{
  "id": "2009.09855",
  "version": "v1",
  "published": "2020-08-05T09:01:20.000Z",
  "updated": "2020-08-05T09:01:20.000Z",
  "title": "The perturbational stability of the Schr$\\ddot{o}$dinger equation",
  "authors": [
    "Xixia Ma"
  ],
  "comment": "21pages. arXiv admin note: text overlap with arXiv:1810.10955, arXiv:1807.05254; text overlap with arXiv:quant-ph/0505004 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "By using the Wigner transform, it is shown that the nonlinear Schr$\\ddot{\\textmd{o}}$dinger equation can be described, in phase space, by a kinetic theory similar to the Vlasov equation which is used for describing a classical collisionless plasma. In this paper we mainly show Landau damping in the quantum sense, namely,quantum Landau damping exists for the Wigner-Poisson system. At the same time, we also prove the existence and the stability of the nonlinear Schr$\\ddot{\\textmd{o}}$dinger equation under the quantum stability assumption.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-05T09:01:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dinger equation",
      "perturbational stability",
      "nonlinear schr",
      "kinetic theory similar",
      "quantum stability assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}