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Strong coupling between a system and its environment leads to the emergenceof non-Markovian dynamics, which cannot be described by a time-local masterequation. One way to capture such dynamics is to use numerical real-time pathintegrals, where assuming a finite bath memory time enables manageablesimulation scaling. However, by comparing to the exactly soluble independentboson model, we show that the presence of transient negative decay rates in theexact dynamics can result in simulations with unphysical exponential growth ofdensity matrix elements when the finite memory approximation is used. Wetherefore reformulate this approximation in such a way that the exact dynamicsare reproduced identically and then apply our new method to the spin-bosonmodel with superohmic environmental coupling, commonly used to model phononenvironments, but which cannot be solved exactly. Our new method allows us toeasily access parameter regimes where we find revivals in population dynamicswhich are due to non-Markovian backflow of information from the bath to thesystem.

Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models