For many open quantum systems, a master equation approach employing the Markov approximation cannot reliably describe the dynamical behaviour. This is the case, for example, in a number of solid state or biological systems, and it has motivated a line of research aimed at quantifying the amount of non-Markovian behaviour in a given model. Within this framework, we investigate the dynamics of a quantum harmonic oscillator linearly coupled to a bosonic bath. We focus on Gaussian states, which are suitably treated using a covariance matrix approach. Concentrating on an entanglement based non-Markovian behaviour quantifier (NMBQ) proposed by Rivas et. al. [1], we consider the role that near resonant and off-resonant modes play in affecting the NMBQ. By using a large but finite bath of oscillators for both Ohmic and super Ohmic spectral densities we find, by systematically increasing the coupling strength, initially the near resonant modes provide the most significant non-Markovian effects, while after a certain threshold of coupling strength the off-resonant modes play the dominant role. We also consider the NMBQ for two other models where we add a single strongly coupled oscillator to the model in extra bath mode and buffer configurations, which affects the modes that determine non-Markovian behaviour.
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