{
  "annotation_id": "e18cc8f7-73b2-4a2b-bc1c-507585686c00",
  "date_created": "2026-03-02T18:02:41.489000Z",
  "date_modified": "2026-03-02T18:02:41.489000Z",
  "file_hash": "ed6e214a9903b8c5ae85db25bd380b9b007ccf1df04cecee32cb2a6f53791670",
  "private": false,
  "record": {
    "abstract": "Simple Hartree-type equations lead to dynamics of a subsystem that is not\ncompletely positive in the sense accepted in mathematical literature. In the\nlinear case this would imply that negative probabilities have to appear for\nsome system that contains the subsystem in question. In the nonlinear case this\ndoes not happen because the mathematical definition is physically unfitting as\nshown on a concrete example.",
    "arxiv_id": "quant-ph/9708029",
    "authors": [
      "Marek Czachor",
      "Maciej Kuna"
    ],
    "categories": [
      "quant-ph",
      "chao-dyn",
      "funct-an",
      "hep-th",
      "math.FA",
      "nlin.CD"
    ],
    "doi": "10.1103/PhysRevA.58.128",
    "journal_ref": "Phys.Rev. A58 (1998) 128",
    "title": "Complete positivity of nonlinear evolution: A case study",
    "url": "https://arxiv.org/abs/quant-ph/9708029"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ce819ed2-72b8-4008-be77-e1307ca3a092",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}