{
  "annotation_id": "7b2684a9-6a0d-4c45-b46f-aec3e4ce294d",
  "date_created": "2026-03-02T18:02:13.030000Z",
  "date_modified": "2026-03-02T18:02:13.030000Z",
  "file_hash": "a99d9b302e76107eef8ba86b3727230373846d782ffdf82d95adfb4e6ca43c5f",
  "private": false,
  "record": {
    "abstract": "A wave function picks up, in addition to the dynamic phase, the geometric\n(Berry) phase when traversing adiabatically a closed cycle in parameter space.\nWe develop a general multidimensional theory of the geometric phase for\n(double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians.\nWe show that the geometric phase is exactly $\\pi$ for symmetric complex\nHamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian\nHamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of\nhigher dimension, the geometric phase tends to $\\pi$ for small cycles and\nchanges as the cycle size and shape are varied. We find explicitly the leading\nasymptotic term of this dependence, and describe it in terms of interaction of\ndifferent energy levels.",
    "arxiv_id": "quant-ph/0501040",
    "authors": [
      "A. A. Mailybaev",
      "O. N. Kirillov",
      "A. P. Seyranian"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevA.72.014104",
    "journal_ref": "Phys. Rev A 72, 014104 (2005)",
    "title": "Geometric phase around exceptional points",
    "url": "https://arxiv.org/abs/quant-ph/0501040"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "51f37107-fabc-46cc-b308-e8feff5a2799",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}