{
  "annotation_id": "9df54668-5064-4536-9895-a0f1a845fb5f",
  "date_created": "2026-03-02T18:01:14.458000Z",
  "date_modified": "2026-03-02T18:01:14.458000Z",
  "file_hash": "be1462b7827879152cd6188e6b1aa1996aab277839f4951019fe7c08c2995d30",
  "private": false,
  "record": {
    "abstract": "Two-frequency Wigner distribution is introduced to capture the asymptotic\nbehavior of the space-frequency correlation of paraxial waves in the radiative\ntransfer limits. The scaling limits give rises to deterministic transport-like\nequations. Depending on the ratio of the wavelength to the correlation length\nthe limiting equation is either a Boltzmann-like integral equation or a\nFokker-Planck-like differential equation in the phase space. The solutions to\nthese equations have a probabilistic representation which can be simulated by\nMonte Carlo method. When the medium fluctuates more rapidly in the longitudinal\ndirection, the corresponding Fokker-Planck-like equation can be solved exactly.",
    "arxiv_id": "physics/0609200",
    "authors": [
      "Albert C. Fannjiang"
    ],
    "categories": [
      "physics.optics",
      "physics.gen-ph"
    ],
    "doi": "10.1088/1751-8113/40/19/007",
    "journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 5025-5044",
    "title": "Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for   Random Paraxial Waves",
    "url": "https://arxiv.org/abs/physics/0609200"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b42cf605-9026-4648-9a1c-10ef25f81786",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}