{
  "abstract": "We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|Ψ|^2$. Relaxation to the Born rule (\"quantum equilibrium\") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03501",
  "author_total": 3,
  "authors": [
    {
      "name": "Tanguy Fontana"
    },
    {
      "name": "Axelle Coulon"
    },
    {
      "name": "Giovanni Manfredi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2q81fe2hd18pn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03501",
  "fulltext_url": null,
  "id": "2q81fe2hd18pn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03501",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "gr-qc"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7220442472",
  "pdf_url": "https://arxiv.org/pdf/2610.03501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2q81fe2hd18pn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03501"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Born rule in Schroedinger-Newton scenarios of semiclassical gravity",
  "title_text": "Born rule in Schroedinger-Newton scenarios of semiclassical gravity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:45Z",
  "url": "https://research.draconitic.com/paper/2q81fe2hd18pn",
  "venue": "arXiv",
  "versions": []
}