{
  "annotation_id": "c137985f-ae36-4a91-8000-08bbd01375b4",
  "date_created": "2026-03-02T18:02:45.136000Z",
  "date_modified": "2026-03-02T18:02:45.136000Z",
  "file_hash": "aeff197f98cb558088bbeb5665bcad800864f8ed5611d4bd918b3780b8a2e385",
  "private": false,
  "record": {
    "abstract": "The Gardiner\u0027s phonon presented for a particle-number conserving\napproximation method to describe the dynamics of Bose-Einstein Condesation\n(BEC) (C.W. Gardiner, Phys. Rev. A 56, 1414 (1997)) is shown to be a physical\nrealization of the $q$-deformed boson, which was abstractly developed in\nquantum group theory. On this observation, the coherent output of BEC atoms\ndriven by a radio frequency (r.f) field is analyzed in the viewpoint of a\n$q$-deformed Fock space. It is illustrated that the $q$-deformation of bosonic\ncommutation relation corresponds to the non-ideal BEC with the finite particle\nnumber $N$ of condensated atoms. Up to order 1/N, the coherent output state of\nthe untrapped atoms minimizes the uncertainty relation like a coherent state\ndoes in the ideal case of BEC that $N$ approaches infinity or $q=1-2/N$\napproaches one.",
    "arxiv_id": "quant-ph/9809079",
    "authors": [
      "C. P. Sun",
      "S. X. Yu",
      "Y. B. Gao"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "title": "Gardiner\u0027s phonon for Bose-Einstein Condensation: A physical realization   of the $q$-deformed Boson",
    "url": "https://arxiv.org/abs/quant-ph/9809079"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e08f78bd-dbfe-429d-a12e-62f919e64d95",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}