Decays of degeneracies in PTPT-symmetric ring-shaped lattices

Many apparently non-Hermitian ring-shaped discrete lattices share the appeal with their more popular linear predecessors. Irrespectively of the change of the topology, their dynamics controlled by the nearest-neighbor interaction is shown to remain phenomenologically interesting. For the perturbation-caused removals of spectral degeneracy at exceptional points, in particular, alternative scenarios are illustrated via solvable examples.

► The old problem of quantum stability addressed from a new perspective.
► Insight in the role of (perturbed) Katoʼs exceptional points gained.
► New non-Hermitian toy-model quantum lattices proposed.
► Discretization shown efficient for periodic (= difficult) boundary conditions.
► Closed-form constructions of physics-determining inner products offered.