{
  "abstract": "We proof the existence of the Integrated Density of States (IDS) for fractional random Schrödinger operators with Gaussian potential based on the theory of isotropic $α$-stable Lévy processes. Further we show that the IDS exhibits Lifshitz tails and determine its asymptotics at the right end of the spectrum. Isotropic$α$-stable Lévy processes are self-similar but not continuous. Thus self-similarity is a fundamental concept for these quantum operators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17075",
  "author_total": 2,
  "authors": [
    {
      "name": "Peter Kern"
    },
    {
      "name": "Leonard Pleschberger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/af6gxpxcsshfr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17075",
  "fulltext_url": null,
  "id": "af6gxpxcsshfr",
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  "landing_url": "https://arxiv.org/abs/2609.17075",
  "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",
      "math-ph"
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      "arxiv",
      "math.MP"
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    [
      "arxiv",
      "math.PR"
    ],
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      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W7213438908",
  "pdf_url": "https://arxiv.org/pdf/2609.17075",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/af6gxpxcsshfr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.17075",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17075"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the Integrated Density of States of Fractional Random Schrödinger Operators",
  "title_text": "On the Integrated Density of States of Fractional Random Schrödinger Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/af6gxpxcsshfr",
  "venue": "arXiv",
  "versions": []
}