Nonperturbative Resummation of Divergent Time-Local Generators

Perturbative van Kampen cumulant expansions of time-local generators of open quantum systems generically diverge at long times, even though the reduced dynamics remains regular.

Here we show that these divergent cumulants nevertheless contain sufficient information to reconstruct the nonperturbative dynamical map.

The resulting dynamical map reveals that the divergence does not signal a breakdown of the reduced dynamics, but the approach to isolated times at which the dynamical map becomes noninvertible.

Rather than arising from special Lindblad-type constructions, the corresponding singular time-local generators emerge generically from microscopic open-system Hamiltonians.

The onset of recurrent noninvertibility identifies the reduced-dynamical-map manifestation of the Khalfin effect, a transition from exponential to algebraic relaxation, establishing a direct connection between long-time quantum decay and noninvertibility of reduced open-system dynamics.

Nevertheless, the distinguishability of quantum superposition states remains governed by an exponential decay law throughout the Khalfin regime, demonstrating that the Markovian loss of distinguishability survives even in the presence of long-lived non-Markovian memory.