{
  "abstract": "We introduce a magnetic coherent--state frame over the Landau levels of the two--dimensional Landau Hamiltonian, indexed by a discrete metric space combining spatial and energy degrees of freedom. Although overcomplete, the frame is almost--orthogonal, and we use it to endow the CAR $C^*$--algebra over the one--particle Hilbert space with an \\emph{asymptotic quasi--local} (AQL) structure, in which graded commutators of observables localized on disjoint index sets decay exponentially rather than vanish exactly. By means of a family of conditional expectations onto the resulting local subalgebras, we construct a Fréchet $*$--subalgebra of almost--local observables, invariant under the discrete group of lattice translations, which act on it by continuous automorphisms. For the full continuous group of magnetic translations we establish a quantitative control on how local observables spread through this almost--local algebra, and we show that this control suffices to extend graded asymptotic abelianness from the lattice to the entire continuous translation group. The results provide a discrete--continuum dictionary intended as the starting point for extending Lieb--Robinson--type techniques from lattice systems to interacting continuum electrons in a magnetic field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26987",
  "author_total": 1,
  "authors": [
    {
      "name": "Giuseppe De Nittis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/am3sz0rbqk88q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26987",
  "fulltext_url": null,
  "id": "am3sz0rbqk88q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26987",
  "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.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.26987",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/am3sz0rbqk88q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.26987",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26987"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Asymptotic quasi--local structure induced by Magnetic field",
  "title_text": "Asymptotic quasi--local structure induced by Magnetic field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/am3sz0rbqk88q",
  "venue": "arXiv",
  "versions": []
}