{
  "id": "1403.7771",
  "version": "v2",
  "published": "2014-03-30T15:15:57.000Z",
  "updated": "2014-08-04T14:47:38.000Z",
  "title": "Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum",
  "authors": [
    "Sonja Barkhofen",
    "Frédéric Faure",
    "Tobias Weich"
  ],
  "journal": "Nonlinearity 27 (2014) 1829-1858",
  "categories": [
    "math-ph",
    "cond-mat.mes-hall",
    "math.DS",
    "math.MP",
    "math.SP"
  ],
  "abstract": "In many non-integrable open systems in physics and mathematics resonances have been found to be surprisingly ordered along curved lines in the complex plane. In this article we provide a unifying approach to these resonance chains by generalizing dynamical zeta functions. By means of a detailed numerical study we show that these generalized zeta functions explain the mechanism that creates the chains of quantum resonance and classical Ruelle resonances for 3-disk systems as well as geometric resonances on Schottky surfaces. We also present a direct system-intrinsic definition of the continuous lines on which the resonances are strung together as a projection of an analytic variety. Additionally, this approach shows that the existence of resonance chains is directly related to a clustering of the classical length spectrum on multiples of a base length. Finally, this link is used to construct new examples where several different structures of resonance chains coexist.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-04T14:47:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25",
      "47A40",
      "58J50",
      "81Q50",
      "81Q05"
    ],
    "keywords": [
      "open systems",
      "clustering",
      "resonance chains coexist",
      "direct system-intrinsic definition",
      "generalized zeta functions explain"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/27/8/1829",
      "journal": "Nonlinearity",
      "year": 2014,
      "month": "Aug",
      "volume": 27,
      "number": 8,
      "pages": 1829
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014Nonli..27.1829B"
    }
  }
}