{
  "id": "1101.4328",
  "version": "v2",
  "published": "2011-01-22T22:45:44.000Z",
  "updated": "2012-01-03T16:27:48.000Z",
  "title": "Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe Strip",
  "authors": [
    "Abel Klein",
    "Christian Sadel"
  ],
  "journal": "Mathematische Nachrichten 285, 5-26 (2012)",
  "doi": "10.1002/mana.201100019",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "The Bethe Strip of width $m$ is the cartesian product $\\B\\times\\{1,...,m\\}$, where $\\B$ is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have \"extended states\" for small disorder. More precisely, we consider Anderson-like Hamiltonians $\\;H_\\lambda=\\frac12 \\Delta \\otimes 1 + 1 \\otimes A + \\lambda \\Vv$ on a Bethe strip with connectivity $K \\geq 2$, where $A$ is an $m\\times m$ symmetric matrix, $\\Vv$ is a random matrix potential, and $\\lambda$ is the disorder parameter. Given any closed interval $I\\subset (-\\sqrt{K}+a_{\\mathrm{max}},\\sqrt{K}+a_{\\mathrm{min}})$, where $a_{\\mathrm{min}}$ and $a_{\\mathrm{max}}$ are the smallest and largest eigenvalues of the matrix $A$, we prove that for $\\lambda$ small the random Schr\\\"odinger operator $\\;H_\\lambda$ has purely absolutely continuous spectrum in $I$ with probability one and its integrated density of states is continuously differentiable on the interval $I$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-03T16:27:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "47B80",
      "60H25"
    ],
    "keywords": [
      "bethe strip",
      "absolutely continuous spectrum",
      "random schroedinger operators",
      "random matrix potential",
      "bethe lattice"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.4328K"
    }
  }
}