Witnessing the boundary between Markovian and non-Markovian quantum dynamics: a Green's function approach

This paper presents a Green's function-based root locus method to investigate the boundary between Markovian and non-Markovian open quantum systems in the frequency domain. A Langevin equation for the boson-boson coupling system is derived, where we show that the structure of the Green's function dominates the system dynamics. In addition, by increasing the coupling between the system and its environment, the system dynamics are driven from Markovian to non-Markovian dynamics, which results from the redistribution in the modes of the Green's function in the frequency domain. Both a critical transition 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.