{
  "abstract": "We propose a $q$-deformation in the single-particle kinetic energy and investigate how it modifies the localization in the one-dimensional Aubry-André (AA) model. We construct a Hermitian $q$-deformed kinetic operator as a nonlinear function of the lattice translation operator, preserving the uniform lattice and recovering the conventional AA Hamiltonian continuously in the undeformed limit $q\\to1$. The deformation generates an infinite set of correlated odd-range kinetic processes, controlled by a single parameter q, rather than phenomenologically involving long-range hopping. Under the dual transformation, this long-range hopping appears as higher harmonics of the dual quasiperiodic potential, providing a controlled route for breaking the exact self-duality of the AA model, with $q$ as the control parameter, consequently modifying the localization structure for $q\\neq1$. In contrast to the conventional AA model, where all eigenstates localize simultaneously at $λ_c=2$, the deformed model exhibits a fraction of delocalized states even beyond $λ_c =2$. An intermediate regime also emerges in the $q-λ$ plane where localized and extended eigenstates coexist across the spectrum. We also propose a possible experimental realization of the hierarchy produced in the $q$-deformed kinetic setting in a periodically driven AA model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36446",
  "author_total": 1,
  "authors": [
    {
      "name": "Arpita Goswami"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwtyn9fet3dwq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36446",
  "fulltext_url": null,
  "id": "cwtyn9fet3dwq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36446",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214911071",
  "pdf_url": "https://arxiv.org/pdf/2609.36446",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwtyn9fet3dwq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36446",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36446"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Localization Transition in Kinetically Deformed one-dimensional Aubry-André Model",
  "title_text": "Localization Transition in Kinetically Deformed one-dimensional Aubry-André Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/cwtyn9fet3dwq",
  "venue": "arXiv",
  "versions": []
}