{
  "id": "2203.11255",
  "version": "v1",
  "published": "2022-03-21T18:29:26.000Z",
  "updated": "2022-03-21T18:29:26.000Z",
  "title": "Effective Dynamics of Interacting Fermions from Semiclassical Theory to the Random Phase Approximation",
  "authors": [
    "Niels Benedikter"
  ],
  "comment": "contribution to the proceedings of ICMP 2021",
  "categories": [
    "math-ph",
    "cond-mat.quant-gas",
    "math.MP"
  ],
  "abstract": "I review results concerning the derivation of effective equations for the dynamics of interacting Fermi gases in a high-density regime of mean-field type. Three levels of effective theories, increasing in precision, can be distinguished: the semiclassical theory given by the Vlasov equation, the mean-field theory given by the Hartree-Fock equation, and the description of the dominant effects of non-trivial entanglement by the random phase approximation. Particular attention is given to the discussion of admissible initial data, and I present an example of a realistic quantum quench that can be approximated by Hartree-Fock dynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-21T18:29:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "82B10",
      "81Q10",
      "35P05"
    ],
    "keywords": [
      "random phase approximation",
      "semiclassical theory",
      "interacting fermions",
      "effective dynamics",
      "realistic quantum quench"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}