{
  "annotation_id": "aa09546e-f700-45b4-a188-5564a2ac0187",
  "date_created": "2026-03-02T18:02:41.090000Z",
  "date_modified": "2026-03-02T18:02:41.090000Z",
  "file_hash": "ffcffc3ca7d5ed8b493de2f21003b9f19df06b5833d42a494f1c4f6a4153b540",
  "private": false,
  "record": {
    "abstract": "We show that the quadratic short time behaviour of transition probability is\na natural consequence of the inner product of the Hilbert space of the quantum\nsystem. We prove that Schr\\\"odinger time evolution between two successive\nmeasurements is not a necessary but only a sufficient condition for predicting\nquantum Zeno effect. We provide a relation between the survival probability and\nthe underlying geometric structure such as the Fubini-Study metric defined on\nthe projective Hilbert space of the quantum system. This predicts the quantum\nZeno effect even for systems described by non-linear and non-unitary evolution\nequations, within the collapse mechanism of the wavefunction during measurement\nprocess. Two examples are studied, one is non-linear Schr\\\"odinger equation and\nother is Gisin\u0027s equation and it is shown that one can observe quantum Zeno\neffect for systems described by these equations.",
    "arxiv_id": "quant-ph/9803082",
    "authors": [
      "A. K. Pati",
      "S. V. Lawande"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.58.831",
    "title": "Geometry of the Hilbert space and the Quantum Zeno Effect",
    "url": "https://arxiv.org/abs/quant-ph/9803082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f75ae07d-17c4-449a-acff-00ed269d2805",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}