{
  "abstract": "We study the long-time behavior of the Hartree--Fock equation with Coulomb interaction in dimensions $d\\geq2$ for small initial density matrices of possibly infinite rank. We prove global well-posedness and modified scattering governed by a resonant Hartree-Fock equation. Our approach is based on the half-density formulation and a final-state construction for the resonant dynamics. We also characterize the stationary states of the resonant Hartree--Fock equation and prove that ordinary linear scattering fails when the initial density matrix has rank at least two. These results extend long-range modified scattering to genuinely operator-valued infinite-rank Hartree-Fock evolution. Despite cancellation between the direct and exchange terms, the long-range effect persists, with resonant dynamics evolving on the same logarithmic time scale as in the Hartree equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38676",
  "author_total": 4,
  "authors": [
    {
      "name": "Masaki Kawamoto"
    },
    {
      "name": "Jinyeop Lee"
    },
    {
      "name": "Changhun Yang"
    },
    {
      "name": "Chanjin You"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29g5amwmqs18a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38676",
  "fulltext_url": null,
  "id": "29g5amwmqs18a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38676",
  "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",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29g5amwmqs18a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Modified Scattering for Infinite-Rank Hartree--Fock Equations",
  "title_text": "Modified Scattering for Infinite-Rank Hartree--Fock Equations",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/29g5amwmqs18a",
  "venue": "arXiv",
  "versions": []
}