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The memory equation of a characteristic function in surface diffusion: a sum rule — arXiv:2609.31344

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.31344
License (as archived): CC0-1.0
Archived: 2026-10-08T03:47:27.855Z
SHA-256 of the archived text: 471e7f371fefa2b2170c08a6bc01e51d096a2ddd520f1c8ee83ea2621bccf152
Stable URL of this page: https://metraipolis.com/documento/dc_358ea8abedef

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The memory equation of a characteristic function in surface diffusion: a sum rule — arXiv:2609.31344 — arXiv (en), https://arxiv.org/abs/2609.31344 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_358ea8abedef (Metraipolis archive dc_358ea8abedef, sha256 471e7f371fefa2b2170c08a6bc01e51d096a2ddd520f1c8ee83ea2621bccf152)

BibTeX

@misc{dc358ea8abedef,
  title = {The memory equation of a characteristic function in surface diffusion: a sum rule — arXiv:2609.31344},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.31344},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_358ea8abedef; sha256 471e7f371fefa2b2170c08a6bc01e51d096a2ddd520f1c8ee83ea2621bccf152},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.31344. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The decay of a density wave in an interacting adlayer obeys an exact memory equation of Mori's form. Being a Fourier component of a conserved density, its correlation function is a characteristic function, and the kernel is built from a second one, that of a single jump. The local rate obeys a sum rule whose momentum dependence is one minus the characteristic function of a single jump, divided by the static structure factor. Detailed balance makes the decay a superposition of relaxation modes of non-negative weight whose moments are static equilibrium averages, so that the truncations of the associated continued fraction form a convergent hierarchy of closed forms, each of them a bound on the decay itself. The single rate a fit returns is shown to be the mean of the instantaneous rate over a time window, hence never above the local rate. At long wavelength, the two coincide, the relaxation spectrum separating there, one collective mode taking almost the whole weight of the density wave and the single exponential usually fitted to spin-echo data being the decay itself. What an experiment reaches at every wavevector is also the area under the decay, a correlation time. Together with the static structure factor and the single-jump geometry, it forms one combination which the theory identifies with the effective hop rate divided by the product of the local rate and the correlation time. That product never falls below unity and tends to unity at long wavelength whenever the rate at which an adparticle leaves a site is independent of the site it leaves for. In the hydrodynamic limit, the sum rule becomes a relation of Darken type in which the rate multiplied by the thermodynamic factor is the effective hop rate and not the mobility of a labelled adparticle.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-28 in cond-mat.stat-mech).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech).
Pagina del lavoro: https://arxiv.org/abs/2609.31344 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T03:15:08.804Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-09-28?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).