{
  "id": "1702.07880",
  "version": "v1",
  "published": "2017-02-25T11:49:58.000Z",
  "updated": "2017-02-25T11:49:58.000Z",
  "title": "Semiclassical Trace Formula and Spectral Shift Function for Systems via a Stationary Approach",
  "authors": [
    "Marouane Assal",
    "Mouez Dimassi",
    "Setsuro Fujiié"
  ],
  "comment": "27 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint Schr\\\"odinger operators with matrix-valued potentials. We give Weyl type semiclassical asymptotics with sharp remainder estimate for the spectral shift function, and, under the existence of a scalar escape function, a full asymptotic expansion in the strong sense for its derivative. A time-independent approach enables us to treat certain potentials with energy-level crossings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-25T11:49:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral shift function",
      "semiclassical trace formula",
      "stationary approach",
      "microhyperbolic hermitian systems",
      "weyl type semiclassical asymptotics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}