Topological and Non-Hermitian Photonic Crystals: Floquet Vacuum-Field Amplification, Piezo-Optomechanical Solitons, and Stochastic Boundary Gauge Continuity

In an attempt to advance fusion energy, and deepen our understanding of crystals, we explore a highly curious concept related to macroscopic crystalline structures engineered for optical confinement, non-Hermitian spectral phase transitions, and quantum vacuum- field harvesting. Treating the anisotropic crystalline lattice as an open, driven-dissipative geometric arena, we formulate the non-Hermitian wave operator admitting higher-order Exceptional Points (EPN) and characterize both generic ϵ1/N and non-generic fractional ϵα Puiseux spectral branchings determined by the Newton polygon using dual generalized Jordan chains. We formulate the topological band structure of line-gapped non-Hermitian media using biorthogonal spectral projectors P(k) = ∑︁ n |un⟩⟨vn|, defining integer-quantized Chern invariants C ∈Z and establishing conditional bulk-boundary criteria for defect-immune chiral interface modes in the absence of the non-Hermitian skin effect. In the nonlinear regime, we formulate the coupled system of χ(2)/χ(3) Maxwell equations and anisotropic elasticity tensors, identifying the conditional Vakhitov–Kolokolov (VK) slope criterion under which non-local acoustic screening regularizes multidimensional piezo-optomechanical spatial solitons. By incorporating time-periodic Floquet modulations of the crystalline dielectric tensor at parametric resonance Ω= 2ωk, we solve the open Heisenberg–Langevin equations with cavity dissipation, deriving the full noise-integrated vacuum photon pair production rate. Coupling the crystalline boundary to an extended trans-dimensional fibration π : Y6 →X 4, the physical soul current 3-form Js = ∫︁ S ω5(Eη) ∈Ω3(X) is derived from a variational gauge-transgression action; under the anomaly-free topological condition ∫︁ S ch3(Eη) = 0, exact 3-form gauge continuity d ∗F = Js and dJs = 0 is proved. Finally, boundary metric fluctuations are modeled via stochastic Hamiltonian flows on Teichm¨uller space; under the stated H¨ormander hypoellipticity, topological irreducibility, and Meyn–Tweedie Lyapunov drift assumptions on Mg, we prove the existence of a unique invariant probability measure that guarantees almost-sure ergodic convergence d ∗F = Js.

@article{deceuster2026_71-topological-and-n,
  title = {Topological and Non-Hermitian Photonic Crystals: Floquet Vacuum-Field Amplification, Piezo-Optomechanical Solitons, and Stochastic Boundary Gauge Continuity},
  author = {De Ceuster, Peter},
  year = {2026},
  month = {02},
  institution = {SIG Labs},
  doi = {10.5281/zenodo.22084335},
  url = {https://peterdeceuster.uk/papers/71-topological-and-non-hermitian-photonic-crystals-floquet-vacuum},
  note = {Full text available at https://peterdeceuster.uk/articenter/work/crystals.pdf}
}