Thresholdless dynamical instability in transverse 𝒫𝒯-symmetric scattering systems: The hidden role of bound states in the continuum

@misc{zheng2026thresholdless,
  title = {{Thresholdless dynamical instability in transverse $\mathcalPT$-symmetric scattering systems: The hidden role of bound states in the continuum}},
  author = {Chao Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29557},
  eprint = {2608.29557},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29557},
}

TY  - UNPB
TI  - Thresholdless dynamical instability in transverse 𝒫𝒯-symmetric scattering systems: The hidden role of bound states in the continuum
AU  - Chao Zheng
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29557
UR  - https://arxiv.org/abs/2608.29557
AB  - The stationary scattering properties of transverse parity-time (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 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 ImE=γ^2Γ_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 𝒫𝒯-symmetric scattering devices.
ER  -