{
  "annotation_id": "5863d018-d9cb-486c-afbf-fbfa62214118",
  "date_created": "2026-03-02T18:01:20.863000Z",
  "date_modified": "2026-03-02T18:01:20.863000Z",
  "file_hash": "fd6864c000aa5a6a3a928d1caa48c7b88511f13ff0536668a71b1bc199ee285a",
  "private": false,
  "record": {
    "abstract": "We show that the decay of a passive scalar $\\theta$ advected by a random\nincompressible flow with zero correlation time in Batchelor limit can be mapped\nexactly to a certain quantum-mechanical system with a finite number of degrees\nof freedom. The Schroedinger equation is derived and its solution is analyzed\nfor the case when at the beginning the scalar has Gaussian statistics with\ncorrelation function of the form $e^{-|x-y|^2}$. Any equal-time correlation\nfunction of the scalar can be expressed via the solution to the Schroedinger\nequation in a closed algebraic form. We find that the scalar is intermittent\nduring its decay and the average of $|\\theta|^\\alpha$ (assuming zero mean value\nof $\\theta$) falls as $e^{-\\gamma_\\alpha Dt}$ at large $t$, where $D$ is a\nparameter of the flow, $\\gamma_\\alpha=\\alpha(6-\\alpha)/4$ for $0\u003c\\alpha\u003c3$, and\n$\\gamma_\\alpha=9/4$ for $\\alpha \\geq 3$, independent of $\\alpha$.",
    "arxiv_id": "physics/9806047",
    "authors": [
      "D. T. Son"
    ],
    "categories": [
      "physics.flu-dyn",
      "chao-dyn",
      "cond-mat.stat-mech",
      "hep-ph",
      "nlin.CD"
    ],
    "doi": "10.1103/PhysRevE.59.R3811",
    "journal_ref": "Phys.Rev. E59 (1999) R3811",
    "title": "Turbulent Decay of a Passive Scalar in Batchelor Limit: Exact Results   from a Quantum-Mechanical Approach",
    "url": "https://arxiv.org/abs/physics/9806047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c431c814-a8d3-4d7f-bca2-72bb69350e87",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}