{
  "id": "1310.0604",
  "version": "v1",
  "published": "2013-10-02T07:20:41.000Z",
  "updated": "2013-10-02T07:20:41.000Z",
  "title": "The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D",
  "authors": [
    "Mathieu Lewin",
    "Julien Sabin"
  ],
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form $f(-\\Delta)$, describing an homogeneous Fermi gas. Under suitable assumptions on the interaction potential and on the momentum distribution $f$, we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of $f(-\\Delta)$ in a Schatten space, the system weakly converges to the stationary state for large times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-02T07:20:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary state",
      "dispersion",
      "nonlinear hartree equation",
      "large times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0604L"
    }
  }
}