{
  "id": "1804.05489",
  "version": "v1",
  "published": "2018-04-16T03:14:45.000Z",
  "updated": "2018-04-16T03:14:45.000Z",
  "title": "Remarks on scattering matrices for Schrödiner operators with critically long-range perturbations",
  "authors": [
    "Shu Nakamura"
  ],
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider scattering matrix for Schr\\\"odinger-type operators on $R^d$ with perturbation $V(x)=O(\\langle x\\rangle^{-1})$ as $|x|\\to\\infty$. We show that the scattering matrix (with time-independent modifiers) is a pseudodifferential operator. We present examples of which the spectrum of the scattering matrix is dense point spectrum, or absolutely continuous spectrum, possibly with discrete point spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-16T03:14:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "35P25",
      "81U05"
    ],
    "keywords": [
      "scattering matrix",
      "critically long-range perturbations",
      "schrödiner operators",
      "dense point spectrum",
      "discrete point spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}