Exploring frequency-domain characteristics of Markovian and non-Markovian quantum dynamics

This paper presents a Green´s function based root locus method to investigate the frequency-domain characteristics of Markovian and non-Markovian open quantum systems. A Langevin equation for the system is derived, where we show the structure of the Green´s function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, variations in the modes of the Green´s function are explored in the frequency domain, where both the critical transition from Markovian to non-Markovian dynamics and a critical point condition under Lorentzian noise are graphically presented using a root locus method. Related results are verified using an example of a boson-boson coupling system.