{
  "annotation_id": "e12b5dff-8936-4368-b06f-838fb1951a1d",
  "date_created": "2026-03-02T18:02:27.465000Z",
  "date_modified": "2026-03-02T18:02:27.465000Z",
  "file_hash": "bdfebb61eba2a537512ef4fa1f7f770a108bda9ae4649fee5812038da74ee655",
  "private": false,
  "record": {
    "abstract": "We derive the momentum space dynamic equations and state functions for one\ndimensional quantum walks by using linear systems and Lie group theory. The\nmomentum space provides an analytic capability similar to that contributed by\nthe z transform in discrete systems theory. The state functions at each time\nstep are expressed as a simple sum of three Chebyshev polynomials. The\nfunctions provide an analytic expression for the development of the walks with\ntime.",
    "arxiv_id": "quant-ph/0604197",
    "authors": [
      "Ian Fuss",
      "Langord B. White",
      "Peter J. Sherman",
      "Sanjeev Naguleswaran"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Momentum Dynamics of One Dimensional Quantum Walks",
    "url": "https://arxiv.org/abs/quant-ph/0604197"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "710f1b72-5b11-45ea-8734-16996a308a24",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}