{
  "abstract": "The intermediate scattering function and its value at zero time, which is the static structure factor, are both characteristic functions. An exact equation of motion for the ISF carrying a local rate and a memory function is then obtained. To interpret this equation, the ISF is expressed in terms of relaxation modes. The local rate is fixed by a sum rule which reversibility turns into an equilibrium average. The de Gennes narrowing is establshed as a theorem. The memory function being non-negative, the closed form that results is a rigorous lower bound on the ISF at every momentum transfer and every time, and its accuracy is itself predicted. In the diffusive regime, the closed form keeps the single-exponential shape to which spin-echo data are routinely fitted, with both coefficients renormalized by the interaction: the amplitude becomes the SSF of the layer and the dephasing rate the dressed one-adsorbate rate divided by it, explicit in momentum transfer, time, coverage and temperature. When introducing the lateral interaction, a single correlation parameter fixes the equilibrium structure and the renormalized hop rate: exactly along a one-dimensional channel, and on the surface as the nearest-neighbour correlation of a pair approximation completed by a collective (random-phase) structure factor. The result contains no adjustable parameter and is exact at vanishing interaction for every coverage and momentum; the Darken relation comes with it, the correlation between successive moves separated off as a computable factor. Applications to Na/Cu(111) and H/Pt(111) are analysed and discussed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.03398",
  "author_total": 1,
  "authors": [
    {
      "name": "S. Miret-Artés"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gd9mwzx555z2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.03398",
  "fulltext_url": null,
  "id": "0gd9mwzx555z2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.03398",
  "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",
      "3104|Theoretical and Computational Physics"
    ]
  ],
  "openalex": "W7172534121",
  "pdf_url": "https://arxiv.org/pdf/2608.03398",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gd9mwzx555z2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2608.03398",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.03398"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Surface diffusion with lateral interactions: a closed-form intermediate scattering function of an Ising adlayer from the memory-equation formalism",
  "title_text": "Surface diffusion with lateral interactions: a closed-form intermediate scattering function of an Ising adlayer from the memory-equation formalism",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/0gd9mwzx555z2",
  "venue": "arXiv",
  "versions": []
}