{
  "id": "math-ph/0001035",
  "version": "v1",
  "published": "2000-01-22T00:38:03.000Z",
  "updated": "2000-01-22T00:38:03.000Z",
  "title": "Constructive Fractional-Moment Criteria for Localization in Random Operators",
  "authors": [
    "M. Aizenman",
    "J. H. Schenker",
    "R. M. Friedrich",
    "D. Hundertmark"
  ],
  "comment": "Announcement and summary of results whose proofs are given elsewhere. LaTex (10 pages), uses Elsevier \"elsart\" files (attached)",
  "journal": "Phys. A 279 (2000), 369",
  "doi": "10.1016/S0378-4371(00)00012-1",
  "categories": [
    "math-ph",
    "cond-mat",
    "math.MP",
    "math.PR",
    "math.SP"
  ],
  "abstract": "We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-01-22T00:38:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "47B80",
      "60H25"
    ],
    "keywords": [
      "constructive fractional-moment criteria",
      "random operators",
      "green functions",
      "preclude fast power-law decay",
      "two-dimensional fermi gases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}