gas",
  "authors": [
    "Niels Benedikter",
    "Phan Thành Nam",
    "Marcello Porta",
    "Benjamin Schlein",
    "Robert Seiringer"
  ],
  "comment": "56 pages",
  "categories": [
    "math-ph",
    "cond-mat.quant-gas",
    "cond-mat.str-el",
    "math.MP"
  ],
  "abstract": "We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree-Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-18T17:57:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "82B10",
      "81Q10",
      "35P05"
    ],
    "keywords": [
      "weakly interacting fermi gas",
      "correlation energy",
      "ground state energy",
      "hartree-fock state",
      "high density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}