{
  "abstract": "We study the symmetric Dyson exclusion process (SDEP)--a lattice gas with exclusion and long-range, Coulomb–type interactions that emerge both as the maximal-activity limit of the symmetric exclusion process and as a discrete version of Dyson's Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling with a conservation law featuring a current that is a genuinely non-local functional of the density. This non-local one-component description is equivalent to a local two-components “complex Hopf’’ system for finite particle density. Closed evolution formulas allow us to solve the melting of single- and double-block initial states, producing limit shapes and arctic curves that agree with large-scale Monte-Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Ali Zahra"
    },
    {
      "name": "J. Dubail"
    },
    {
      "name": "Gunther M. Schütz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2106az3recdwf.bib",
  "cited_by": 1,
  "doi": "10.21468/scipostphys.20.5.141",
  "fulltext_url": null,
  "id": "2106az3recdwf",
  "issns": [
    "2542-4653"
  ],
  "landing_url": "https://hal.science/hal-05267122v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W4415240073",
  "pdf_url": "https://hal.science/hal-05267122/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": "SciPost Foundation",
  "ris": "https://research.draconitic.com/paper/2106az3recdwf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:42Z",
      "native_id": "hal-05267122",
      "source": "hal",
      "url": "https://hal.science/hal-05267122v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions",
  "title_text": "Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:42Z",
  "url": "https://research.draconitic.com/paper/2106az3recdwf",
  "venue": "SciPost Physics",
  "versions": []
}