{
  "id": "math-ph/0412078",
  "version": "v1",
  "published": "2004-12-21T22:41:15.000Z",
  "updated": "2004-12-21T22:41:15.000Z",
  "title": "Bounds on the spectral shift function and the density of states",
  "authors": [
    "Dirk Hundertmark",
    "Rowan Killip",
    "Shu Nakamura",
    "Peter Stollmann",
    "Ivan Veselic'"
  ],
  "comment": "Latex 2e, 15 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study spectra of Schr\\\"odinger operators on $\\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values $\\mu_n$ of the difference of the semigroups as $n\\to \\infty$ and deduce bounds on the spectral shift function of the pair of operators. Thereafter we consider alloy type random Schr\\\"odinger operators. The single site potential $u$ is assumed to be non-negative and of compact support. The distributions of the random coupling constants are assumed to be H\\\"older continuous. Based on the estimates for the spectral shift function, we prove a Wegner estimate which implies H\\\"older continuity of the integrated density of states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-21T22:41:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J10",
      "81Q10"
    ],
    "keywords": [
      "spectral shift function",
      "alloy type random",
      "single site potential",
      "semigroups",
      "exponential decay"
    ],
    "publication": {
      "doi": "10.1007/s00220-005-1460-0",
      "journal": "Communications in Mathematical Physics",
      "year": 2006,
      "month": "Mar",
      "volume": 262,
      "number": 2,
      "pages": 489
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006CMaPh.262..489H"
    }
  }
}