{
  "annotation_id": "28763689-1622-4e20-85af-8b0d748855fc",
  "date_created": "2026-03-02T18:01:45.335000Z",
  "date_modified": "2026-03-02T18:01:45.335000Z",
  "file_hash": "7a13dfbcf3c95981d581ff575279909c78128dbd44cabc9bab54b3672436eac5",
  "private": false,
  "record": {
    "abstract": "We investigate the geometric phases and the Bargmann invariants associated\nwith a multi-level quantum systems. In particular, we show that a full set of\n`gauge-invariant\u0027 objects for an $n$-level system consists of $n$ geometric\nphases and ${1/2}(n-1)(n-2)$ algebraically independent 4-vertex Bargmann\ninvariants. In the process of establishing this result we develop a canonical\nform for U(n) matrices which is useful in its own right. We show that the\nrecently discovered `off-diagonal\u0027 geometric phases [N. Manini and F.\nPistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analysed in terms\nof the basic building blocks developed in this work. This result liberates the\noff-diagonal phases from the assumption of adiabaticity used in arriving at\nthem.",
    "arxiv_id": "quant-ph/0107006",
    "authors": [
      "N. Mukunda",
      "Arvind",
      "S. Chaturvedi",
      "R. Simon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.65.012102",
    "journal_ref": "Phys. Rev. A 65, art. no. 012102, 1-10 (2003)",
    "title": "Bargmann invariants and off-diagonal geometric phases for multi-level   quantum systems -- a unitary group approach",
    "url": "https://arxiv.org/abs/quant-ph/0107006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "92b03f68-06ad-4215-98ee-e2db4fc233c9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}