{
  "id": "1106.1689",
  "version": "v2",
  "published": "2011-06-08T23:55:29.000Z",
  "updated": "2011-07-13T11:26:35.000Z",
  "title": "Ballistic Behavior for Random Schrödinger Operators on the Bethe Strip",
  "authors": [
    "Abel Klein",
    "Christian Sadel"
  ],
  "comment": "33 pages, revised version, to appear in Journal of Spectral Theory",
  "journal": "J. Spectr. Theory 1, 409-442 (2011)",
  "doi": "10.4171/JST/18",
  "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 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. Under certain conditions on $A$ and $K$, for which we previously proved the existence of absolutely continuous spectrum for small $\\lambda$, we now obtain ballistic behavior for the spreading of wave packets evolving under $H_\\lambda$ for small $\\lambda$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-13T11:26:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "47B80",
      "60H25"
    ],
    "keywords": [
      "random schrödinger operators",
      "bethe strip",
      "ballistic behavior",
      "random matrix potential",
      "cayley tree"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.1689K"
    }
  }
}