{
  "annotation_id": "b560b189-2a0f-4bfd-92c1-ddcdbf9e353d",
  "date_created": "2026-03-02T18:02:10.345000Z",
  "date_modified": "2026-03-02T18:02:10.345000Z",
  "file_hash": "e8b902259e048e5554276bc8c034157a57ad22d2292b1593ce8897697c11d001",
  "private": false,
  "record": {
    "abstract": "We use spectral projections of time operator in the Liouville space for\nsimple quantum scattering systems in order to define a space of unstable\nparticle states evolving under a contractive semi-group. This space includes\npurely exponentially decaying states that correspond to complex eigenvalues of\nthis semi-group. The construction provides a probabilistic interpretation of\nthe resonant states characterized in terms of the Hardy class.",
    "arxiv_id": "quant-ph/0410082",
    "authors": [
      "Maurice Courbage"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Semi-groups and time operators for quantum unstable systems",
    "url": "https://arxiv.org/abs/quant-ph/0410082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8bd625f0-2501-456e-8c77-f8c9597af46e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}