{
  "id": "1912.07454",
  "version": "v1",
  "published": "2019-12-16T15:35:23.000Z",
  "updated": "2019-12-16T15:35:23.000Z",
  "title": "Hartree-Fock analysis of the effects of long-range interactions on the Bose-Einstein condensation",
  "authors": [
    "A. Alastuey",
    "J Piasecki",
    "P. Szymczak"
  ],
  "journal": "Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2019",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We consider a Bose gas with two-body Kac-like scaled interactions V $\\gamma$ (r) = $\\gamma$ 3 v($\\gamma$r) where v(x) is a given repulsive and integrable potential, while $\\gamma$ is a positive parameter which controls the range of the interactions and their amplitude at a distance r. Using the Hartree-Fock approximation we find that, at finite non-zero temperatures, the Bose-Einstein condensation is destroyed by the repulsive interactions when they are sufficiently long-range. More precisely, we show that for $\\gamma$ sufficiently small but finite the off-diagonal part of the one-body density matrix always vanishes at large distances. Our analysis sheds light on the coupling between critical correlations and long-range interactions, which might lead to the breakdown of the off-diagonal long-range order even beyond the Hartree-Fock approximation. Furthermore, our Hartree-Fock analysis shows the existence of a threshold value $\\gamma$ 0 above which the Bose-Einstein condensation is restored. Since $\\gamma$ 0 is an unbounded increasing function of the temperature this implies for a fixed $\\gamma$, namely for a fixed scaled potential, that a condensate cannot form above some critical temperature whatever the value of the density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-16T15:35:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bose-einstein condensation",
      "hartree-fock analysis",
      "long-range interactions",
      "hartree-fock approximation",
      "analysis sheds light"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}