{
  "abstract": "We derive the late-time ramp of the finite-temperature spectral form factor in the double-scaled SYK model directly from cactus diagrams, which is introduced as a multi-trace generalization of chord diagram in Ref \\cite{Berkooz:2020fvm}. Although single-trace observables admit an exact chord-diagram description, multi-trace sums are obstructed by the chord-intersection weights $q_{IJ}$, which cannot be averaged independently to $q$. Our key idea is that the non-analytic contribution responsible for the ramp is controlled by the large-order tail of the Cactus-diagram expansion and is insensitive to finite changes in its low-order analytic terms. Decomposing the contribution with $n$-cross-trace-pairings Cactus diagram into two buds $B_n$ and a kernel $\\mathcal K_n$, we determine their large-$n$ asymptotics with fixed $0\\leq q<1$ and resum the resulting tail. For $β_L=β+it$ and $β_R=β-it$, we obtain \\begin{equation*} Z_s^{\\mathrm{sing}}(β+it,β-it) =s_p c_N \\frac{|t|}{2π} \\int_{E_{min}}^{E_{max}} e^{-2βE} dE+O(1), \\qquad s_p=\\begin{cases}2,&4\\mid p,\\\\1,&4\\nmid p.\\end{cases} \\end{equation*} This result reproduces the linear ramp predicted by random matrix theory, including its temperature dependence and symmetry factor, and agrees with the semiclassical predictions. It provides a direct microscopic origin of the ramp within the general $q$-deformed quantum algebra. While the plateau lies beyond the scope of the present analysis and calculation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27627",
  "author_total": 1,
  "authors": [
    {
      "name": "Yao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fgz6zmwnk8e9s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27627",
  "fulltext_url": null,
  "id": "fgz6zmwnk8e9s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27627",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7204805956",
  "pdf_url": "https://arxiv.org/pdf/2608.27627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fgz6zmwnk8e9s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "2608.27627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27627"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "The Late-time Ramp of the Double-Scaled SYK Model from the large-$n$ tail of Cactus Diagram",
  "title_text": "The Late-time Ramp of the Double-Scaled SYK Model from the large-n tail of Cactus Diagram",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/fgz6zmwnk8e9s",
  "venue": "arXiv",
  "versions": []
}