Eternal adiabaticity in quantum evolution

We iteratively apply a recently formulated adiabatic theorem for the strong-coupling limit in finite-dimensional quantum systems. This allows us to improve approximations perturbed dynamics, beyond standard approximation based on Zeno dynamics and elimination. The effective generators describing approximate evolutions are endowed with same block structure as unperturbed part of generator, exhibit evolutions. iterative reveals that adiabaticity holds eternally, is, system evolves within each eigenspace an error bounded by $O(1/\gamma)$ uniformly time, where $\gamma$ characterizes strength generator. prove reproduces Bloch's perturbation theory unitary case, is therefore full generalization open furthermore equivalence Schrieffer-Wolff des Cloiseaux approaches case generalize both arbitrary systems, showing they share eternal adiabaticity, providing explicit bounds. Finally we discuss physical show ideal systems do not exist general.