Abstract
Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.
Highlights
Finding accurate descriptions of open quantum systems strongly coupled to external environments is essential for understanding how quantum systems lose their coherence. [1, 2]
The long time dynamics predicted by the polaron equation are qualitatively correct, taking the form of an exponentially decaying oscillation, but as anticipated it completely fails to capture the non-Markovian revival which we found above using the improved Augmented Density Tensor (ADT)
We have shown how the standard finite memory approximation in the ADT numerical scheme can cause unphysical behaviour resulting in periods of non-positive evolution
Summary
Finding accurate descriptions of open quantum systems strongly coupled to external environments is essential for understanding how quantum systems lose their coherence. [1, 2]. We will show how a technique based on discretisation of the Feynman influence functional – the so-called Augmented Density Tensor (ADT) can be modified to significantly improve the convergence of simulations in its numerical implementation This allows us to study the spin-boson model in a very strong coupling regime that shows clear non-Markovian behaviour that we quantify with the widely-used trace distance measure [17]. All effects of the system-environment coupling are described by an influence functional [13] that acts only on the reduced system trajectories This representation of an open quantum system has proved useful in developing both analytical and numerical methods.
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