{
  "annotation_id": "9b8e8be1-7f73-4c0b-9e1c-a0096a219c6d",
  "date_created": "2026-03-02T18:00:46.849000Z",
  "date_modified": "2026-03-02T18:00:46.849000Z",
  "file_hash": "cd6b95b91a210b51197ccb330e58b1671396facedbc846609f2a4ee884a39479",
  "private": false,
  "record": {
    "abstract": "We study the continuous limit of a multibox Erhenfest urn model proposed\nbefore by the authors. The evolution of the resulting continuous system is\ngoverned by a differential equation, which describes a diffusion process on a\ncircle with a nonzero drifting velocity. The short time behavior of this\ndiffusion process is obtained directly by solving the equation, while the long\ntime behavior is derived using the Poisson summation formula. They reproduce\nthe previous results in the large $M$ (number of boxes) limit. We also discuss\nthe connection between this diffusion equation and the Schr$\\ddot{\\rm o}$dinger\nequation of some quantum mechanical problems.",
    "arxiv_id": "physics/0308023",
    "authors": [
      "Pi-Gang Luan",
      "Yee-Mou Kao"
    ],
    "categories": [
      "physics.atom-ph",
      "physics.gen-ph"
    ],
    "doi": "10.1103/PhysRevE.69.022102",
    "title": "Drifting diffusion on a circle as continuous limit of a multiurn   Ehrenfest model",
    "url": "https://arxiv.org/abs/physics/0308023"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f6f5182f-d167-4382-91b4-b48497405c29",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}