"Dark poles" in the scattering amplitude of non-Hermitian lattices

In this work, we reveal that in non-Hermitian systems, the eigenstates of the system do not exhaust the dynamical content of scattering. We identify and characterize a new class of contributions—dark-pole states (DPS)—that are not eigenvectors nor branch points of the Hamiltonian, yet govern measurable time-domain responses. They appear as poles of an analytically continued local Green’s function across point gaps and shape the dynamics of observables.

Our work establishes a non-eigenstate dynamical sector in non-Hermitian scattering and a clean bridge between point-gap topology and real-time measurements. It reframes what “states” control dynamics: not just eigenmodes, but also dark-pole states living in the analytic structure of the Green's function.