{
  "annotation_id": "7014ca0a-1d95-4e35-810b-e517f74a8e48",
  "date_created": "2026-03-02T18:02:37.425000Z",
  "date_modified": "2026-03-02T18:02:37.425000Z",
  "file_hash": "6089dad61673b1364d5f399632fe254d8f880defffb08a59431426eceeb285dd",
  "private": false,
  "record": {
    "abstract": "We describe a generalisation of the well known Pancharatnam geometric phase\nformula for two level systems, to evolution of a three-level system along a\ngeodesic triangle in state space. This is achieved by using a recently\ndeveloped generalisation of the Poincare sphere method, to represent pure\nstates of a three-level quantum system in a convenient geometrical manner. The\nconstruction depends on the properties of the group $SU(3)\\/$ and its\ngenerators in the defining representation, and uses geometrical objects and\noperations in an eight dimensional real Euclidean space. Implications for an\nn-level system are also discussed.",
    "arxiv_id": "quant-ph/9605042",
    "authors": [
      "Arvind",
      "K. S. Mallesh",
      "N. Mukunda"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/30/7/021",
    "journal_ref": "J.Phys.A30:2417-2431,1997",
    "title": "A generalized Pancharatnam geometric phase formula for three level   systems",
    "url": "https://arxiv.org/abs/quant-ph/9605042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8fa1c742-9c08-43f3-818c-5f2cdb41600d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}