{
  "annotation_id": "2746d860-d337-4b6c-927f-40ba07c3bc1f",
  "date_created": "2026-03-02T18:01:59.594000Z",
  "date_modified": "2026-03-02T18:01:59.594000Z",
  "file_hash": "1bb999937a05fd6e64b91ffac96f4266cfbdb150e19add5792be7302ab18ef51",
  "private": false,
  "record": {
    "abstract": "The Wigner function is known to evolve classically under the exclusive action\nof a quadratic hamiltonian. If the system does interact with the environment\nthrough Lindblad operators that are linear functions of position and momentum,\nwe show that the general evolution is the convolution of the classically\nevolving Wigner function with a phase space gaussian that broadens in time. We\nanalyze the three generic cases of elliptic, hyperbolic and parabolic\nHamiltonians. The Wigner function always becomes positive in a definite time,\nwhich is shortest in the hyperbolic case. We also derive an exact formula for\nthe evolving linear entropy as the average of a narrowing gaussian taken over a\nprobability distribution that depends only on the initial state. This leads to\na long time asymptotic formula for the growth of linear entropy.",
    "arxiv_id": "quant-ph/0304087",
    "authors": [
      "O. Brodier",
      "A. M. Ozorio de Almeida"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevE.69.016204",
    "journal_ref": "Phys. Rev. E 69, 016204 (2004)",
    "title": "Symplectic evolution of Wigner functions in markovian open systems",
    "url": "https://arxiv.org/abs/quant-ph/0304087"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1acc35cf-4660-4b92-a99c-1938d25f17a4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}