{
  "annotation_id": "a4fb076e-f08f-42d4-8efe-49e49b6006c9",
  "date_created": "2026-03-02T18:02:41.235000Z",
  "date_modified": "2026-03-02T18:02:41.235000Z",
  "file_hash": "e9b4ec745289a84ac1d8a9b8f6bd652fab27291c38182e8d9ec7a6a94b2c8aa8",
  "private": false,
  "record": {
    "abstract": "We examine the reduced density matrix of the centre of mass on position basis\nconsidering a one-dimensional system of $N$ non-interacting distinguishable\nparticles in a infinitely deep square potential well. We find a class of pure\nstates of the system for which the off-diagonal elements of the matrix above go\nto zero as $N$ increases. This property holds too for the state vectors which\nare factorized in the single particle wave functions. In this last case, if the\naverage energy of each particle is less than a common bound, the diagonal\nelements are distributed according to the normal law with a mean square\ndeviation which becomes smaller and smaller as $N$ increases towards infinity.\nTherefore when the state vectors are of the type considered we cannot\nexperience spatial superpositions of the centre of mass and we may conclude\nthat position is a preferred basis for the collective variable.",
    "arxiv_id": "quant-ph/9711005",
    "authors": [
      "B. Carazza"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1023/A:1022449319701",
    "journal_ref": "Found.Phys.Lett.10:581-590,1997",
    "title": "On the Spatial Density Matrix for the Centre of Mass of a one   dimensional Perfect Gas",
    "url": "https://arxiv.org/abs/quant-ph/9711005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a7d1f808-b343-4af9-bc81-7846538dbfd3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}