{
  "abstract": "We prove a nonlinear adiabatic theorem for the repulsive Gross-Pitaevskii (GP) equation with a time-dependent trapping potential $V(x,t)$. If either (i) $V(\\cdot,t)$ is smooth, subquadratic in space and with uniformly bounded spatial derivatives of order $\\geq 2$, or (ii) $V(\\cdot,t)$ is a uniformly bounded perturbation of a fixed non-negative potential which is asymptotically $|x|^m, m\\geq 2$, then the GP equation has a global solution, which remains uniformly close to the instantaneous minimizer of the time-independent GP functional, provided the initial condition is a ground state. In fact, we show that the existence of a solution of the GP equation is the real bottleneck: If existence is assumed, then adiabaticity holds under very minimal assumptions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02231",
  "author_total": 2,
  "authors": [
    {
      "name": "Sven Bachmann"
    },
    {
      "name": "Severin Schraven"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqayvgprhrx4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02231",
  "fulltext_url": null,
  "id": "fqayvgprhrx4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02231",
  "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"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqayvgprhrx4k.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02231"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Nonlinear adiabatic theorem for the Gross-Pitaevskii equation",
  "title_text": "Nonlinear adiabatic theorem for the Gross-Pitaevskii equation",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fqayvgprhrx4k",
  "venue": "arXiv",
  "versions": []
}