{
  "annotation_id": "99b3dc15-29d7-4352-92df-4e6111c73d37",
  "date_created": "2026-03-02T18:01:49.336000Z",
  "date_modified": "2026-03-02T18:01:49.336000Z",
  "file_hash": "2834165d5789f4b11f15f21f21c74549687e54998916578daaca9eb0ec6e2ee6",
  "private": false,
  "record": {
    "abstract": "We consider the time evolution of the density matrix $\\rho$ in a\n2-dimensional complex Hilbert space. We allow for dissipation by adding to the\nvon Neumann equation a term $D[\\rho]$, which is of Lindblad type in order to\nassure complete positivity of the time evolution. We present five equivalent\nforms of $D[\\rho]$. In particular, we connect the familiar dissipation matrix\n$L$ with a geometric version of $D[\\rho]$, where $L$ consists of a positive sum\nof projectors onto planes in $\\mathbf{R}^3$. We also study the minimal number\nof Lindblad terms needed to describe the most general case of $D[\\rho]$. All\nproofs are worked out comprehensively, as they present at the same time a\npractical procedure how to determine explicitly the different forms of\n$D[\\rho]$. Finally, we perform a general discussion of the asymptotic behaviour\n$t \\to \\infty$ of the density matrix and we relate the two types of asymptotic\nbehaviour with our geometric version of $D[\\rho]$.",
    "arxiv_id": "quant-ph/0201142",
    "authors": [
      "R. A. Bertlmann",
      "W. Grimus"
    ],
    "categories": [
      "quant-ph",
      "hep-ph"
    ],
    "doi": "10.1016/S0375-9601(02)00816-2",
    "journal_ref": "Phys.Lett. A300 (2002) 107-114",
    "title": "Dissipation in a 2-dimensional Hilbert space: Various forms of complete   positivity",
    "url": "https://arxiv.org/abs/quant-ph/0201142"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ba263470-a8a8-42b9-ac90-13a69648d7cc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}