{
  "id": "1011.5648",
  "version": "v2",
  "published": "2010-11-25T16:41:06.000Z",
  "updated": "2011-03-12T20:09:41.000Z",
  "title": "Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method",
  "authors": [
    "Alexander Elgart",
    "Martin Tautenhahn",
    "Ivan Veselic'"
  ],
  "comment": "29 pages, 1 figure, to appear in AHP",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-12T20:09:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "60H25",
      "35J10"
    ],
    "keywords": [
      "sign-indefinite single-site potential",
      "anderson localization",
      "fractional moment decay property holds",
      "satisfy lifshitz tail estimates",
      "fractional moment method facilitates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011AnHP...12.1571E"
    }
  }
}