{
  "id": "cond-mat/0702058",
  "version": "v5",
  "published": "2007-02-05T19:55:30.000Z",
  "updated": "2010-03-08T19:33:46.000Z",
  "title": "Nature of the Bogoliubov ground state of a weakly interacting Bose gas",
  "authors": [
    "A. M. Ettouhami"
  ],
  "comment": "major revision of previous version; 4.2 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.other",
    "cond-mat.quant-gas"
  ],
  "abstract": "As is well-known, in Bogoliubov's theory of an interacting Bose gas the ground state of the Hamiltonian $\\hat{H}=\\sum_{\\bf k\\neq 0}\\hat{H}_{\\bf k}$ is found by diagonalizing each of the Hamiltonians $\\hat{H}_{\\bf k}$ corresponding to a given momentum mode ${\\bf k}$ independently of the Hamiltonians $\\hat{H}_{\\bf k'(\\neq k)}$ of the remaining modes. We argue that this way of diagonalizing $\\hat{H}$ may not be adequate, since the Hilbert spaces where the single-mode Hamiltonians $\\hat{H}_{\\bf k}$ are diagonalized are not disjoint, but have the ${\\bf k}=0$ in common. A number-conserving generalization of Bogoliubov's method is presented where the total Hamiltonian $\\hat{H}$ is diagonalized directly. When this is done, the spectrum of excitations changes from a gapless one, as predicted by Bogoliubov's method, to one which has a finite gap in the $k\\to 0$ limit.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-03-08T19:33:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weakly interacting bose gas",
      "bogoliubov ground state",
      "bogoliubovs method",
      "momentum mode",
      "bogoliubovs theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007cond.mat..2058E"
    }
  }
}