{
  "id": "1907.03388",
  "version": "v1",
  "published": "2019-07-08T02:44:09.000Z",
  "updated": "2019-07-08T02:44:09.000Z",
  "title": "Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data",
  "authors": [
    "Jinyeop Lee"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a system of $p$ components of bosons, each of which consists of $N_{1},N_{2},\\dots,N_{p}$ particles, respectively. The bosons are in three dimensions with interactions via a generalized interaction potential which includes the Coulomb interaction. We set the initial condition to describe a mixture condensate, i.e., a tensor product of factorized states. We show that the difference between the many-body Schr\\\"odinger evolution in the mean-field regime and the corresponding $p$-particle dynamics due to a system of Hartree equation is $O(N^{-1})$ where $N=\\sum_{q=1}^{p}N_{q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-08T02:44:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81V70",
      "82C10",
      "81U30"
    ],
    "keywords": [
      "factorized initial data",
      "mixture condensate",
      "hartree type",
      "convergence",
      "tensor product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}