{
  "annotation_id": "d086513b-2b0d-4d22-9174-dccf339f78fe",
  "date_created": "2026-03-02T18:01:59.809000Z",
  "date_modified": "2026-03-02T18:01:59.809000Z",
  "file_hash": "83793940c4202a302e41e1e8d02ce1707149dc240159e37c31d2748427b4e60a",
  "private": false,
  "record": {
    "abstract": "The properties of open quantum systems are described well by an effective\nHamiltonian ${\\cal H}$ that consists of two parts: the Hamiltonian $H$ of the\nclosed system with discrete eigenstates and the coupling matrix $W$ between\ndiscrete states and continuum. The eigenvalues of ${\\cal H}$ determine the\npoles of the $S$ matrix. The coupling matrix elements $\\tilde W_k^{cc\u0027}$\nbetween the eigenstates $k$ of ${\\cal H}$ and the continuum may be very\ndifferent from the coupling matrix elements $W_k^{cc\u0027}$ between the eigenstates\nof $H$ and the continuum. Due to the unitarity of the $S$ matrix, the\n$\\TW_k^{cc\u0027}$ depend on energy in a non-trivial manner, that conflicts with the\nassumptions of some approaches to reactions in the overlapping regime. Explicit\nexpressions for the wave functions of the resonance states and for their phases\nin the neighbourhood of, respectively, avoided level crossings in the complex\nplane and double poles of the $S$ matrix are given.",
    "arxiv_id": "quant-ph/0304197",
    "authors": [
      "I. Rotter"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.mes-hall",
      "nucl-th"
    ],
    "doi": "10.1103/PhysRevE.68.016211",
    "journal_ref": "Phys.Rev. E68 (2003) 016211",
    "title": "Effective Hamiltonian and unitarity of the S matrix",
    "url": "https://arxiv.org/abs/quant-ph/0304197"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "73eb88c4-8148-4630-a1b6-94c6b7144a05",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}