{
  "abstract": "We develop a general framework for the scattering of a plane wave by a class of Gaudin kaleidoscope models: straight $δ$-potential barriers intersecting at a common point. The projected Lippmann-Schwinger equations split into a singular part, a finite pole closure generated by a geometric moving rule, and a regular remainder, the outgoing state being an atomic measure on the circle. At the special angles $π/N$, where the intersecting barriers generate the dihedral group $D_N$, the number of channels stays fixed, whereas at generic angles channels are created and destroyed, opening smoothly from zero weight as a critical direction is crossed. This leaves no singular trace in the probabilities, being carried instead by the phase shifts, a quantum-classical correspondence beyond the reach of the coordinate Bethe ansatz. The same equations solve the quantum Galperin billiards exactly, the method of images reducing them to a single linear system whose phase shifts follow in closed form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23406",
  "author_total": 3,
  "authors": [
    {
      "name": "Yi-Cong Yu"
    },
    {
      "name": "Wen-Jie Qiu"
    },
    {
      "name": "Xiaoming Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/em3myw51gj1rn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23406",
  "fulltext_url": null,
  "id": "em3myw51gj1rn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23406",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214001485",
  "pdf_url": "https://arxiv.org/pdf/2609.23406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/em3myw51gj1rn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.23406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23406"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum scattering by intersecting δ-potential barriers: from Gaudin's kaleidoscope to quantum Galperin billiards",
  "title_text": "Quantum scattering by intersecting δ-potential barriers: from Gaudin's kaleidoscope to quantum Galperin billiards",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/em3myw51gj1rn",
  "venue": "arXiv",
  "versions": []
}