{
  "id": "math-ph/0604068",
  "version": "v1",
  "published": "2006-04-27T12:33:55.000Z",
  "updated": "2006-04-27T12:33:55.000Z",
  "title": "Bose-Einstein Condensation in the Luttinger-Sy Model",
  "authors": [
    "Olivier Lenoble",
    "Valentin Zagrebnov"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a rigorous study of the Bose-Einstein condensation in the Luttinger-Sy model. We prove the existence of the condensation in this one-dimensional model of the perfect boson gas placed in the Poisson random potential of singular point impurities. To tackle the off-diagonal long-range order we calculate explicitly the corresponding space-averaged one-body reduced density matrix. We show that mathematical mechanism of the Bose-Einstein condensation in this random model is similar to condensation in a one-dimensional nonrandom hierarchical model of scaled intervals. For the Luttinger-Sy model we prove the Kac-Luttinger conjecture, i.e., that this model manifests a type I BEC localized in a single \"largest\" interval of logarithmic size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-27T12:33:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bose-einstein condensation",
      "luttinger-sy model",
      "perfect boson gas",
      "poisson random potential",
      "space-averaged one-body reduced density matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.ph...4068L"
    }
  }
}