{
  "abstract": "The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. In this work, we extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet-Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet-Magnus expansion, a condition that is already highly restrictive even in the bounded setting. We illustrate the scope of the method on representative models: the quantum Rabi Hamiltonian in the interaction picture, and the periodically driven quantum harmonic oscillator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.23734",
  "author_total": 4,
  "authors": [
    {
      "name": "Daniel Burgarth"
    },
    {
      "name": "Robin Hillier"
    },
    {
      "name": "Davide Lonigro"
    },
    {
      "name": "Leonhard Richter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/87nd0j2exqssm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.23734",
  "fulltext_url": null,
  "id": "87nd0j2exqssm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.23734",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7162339881",
  "pdf_url": "https://arxiv.org/pdf/2605.23734",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/87nd0j2exqssm.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:14Z",
      "native_id": "2605.23734",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.23734"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Floquet-Magnus expansion of unbounded operators",
  "title_text": "The Floquet-Magnus expansion of unbounded operators",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/87nd0j2exqssm",
  "venue": "arXiv",
  "versions": []
}