{
  "id": "1804.07697",
  "version": "v1",
  "published": "2018-04-20T15:56:15.000Z",
  "updated": "2018-04-20T15:56:15.000Z",
  "title": "Bose--Einstein condensation in the Luttinger--Sy model with contact interaction",
  "authors": [
    "Joachim Kerner",
    "Maximilian Pechmann",
    "Wolfgang Spitzer"
  ],
  "comment": "35 pages",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "We study bosons on the real line in a Poisson random potential (Luttinger--Sy model) with contact interaction in the thermodynamic limit at absolute zero temperature. We prove that generalized Bose--Einstein condensation (BEC) occurs almost surely if the intensity $\\nu_N$ of the Poisson potential satisfies $[\\ln (N)]^4/N^{1 - 2\\eta} \\ll \\nu_N \\lesssim 1$ for arbitrary $0 < \\eta \\leq 1/3$. We also show that the contact interaction alters the type of condensation, going from a type-I BEC to a type-III BEC as the strength of this interaction is increased. Furthermore, for sufficiently strong contact interactions and $0 < \\eta < 1/6$ we prove that the mean particle density in the largest interval is almost surely bounded asymptotically by $\\nu_NN^{3/5+\\delta}$ for $\\delta > 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-20T15:56:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "81V70",
      "82B10"
    ],
    "keywords": [
      "luttinger-sy model",
      "mean particle density",
      "sufficiently strong contact interactions",
      "contact interaction alters",
      "poisson potential satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}