{
  "id": "2106.11161",
  "version": "v1",
  "published": "2021-06-21T14:59:56.000Z",
  "updated": "2021-06-21T14:59:56.000Z",
  "title": "The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime",
  "authors": [
    "Martin Ravn Christiansen",
    "Christian Hainzl",
    "Phan Thành Nam"
  ],
  "categories": [
    "math-ph",
    "cond-mat.quant-gas",
    "cond-mat.str-el",
    "math.MP"
  ],
  "abstract": "We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three-dimensions in the mean-field scaling regime. We consider a system of $N$ fermions on a torus, interacting via a two-body repulsive potential proportional to $N^{-\\frac{1}{3}}$. In the limit $N\\rightarrow\\infty$, we derive the exact leading order of the correlation energy of the system, which coincides with the prediction of Gell-Mann and Brueckner in 1957.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-21T14:59:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random phase approximation",
      "interacting fermi gases",
      "mean-field regime",
      "two-body repulsive potential proportional",
      "homogeneous fermi gas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}