{
  "abstract": "The stationary scattering properties of transverse parity-time ($\\mathcal{PT}$) symmetric systems have been extensively studied, yet their dynamical stability, a prerequisite for any stationary description, remains largely unexplored. Here we uncover a thresholdless dynamical instability in such systems, driven by symmetry-protected bound states in the continuum (BICs). Without gain and loss, the up-down mirror symmetry of the transverse geometry generically protects a BIC, which manifests as the coalescence of an $S$-matrix pole and zero on the real axis of the complex wave-number plane. A Hermitian symmetry-breaking perturbation shifts the poles into the lower half-plane, converting the BIC into a resonance with a Fermi-golden-rule decay width. An anti-Hermitian $\\mathcal{PT}$-symmetric perturbation instead reverses the sign of the second-order energy shift, driving the poles into the upper half-plane and producing a time-growing bound state with $\\operatorname{Im}E=γ^{2}Γ_{V}/2+O(γ^{3})$, where $γ$ is the gain-loss strength and $Γ_{V}$ is the golden-rule coupling of the BIC to the continuum. The instability therefore sets in at arbitrarily small $γ$ whenever $Γ_{V}>0$. We confirm this mechanism in a three-site side-coupled model that is unstable despite possessing a unitary scattering matrix, and in a four-site rhombic model where transverse and longitudinal gain-loss placements yield vanishing and finite thresholds, respectively. These results establish a microscopic stability criterion and a design principle for stable $\\mathcal{PT}$-symmetric scattering devices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29557",
  "author_total": 1,
  "authors": [
    {
      "name": "Chao Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1e98pkrsf44tq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29557",
  "fulltext_url": null,
  "id": "1e98pkrsf44tq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29557",
  "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",
      "physics.optics"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7204928575",
  "pdf_url": "https://arxiv.org/pdf/2608.29557",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1e98pkrsf44tq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29557",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29557"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Thresholdless dynamical instability in transverse $\\mathcal{PT}$-symmetric scattering systems: The hidden role of bound states in the continuum",
  "title_text": "Thresholdless dynamical instability in transverse 𝒫𝒯-symmetric scattering systems: The hidden role of bound states in the continuum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/1e98pkrsf44tq",
  "venue": "arXiv",
  "versions": []
}