{
  "annotation_id": "9aa63f8e-2030-469e-893a-13a9c4a9a75a",
  "date_created": "2026-03-02T18:02:40.783000Z",
  "date_modified": "2026-03-02T18:02:40.783000Z",
  "file_hash": "8532da4dcb90de22764f30b76be71ed5f78ce7454bd0ba3f2bd4890c8e043c2b",
  "private": false,
  "record": {
    "abstract": "In analogy to Gamow vectors that are obtained from first order resonance\npoles of the S-matrix, one can also define higher order Gamow vectors which are\nderived from higher order poles of the S-matrix. An S-matrix pole of r-th order\nat z_R=E_R-i\\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ...\n, r-1, which are also Jordan vectors of degree (k+1) with generalized\neigenvalue (E_R-i\\Gamma/2). The Gamow-Jordan vectors are elements of a\ngeneralized complex eigenvector expansion, whose form suggests the definition\nof a state operator (density matrix) for the microphysical decaying state of\nthis higher order pole. This microphysical state is a mixture of non-reducible\ncomponents. In spite of the fact that the k-th order Gamow-Jordan vectors has\nthe polynomial time-dependence which one always associates with higher order\npoles, the microphysical state obeys a purely exponential decay law.",
    "arxiv_id": "quant-ph/9705011",
    "authors": [
      "A. Bohm",
      "M. Loewe",
      "S. Maxson",
      "P. Patuleanu",
      "C. Puntmann",
      "M. Gadella"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.532203",
    "journal_ref": "J.Math.Phys. 38 (1997) 6072-6100",
    "title": "Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher   Order S-Matrix Poles",
    "url": "https://arxiv.org/abs/quant-ph/9705011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ccc126c2-f785-445e-999b-eb5ab38ebee8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}