{
  "annotation_id": "00a73260-a27a-4615-b29a-5a9107d55e40",
  "date_created": "2026-03-02T18:01:38.368000Z",
  "date_modified": "2026-03-02T18:01:38.368000Z",
  "file_hash": "114c80a4abb9c0f8309cc6e01f4dfdfc20fabac12125e307eba806a95ea8e23d",
  "private": false,
  "record": {
    "abstract": "Starting from a forward--backward path integral of a point particle in a bath\nof harmonic oscillators, we derive the Fokker-Planck and Langevin equations\nwith and without inertia. Special emphasis is placed upon the correct operator\norder in the time evolution operator. The crucial step is the evaluation of a\nJacobian with a retarded time derivative by analytic regularization.",
    "arxiv_id": "quant-ph/0008109",
    "authors": [
      "Hagen Kleinert"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1006/aphy.2001.6158",
    "journal_ref": "Ann. Phys. 291 (2001) 14",
    "title": "Fokker-Planck and Langevin Equations from Forward--Backward Path   Integral",
    "url": "https://arxiv.org/abs/quant-ph/0008109"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "be894437-e64c-4de0-9daa-068810d53d11",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}