{
  "annotation_id": "de791248-2da9-4819-ba82-572805ccf35c",
  "date_created": "2026-03-02T18:01:49.382000Z",
  "date_modified": "2026-03-02T18:01:49.382000Z",
  "file_hash": "a89e5091300a9e166241fb70e251844497c42eaebb0fe5aee190fa7e9be0e186",
  "private": false,
  "record": {
    "abstract": "A quantum linear Boltzmann equation is proposed, constructed in terms of the\noperator-valued dynamic structure factor of the macroscopic system the test\nparticle is interacting with. Due to this operator structure it is a\nnon-Abelian linear Boltzmann equation and when expressed through the Wigner\nfunction it allows for a direct comparison with the classical one. Considering\na Brownian particle the corresponding Fokker-Planck equation is obtained in a\nmost direct way taking the limit of small energy and momentum transfer. A\ntypically quantum correction to the Kramers equation thus appears, describing\ndiffusion in position and further implying a correction to Einstein\u0027s diffusion\ncoefficient in the high temperature and friction limit in which Smoluchowski\nequation emerges.",
    "arxiv_id": "quant-ph/0204114",
    "authors": [
      "Bassano Vacchini"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech"
    ],
    "doi": "10.1103/PhysRevE.66.027107",
    "journal_ref": "Phys. Rev. E 66 (2002) 027107",
    "title": "Non-Abelian linear Boltzmann equation and quantum correction to Kramers   and Smoluchowski equation",
    "url": "https://arxiv.org/abs/quant-ph/0204114"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ea62f5c1-e402-4761-8e25-2fed31be8e0b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}