{
  "annotation_id": "2f7e7059-8ff5-428d-9ac8-1d66fce2315d",
  "date_created": "2026-03-02T18:02:13.631000Z",
  "date_modified": "2026-03-02T18:02:13.631000Z",
  "file_hash": "5e118111363f81354593cd1a63d51e26bdddd745f90a89612ae1fcc2231fb355",
  "private": false,
  "record": {
    "abstract": "We present a N-dimensional quantization a la Berezin-Klauder or frame\nquantization of the complex plane based on overcomplete families of states\n(coherent states) generated by the N first harmonic oscillator eigenstates. The\nspectra of position and momentum operators are finite and eigenvalues are\nequal, up to a factor, to the zeros of Hermite polynomials. From numerical and\ntheoretical studies of the large $N$ behavior of the product $\\lambda\\_m(N)\n\\lambda\\_M(N)$ of non null smallest positive and largest eigenvalues, we infer\nthe inequality $\\delta\\_N(Q) \\Delta\\_N(Q) = \\sigma\\_N \\overset{\u003c}{\\underset{N\n\\to \\infty}{\\to}} 2 \\pi$ (resp. $\\delta\\_N(P) \\Delta\\_N(P) = \\sigma\\_N\n\\overset{\u003c}{\\underset{N \\to \\infty}{\\to}} 2 \\pi $) involving, in suitable\nunits, the minimal ($\\delta\\_N(Q)$) and maximal ($\\Delta\\_N(Q)$) sizes of\nregions of space (resp. momentum) which are accessible to exploration within\nthis finite-dimensional quantum framework. Interesting issues on the\nmeasurement process and connections with the finite Chern-Simons matrix model\nfor the Quantum Hall effect are discussed.",
    "arxiv_id": "quant-ph/0411210",
    "authors": [
      "Jean-Pierre Gazeau",
      "Fran\u00e7ois-Xavier Josse-Michaux",
      "Pascal Monceau"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1142/S0217979206034285",
    "journal_ref": "International Journal of Modern Physics B 20, 11/13 (2006) 1778 -\n  1791",
    "title": "Finite dimensional quantizations of the (q,p) plane : new space and   momentum inequalities",
    "url": "https://arxiv.org/abs/quant-ph/0411210"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6bc4d98e-f32b-4365-a6bc-3bf3694b1d4c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}