{
  "annotation_id": "1bb4d32d-aa81-4c7e-bf87-d62adde24f56",
  "date_created": "2026-03-02T18:02:33.510000Z",
  "date_modified": "2026-03-02T18:02:33.510000Z",
  "file_hash": "d7256abe450a714fe4f2b22715a7cdba335809274e150184a30de0248ace6871",
  "private": false,
  "record": {
    "abstract": "We study main features of the exotic case of q-deformed oscillators\n(so-called Tamm-Dancoff cutoff oscillator) and find some special properties:\n(i) degeneracy of the energy levels E_{n_1} = E_{n_1+1}, n_1\\ge 1, at the {\\em\nreal value} q=\\sqrt{\\frac{n_1}{n_1+2}} of deformation parameter, as well as the\noccurrence of other degeneracies E_{n_1} = E_{n_1+k}, for k \\ge 2, at the\ncorresponding values of q which depend on both n_1 and k; (ii) the position and\nmomentum operators X and P {\\em commute on the state} |m\u003e if q is fixed as\nq=\\frac{m}{m+1}, that implies unusual uncertainty relation; (iii) two commuting\ncopies of the creation, annihilation, and number operators of this q-oscillator\ngenerate the corresponding q-deformation of the {\\em non-simple} Lie algebra\nsu(2)\\oplus u(1) whose nontrivial q-deformed commutation relation is: [ J_+,\nJ_- ] = 2 J_0 q^{2J_3-1} where J_0\\equiv \\frac12 (N_1-N_2) and J_3\\equiv\n\\frac12 (N_1+N_2).",
    "arxiv_id": "quant-ph/0612122",
    "authors": [
      "A. M. Gavrilik",
      "A. P. Rebesh"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.stat-mech",
      "hep-th",
      "math-ph",
      "math.MP",
      "nucl-th"
    ],
    "doi": "10.1142/S0217732307022827",
    "journal_ref": "Mod.Phys.Lett.A22:949-960,2007",
    "title": "A q-Oscillator with \u0027Accidental\u0027 Degeneracy of Energy Levels",
    "url": "https://arxiv.org/abs/quant-ph/0612122"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a602ce43-bf8c-45c9-ba4a-133b809e6e38",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}