{
  "annotation_id": "509d20dc-0b06-4102-b963-abcdd71c040b",
  "date_created": "2026-03-02T18:02:16.227000Z",
  "date_modified": "2026-03-02T18:02:16.227000Z",
  "file_hash": "fc0bb07e20c28306cde9b4695dc40c4bb23bbe6e465e1769f4f83b45fbe37d67",
  "private": false,
  "record": {
    "abstract": "In this paper we complete the analysis begun by two of the authors in a\nprevious work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795\n(2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the\n\"exponential decay\u0027\u0027 regions at the leading edges of the main peaks in the\nSchr{\\\"o}dinger (or wave-mechanics) picture. This calculation required us to\ngeneralise the method of stationary phase and we describe this extension in\nsome detail, including self-contained proofs of all the technical lemmas\nrequired. We also rigorously establish the exact Feynman equivalence between\nthe path-integral and wave-mechanics representations for this system using some\ntechniques from the theory of special functions. Taken together with the\nprevious work, we can now prove every theorem by both routes.",
    "arxiv_id": "quant-ph/0506048",
    "authors": [
      "Hilary A. Carteret",
      "Bruce Richmond",
      "Nico Temme"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/38/40/011",
    "journal_ref": "J. Phys. A: Math. Gen. 38 (2005) 8641-8665",
    "title": "Evanescence in Coined Quantum Walks",
    "url": "https://arxiv.org/abs/quant-ph/0506048"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "edba6b84-a98f-4a35-9abd-dbf4862ab29f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}