{
  "abstract": "I show that finite-difference time-domain (FDTD) dynamics can be reproduced using field variables restricted to the ternary alphabet ${-1,0,+1}$. The integration is carried out by a state accumulator, while quantisation is done by a second-order noise-shaped encoder with a separate error register. The Courant number $S$ plays two roles: it is the exact fixed-point ratio and also sets the encoder's oversampling ratio. When $S$ is chosen as a power of two, each cell update requires neither run-time multiplication nor floating-point arithmetic, and each emitted field symbol is represented by just two bits. The ternary scheme converges asymptotically to the standard Yee scheme as $S$ decreases towards zero. I report wall-clock and instruction counts relative to a floating-point reference, long-time energy integrations over $2\\times10^{5}$ steps and the $S$ required to achieve a prescribed accuracy for the driven mode. Extending the approach to acoustics, Virieux-type elastodynamics and Schrodinger-equation solvers is a prospective direction towards a broader class of quantised physics solvers for resource-constrained and specialised hardware.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27069",
  "author_total": 1,
  "authors": [
    {
      "name": "Ivan S. Maksymov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4t3312nfenxvb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27069",
  "fulltext_url": null,
  "id": "4t3312nfenxvb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27069",
  "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",
      "physics.app-ph"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2208|Electromagnetic Simulation and Numerical Methods"
    ]
  ],
  "openalex": "W7204549991",
  "pdf_url": "https://arxiv.org/pdf/2608.27069",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4t3312nfenxvb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2608.27069",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27069"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.app-ph",
      "subfield": "applied-instrumentation"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Ternary-Valued Finite-Difference Time-Domain Method: Asymptotic Agreement with the Yee Scheme Through Noise-Shaped Quantisation",
  "title_text": "Ternary-Valued Finite-Difference Time-Domain Method: Asymptotic Agreement with the Yee Scheme Through Noise-Shaped Quantisation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/4t3312nfenxvb",
  "venue": "arXiv",
  "versions": []
}