{
  "id": "1710.03618",
  "version": "v1",
  "published": "2017-10-10T14:14:35.000Z",
  "updated": "2017-10-10T14:14:35.000Z",
  "title": "Asymptotic expansion of the mean-field approximation",
  "authors": [
    "Thierry Paul",
    "Mario Pulvirenti"
  ],
  "categories": [
    "quant-ph",
    "math-ph",
    "math.AP",
    "math.DS",
    "math.MP"
  ],
  "abstract": "We established and estimate the full asymptotic expansion in integer powers of 1 N of the [ $\\sqrt$ N ] first marginals of N-body evolutions lying in a general paradigm containing Kac models and non-relativistic quantum evolution. We prove that the coefficients of the expansion are, at any time, explicitly computable given the knowledge of the linearization on the one-body meanfield kinetic limit equation. Instead of working directly with the corresponding BBGKY-type hierarchy, we follows a method developed in [22] for the meanfield limit, dealing with error terms analogue to the v-functions used in previous works. As a by-product we get that the rate of convergence to the meanfield limit in 1 N is optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T14:14:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field approximation",
      "one-body meanfield kinetic limit equation",
      "meanfield limit",
      "general paradigm containing kac models",
      "full asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}