{
  "abstract": "The relaxation of the discrete nonlinear Schrödinger equation is known to slow down dramatically when the energy density $\\varepsilon$ exceeds a critical value $\\varepsilon_c$, where the system enters a condensed phase. Replacing the Hamiltonian dynamics by Brownian motion on the microcanonical surface of $N$ sites at fixed mass and energy, we prove rigorous upper and lower bounds on the equilibration time $τ_{\\mathrm{eq}}$, which is governed by the first non-zero eigenvalue $λ_1$ of the Laplacian on this surface. In the condensed phase the equilibration time is stretched exponential, not exponential, in the system size. The upper bounds on $λ_1$ come from trial functions: of one occupation for $\\varepsilon<\\varepsilon_c$, where the problem reduces to a Sturm-Liouville equation, and of two occupations for $\\varepsilon>\\varepsilon_c$, where they cross the bottleneck through which the condensate moves between sites. The lower bounds on $λ_1$ come from a Bochner-Reilly argument, with a vector field that compensates the concavity of the boundary. As a result, $τ_{\\mathrm{eq}}=O(1)$ for $\\varepsilon<\\varepsilon_c$, while for $\\varepsilon>\\varepsilon_c$, asymptotically in $N$, $(\\sqrt{2}-1)\\sqrt{\\varepsilon-\\varepsilon_c}\\leq\\lnτ_{\\mathrm{eq}}/\\sqrt{N}\\leq\\sqrt{\\varepsilon-\\varepsilon_c}$. We conjecture that the left-hand bound is sharp and the right-hand one is not.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02025",
  "author_total": 2,
  "authors": [
    {
      "name": "Claudio Arezzo"
    },
    {
      "name": "Antonello Scardicchio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49m65fyhk6wxr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02025",
  "fulltext_url": null,
  "id": "49m65fyhk6wxr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02025",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02025",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49m65fyhk6wxr.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.02025",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02025"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "An entropic barrier to equilibration in the discrete nonlinear Schrödinger equation: Rigorous bounds for the microcanonical Brownian motion",
  "title_text": "An entropic barrier to equilibration in the discrete nonlinear Schrödinger equation: Rigorous bounds for the microcanonical Brownian motion",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/49m65fyhk6wxr",
  "venue": "arXiv",
  "versions": []
}