{
  "abstract": "We prove lower bounds on the relaxation time $1/γ_{N,β}$ of Langevin dynamics for mixed spherical spin glasses with even mixture $ξ(x)=\\sum_{p\\ge4}γ_p^2x^p$, under a one-step-replica-symmetry-breaking-type standing assumption of strict threshold separation $E_0(ξ)>E_1(ξ)>E_2(ξ)$; the pure spherical $p$-spin glass with even $p\\ge4$, for which the assumption is a theorem, is recovered as a corollary. The main result is an aggregate Eyring-Kramers bound whose exponent sums conductances over the exponentially many index-one saddles above the lowest saddle level $-NE_1(ξ)$, combining the saddle complexity $Θ_{1,ξ}$ with a half-determinant Hessian statistic -- an entropic contribution that the classical single-saddle picture misses. The single new random-matrix ingredient of the mixed model is that the conditional Hessian at a critical point is a randomly shifted GOE matrix: the radial derivative is no longer determined by the energy (Euler's identity degenerates exactly in the pure case), and every landscape rate becomes a one-dimensional supremum over the scalar shift with a Gaussian penalty. At low temperature the aggregate exponent exceeds the unconditional free-energy bound by $\\frac12\\log(βe)-Ξ^{\\mathrm{EK}}_{1,ξ}(-E_1(ξ))-C_{ξ,b}β^{-1/2}$ with $-Ξ^{\\mathrm{EK}}_{1,ξ}(-E_1(ξ))\\ge\\frac14\\logξ''(1)+\\frac14>0$, so the refinement is a strict improvement for all sufficiently large fixed $β$; the onset temperature and constants $b_*(ξ)$ and $C_{ξ,b}$ produced by the proof are not numerically explicit. Two companion results -- a sequential Arrhenius bound with the explicit constant $E_0(ξ)-E_1(ξ)$ and a fixed-temperature free-energy bound -- come with complete, self-contained proofs. All bounds are one-sided; identifying the mechanism the dynamics actually realizes would require a matching upper bound, which remains open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15157",
  "author_total": 1,
  "authors": [
    {
      "name": "Masoud Badiei Khuzani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8cavf8pg3jgm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15157",
  "fulltext_url": null,
  "id": "a8cavf8pg3jgm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15157",
  "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.PR"
    ],
    [
      "openalex",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7213368405",
  "pdf_url": "https://arxiv.org/pdf/2609.15157",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8cavf8pg3jgm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2609.15157",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15157"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Spectral Gap Bounds for Langevin Dynamics in Mixed Spherical Spin Glasses",
  "title_text": "Spectral Gap Bounds for Langevin Dynamics in Mixed Spherical Spin Glasses",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/a8cavf8pg3jgm",
  "venue": "arXiv",
  "versions": []
}