{
  "abstract": "We discuss the application of $L^2$-based velocity averaging to the Wigner kinetic equation governing the quantum evolution of the Wigner transform of a density operator of a particle subjected to an external electromagnetic field. This extends the $L^2$-based averaging lemma from [F. Golse, J. Möller: Commun. Math. Sci. (2026)] to electromagnetic fields. We make use of the magnetic or gauge-invariant Wigner transform due to Stratonovich [Sov. Phys. D., (1)414-418, 1956] which differs from the usual definition by a phase factor involving the circulation of the magnetic vector potential along a line segment. The magnetic Wigner transform obeys the Wigner equation in the generalized phase space variables $(x,v=ξ-A(t,x))$, which is a more natural setting for the application of velocity averaging. Since the magnetic Wigner equation contains a first order derivative in the spatial variable, we obtain compactness in $L^2$ but no gain in regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21885",
  "author_total": 2,
  "authors": [
    {
      "name": "François Golse"
    },
    {
      "name": "Jakob Möller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8g9ma8c87jg99.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21885",
  "fulltext_url": null,
  "id": "8g9ma8c87jg99",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21885",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7213871500",
  "pdf_url": "https://arxiv.org/pdf/2609.21885",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8g9ma8c87jg99.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.21885",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21885"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Velocity Averaging for the Wigner Equation with Electromagnetic Fields",
  "title_text": "Velocity Averaging for the Wigner Equation with Electromagnetic Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/8g9ma8c87jg99",
  "venue": "arXiv",
  "versions": []
}