{
  "annotation_id": "336b5d73-b99a-406f-bf5f-5ff7467e607b",
  "date_created": "2026-03-02T18:01:48.553000Z",
  "date_modified": "2026-03-02T18:01:48.553000Z",
  "file_hash": "a5eee27ec7a9e9d804742d9b37962768b06ae70d412a6ab983f5493c822bcc28",
  "private": false,
  "record": {
    "abstract": "An accidental degeneracy of resonances gives rise to a double pole in the\nscattering matrix, a double zero in the Jost function and a Jordan chain of\nlength two of generalized Gamow-Jordan eigenfunctions of the radial\nSchroedinger equation. The generalized Gamow-Jordan eigenfunctions are basis\nelements of an expansion in bound and resonant energy eigenfunctions plus a\ncontinuum of scattering wave functions of complex wave number. In this\nbiorthonormal basis, any operator which is a regular function of the\nHamiltonian is represented by a complex matrix which is diagonal except for a\nJordan block of rank two. The occurrence of a double pole in the Green\u0027s\nfunction, as well as the non-exponential time evolution of the Gamow-Jordan\ngeneralized eigenfunctions are associated to the Jordan block in the complex\nenergy representation.",
    "arxiv_id": "quant-ph/0204084",
    "authors": [
      "E. Hernandez",
      "A. Jauregui",
      "A. Mondragon"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.67.022721",
    "journal_ref": "Phys.Rev.A67:022721,2003",
    "title": "Jordan blocks and Gamow-Jordan eigenfunctions associated to a double   pole of the S-matrix",
    "url": "https://arxiv.org/abs/quant-ph/0204084"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ca2776e3-9ab2-46b3-ad2f-ef8cded6ee10",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}