{
  "id": "1801.04799",
  "version": "v1",
  "published": "2018-01-15T13:43:03.000Z",
  "updated": "2018-01-15T13:43:03.000Z",
  "title": "Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials",
  "authors": [
    "Maximilian Jeblick",
    "Peter Pickl"
  ],
  "comment": "34 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We present a microscopic derivation of the time-dependent Gross-Pitaevskii equation starting from an interacting N-particle system of Bosons. We prove convergence of the reduced density matrix corresponding to the exact time evolution to the projector onto the solution of the respective Gross-Pitaevskii equation. Our work extends a previous result by one of us (P.P.[44]) to interaction potentials which need not to be nonnegative, but may have a sufficiently small negative part. One key estimate in our proof is an operator inequality which was first proven by Jun Yin, see [49].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-15T13:43:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time dependent gross-pitaevskii equation",
      "non purely positive potentials",
      "derivation",
      "exact time evolution",
      "time-dependent gross-pitaevskii equation starting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}