Nonperturbative Resummation of Divergent Time-Local Generators: Disentangling Non-Markovian Dynamics

Abstract:Perturbative van Kampen cumulant expansions of time-local generators of open quantum systems generically diverge at long times, but the reduced dynamics is regular. We show that the divergent cumulants nevertheless contain information sufficient to reconstruct the nonperturbative dynamical map. The map reveals that the divergence does not signal a breakdown of the reduced dynamics, but the approach to isolated times at which it becomes noninvertible. Singular time-local generators thus arise naturally from microscopic open-system Hamiltonians, without requiring special Lindblad-type constructions. For the weak-coupling spin--boson model, the reconstructed non-Markovian dynamics takes the explicit disentangled form \begin{equation*} \Phi=\Phi_{\mathrm{GAD}}+\Phi_{\mathrm{NS}}+\Phi_{\mathrm{Khal}}, \end{equation*} separating generalized amplitude damping, exponentially damped nonsecular coherence mixing, and a projective, phase-selective Khalfin map. 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 after the Khalfin transition. Comparison with numerically exact TEMPO dynamics validates the disentanglement and shows that apparently complex non-Markovian dynamics can resolve into a small number of physically transparent and distinct dynamical processes.

arXiv:2603.25512 [quant-ph]

(or arXiv:2603.25512v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.25512 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.