{
  "abstract": "We derive maximal mean-square adiabatic estimates for finite-dimensional stochastic Schrödinger equations with Hamiltonian-proportional Wiener noise. For deterministic $C^2$ Hamiltonians whose eigenvalues have constant multiplicities and do not cross on $[0,1]$, we construct a unitary stochastic adiabatic intertwiner driven by the same Wiener process as the exact propagator. A commutator argument, Itô calculus, and Doob's maximal inequality yield an explicit bound for the expected supremum of their squared operator-norm difference on a selected initial eigenspace. Under uniform coefficient bounds, the physical noise scaling $α=σT^{-γ}$, where $T$ is the total evolution time and $σ\\geq0$ and $γ\\geq0$ are fixed, gives maximal mean-square error $O(T^{-2}+σ^4T^{-4γ}+σ^2T^{-(2γ+1)})$. Consequently, adiabatic convergence holds for every $γ>0$ as $T\\to\\infty$, while $γ\\geq1/2$ recovers the deterministic $O(T^{-1})$ bound for the root-mean-square maximal error. For fixed nonzero physical noise amplitude, the estimate leaves convergence unresolved.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06029",
  "author_total": 4,
  "authors": [
    {
      "name": "A. M. H. H. Caldera"
    },
    {
      "name": "R. P. K. DeSilva"
    },
    {
      "name": "K. K. W. A. S. Kumara"
    },
    {
      "name": "B. P. W. Fernando"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ftqt04cxnndf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06029",
  "fulltext_url": null,
  "id": "5ftqt04cxnndf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06029",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ftqt04cxnndf.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quantum Adiabatic Theorem under Wiener Noise:Maximal Mean-SquareEstimates",
  "title_text": "Quantum Adiabatic Theorem under Wiener Noise:Maximal Mean-SquareEstimates",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:46Z",
  "url": "https://research.draconitic.com/paper/5ftqt04cxnndf",
  "venue": "arXiv",
  "versions": []
}