{
  "annotation_id": "0f22071c-b7ea-4400-bfac-e86dcf18b2aa",
  "date_created": "2026-03-02T18:01:03.610000Z",
  "date_modified": "2026-03-02T18:01:03.610000Z",
  "file_hash": "75934a3f0e316b9eff67b6dc445360d3dcb2cd8e981c40d121a73e86474a89ee",
  "private": false,
  "record": {
    "abstract": "We investigate the classical evolution of a $\\phi^4$ scalar field theory,\nusing in the initial state random field configurations possessing a fractal\nmeasure expressed by a non-integer mass dimension. These configurations\nresemble the equilibrium state of a critical scalar condensate. The measures of\nthe initial fractal behavior vary in time following the mean field motion. We\nshow that the remnants of the original fractal geometry survive and leave an\nimprint in the system time averaged observables, even for large times compared\nto the approximate oscillation period of the mean field, determined by the\nmodel parameters. This behavior becomes more transparent in the evolution of a\ndeterministic Cantor-like scalar field configuration. We extend our study to\nthe case of two interacting scalar fields, and we find qualitatively similar\nresults. Therefore, our analysis indicates that the geometrical properties of a\ncritical system initially at equilibrium could sustain for several periods of\nthe field oscillations in the phase of non-equilibrium evolution.",
    "arxiv_id": "physics/0512053",
    "authors": [
      "N. G. Antoniou",
      "F. K. Diakonos",
      "E. N. Saridakis",
      "G. A. Tsolias"
    ],
    "categories": [
      "physics.comp-ph",
      "hep-ph"
    ],
    "doi": "10.1142/S0217751X0904292X",
    "journal_ref": "Int.J.Mod.Phys.A24:2317-2334,2009",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Classical evolution of fractal measures generated by a scalar field on   the lattice",
    "url": "https://arxiv.org/abs/physics/0512053"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "20887e0b-f70f-4170-b633-821f598535ef",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}