{
  "abstract": "Two physical consequences of the recent topological classification of 2d Fermi seas for free particles based on flat orbifolds $\\mathbb{R}^2/Γ$ of discrete symmetry $Γ$, are explored. The first is a study of the spatial density behavior inside the mesoscopic window enclosed by the Fermi and (infinite) thermal lengths. It is shown that the single-particle density matrix exhibits a sharp directional anisotropy, encoding a real space diffraction pattern, {\\it i.e.}, a Fraunhofer-like diagram of the Fermi sea, that reveals the point-group symmetries of the background lattice $Γ$ in the form of anisotropic Friedel oscillations. As examples, the special cases of the $p4m$ and $p6m$ crystallographic flat orbifolds are treated in some detail. The second physical consequence is the establishment of an explicit geometric correspondence between momentum-space packing and electrical transport. A mean-field expression for the longitudinal electrical conductivity $σ_{xx}$ as a function of the {\\it isoperimetric parameter} $\\cal{I}$ of the occupied orbifold domain by utilizing geometric measure theory is presented, satisfiying the scaling law $ σ_{xx} \\propto 1/\\sqrt{\\cal{I}}$. The topological transport formula naturally incorporates the vanishing conductivity ($σ_{xx} \\to 0$) of the previously described ``geometric insulators,'' promoting the isoperimetric parameter as an efficient descriptor for topological and geometric phases in conductors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04724",
  "author_total": 1,
  "authors": [
    {
      "name": "Guillermo R. Zemba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rq5gakar1h05.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04724",
  "fulltext_url": null,
  "id": "1rq5gakar1h05",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04724",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
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      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
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      "arxiv",
      "math.MP"
    ],
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      "openalex",
      "3107|Topological Materials and Phenomena"
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  ],
  "openalex": "W7220744957",
  "pdf_url": "https://arxiv.org/pdf/2610.04724",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rq5gakar1h05.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.04724",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04724"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Anisotropic Friedel oscillations and isoperimetric transport in two-dimensional free lattice Fermi seas",
  "title_text": "Anisotropic Friedel oscillations and isoperimetric transport in two-dimensional free lattice Fermi seas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/1rq5gakar1h05",
  "venue": "arXiv",
  "versions": []
}