{
  "id": "cond-mat/0108216",
  "version": "v3",
  "published": "2001-08-14T02:03:13.000Z",
  "updated": "2002-03-14T19:58:54.000Z",
  "title": "On \"Do the attractive bosons condense?\" by N. K. Wilkin, J. M. F. Gunn, R. A. Smith",
  "authors": [
    "M. S. Hussein",
    "O. K. Vorov"
  ],
  "comment": "5 pages, minor textual revisions",
  "categories": [
    "cond-mat.stat-mech",
    "nucl-th",
    "physics.atom-ph",
    "quant-ph"
  ],
  "abstract": "Using Perron-Frobenius theorem, we prove that the results by Wilkin, Gunn and Smith [1] for the ground states of N Bose atoms rotating at the angular momentum L in a harmonic atomic trap with frequency omega interacting via attractive delta^2(r) forces, are valid for a broad class of predominantly attractive interactions V(r), not necessarily attractive for any r. The sufficient condition for the interaction is that all the two-body matrix elements <z_1^k z_2^l |V| z_2^m z_1^n> allowed by the conservation of angular momentum k+l = m+n, are negative. This class includes, in particular, the Gaussian attraction of arbitrary radius, -1/r - Coulomb and log(r)-Coulomb forces, as well as all the short-range R << omega^{-1/2} interactions satisfying inequality int d^2r V(r) < 0. There is no condensation at L>> 1, and the angular momentum is concentrated in the collective ``center-of-mass'' mode.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2002-03-14T19:58:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "attractive bosons condense",
      "angular momentum",
      "two-body matrix elements",
      "harmonic atomic trap",
      "bose atoms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 561737,
      "adsabs": "2001cond.mat..8216H"
    }
  }
}