{
  "annotation_id": "21f8aa40-1c52-40a4-9272-67b545cd1775",
  "date_created": "2026-03-02T18:01:49.510000Z",
  "date_modified": "2026-03-02T18:01:49.510000Z",
  "file_hash": "4a9aade7c9e16c1fa74498d6ce2a9ec38667645ff2d9a89a4d657785895b6c12",
  "private": false,
  "record": {
    "abstract": "Structures of quantum Fokker-Planck equations are characterized with respect\nto the properties of complete positivity, covariance under symmetry\ntransformations and satisfaction of equipartition, referring to recent\nmathematical work on structures of unbounded generators of covariant quantum\ndynamical semigroups. In particular the quantum optical master-equation and the\nquantum Brownian motion master-equation are shown to be associated to\n$\\mathrm{U(1)}$ and $\\mathrm{R}$ symmetry respectively. Considering the motion\nof a Brownian particle, where the expression of the quantum Fokker-Planck\nequation is not completely fixed by the aforementioned requirements, a recently\nintroduced microphysical kinetic model is briefly recalled, where a quantum\ngeneralization of the linear Boltzmann equation in the small energy and\nmomentum transfer limit straightforwardly leads to quantum Brownian motion.",
    "arxiv_id": "quant-ph/0204071",
    "authors": [
      "Bassano Vacchini"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1505126",
    "journal_ref": "J. Math. Phys. 43 (2002) 5446-5458",
    "title": "Quantum optical versus quantum Brownian motion master-equation in terms   of covariance and equilibrium properties",
    "url": "https://arxiv.org/abs/quant-ph/0204071"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0a9ccd66-3424-4692-9474-a5f5de93473c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}