Nonperturbative resummation of divergent time-local generators: disentangling non-Markovian dynamics

Perturbative van Kampen cumulant expansions of time-local generators of open quantum systems generically diverge at long times, while the reduced dynamics remains regular. We show that these divergences encode information sufficient to reconstruct an approximate nonperturbative dynamical map. Although their resummation remains divergent, disentangling the dynamics according to its van Hove limit resolves the divergence and exposes its dynamical origin: the map approaches isolated times at which it becomes noninvertible. For the weak-coupling unbiased spin--boson model, the reconstructed non-Markovian dynamics takes the disentangled form {equation*} Φ=ΦGAD+ΦNS+ΦKhal, {equation*} separating generalized amplitude damping, exponentially damped nonsecular coherence mixing, and a projective, phase-selective Khalfin map. Thus, the onset of recurrent noninvertibility is the reduced-dynamical-map manifestation of the Khalfin transition from exponential to algebraic relaxation. Although the coherences acquire algebraic Khalfin tails, the distinguishability of quantum superposition states remains governed by an exponential decay law well after the Khalfin transition. Comparison with numerically exact TEMPO dynamics validates the procedure and shows that apparently complex non-Markovian dynamics can resolve into a small number of distinct, physically transparent dynamical processes.