{
  "id": "2211.13076",
  "version": "v1",
  "published": "2022-11-23T16:08:34.000Z",
  "updated": "2022-11-23T16:08:34.000Z",
  "title": "Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator",
  "authors": [
    "Charbella Abou Khalil"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Given small initial solutions of the nonlinear quantum harmonic oscillator on $\\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as multiplicative potentials, in a way that the linear frequencies satisfy a non-resonance condition. More precisely, we prove that for almost all potentials $V$, the low modes of the solution are almost preserved for very long times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-23T16:08:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear quantum harmonic oscillator",
      "birkhoff normal form",
      "low regularity",
      "long time behavior",
      "small initial solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}