{
  "annotation_id": "56be2b7b-9d72-411f-aa07-d7ef5534c106",
  "date_created": "2026-03-02T18:02:13.038000Z",
  "date_modified": "2026-03-02T18:02:13.038000Z",
  "file_hash": "554ae82fd1eaf679c3560c26a87ffb881bc19bfe95bbf0e2f1df98abde29cec6",
  "private": false,
  "record": {
    "abstract": "We show that when an isolated doublet of unbound states of a physical system\nbecomes degenerate for some values of the control parameters of the system, the\nenergy hypersurfaces representing the complex resonance energy eigenvalues as\nfunctions of the control parameters have an algebraic branch point of rank one\nin parameter space. Associated with this singularity in parameter space, the\nscattering matrix, S_l(E), and the Green\u0027s function, G_l^(+)(k; r,r\u0027), have one\ndouble pole in the unphysical sheet of the complex energy plane. We\ncharacterize the universal unfolding or deformation of a typical degeneracy\npoint of two unbound states in parameter space by means of a universal\n2-parameter family of functions which is contact equivalent to the pole\nposition function of the isolated doublet of resonances at the exceptional\npoint and includes all small perturbations of the degeneracy condition up to\ncontact equivalence.",
    "arxiv_id": "quant-ph/0501124",
    "authors": [
      "E. Hernandez",
      "A. Jauregui",
      "A. Mondragon",
      "L. Nellen"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Unfolding a degeneracy point of two unbound states: Crossings and   anticrossings of energies and widths",
    "url": "https://arxiv.org/abs/quant-ph/0501124"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "733c07bc-b603-4b3f-aee1-d00eee18cad3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}