{
  "id": "1910.03681",
  "version": "v1",
  "published": "2019-10-07T13:20:48.000Z",
  "updated": "2019-10-07T13:20:48.000Z",
  "title": "Large time behavior of Solutions to Schrödinger equation with complex-valued potential",
  "authors": [
    "Maha Aafarani"
  ],
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We study the large-time behavior of the solutions to the Schr\\\"odinger equation associated with a non-selfadjoint operator having zero energy eigenvalue and real resonances. Our results extend those of Jensen and Kato in the three-dimensional selfadjoint case. We consider a model of Schr\\\"odinger operator with a quickly decaying potential in dimension three. We assume that the latter has a finite number of real resonances. We are interested in the expansions of the resolvent in the low energy part and near positive resonances. In particular, we discuss, under different conditions, the three situations of zero energy: zero is an eigenvalue or a resonance, or both.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-07T13:20:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large time behavior",
      "schrödinger equation",
      "complex-valued potential",
      "real resonances",
      "zero energy eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}