Perturbative dynamics in the pseudocoherent phase of the spin-boson model

We propose a time-dependent perturbation theory to study a newly discovered pseudocoherent phase of the spin-boson model. Effectiveness of the method is confirmed by comparing its results with that calculated from the numerically exact quantum dynamics method, which exhibits good agreements. We then describe how an incoherent nature of the pseudocoherent phase emerges from explicit expressions of the proposed method, and properties of invariant time of extreme values and scaling of amplitudes resulting from a second-order approximation. Correction effects of higher-order terms are also discussed. In addition, we utilize trace distance to investigate non-Markovianity and influences of model parameters. We find propagations in the pseudocoherent phase are always non-Markovian because of bath-driving oscillations. The non-Markovianity shows different dependence on cutoff frequency of bosonic baths from coherent and incoherent phases, which can be applied for qualitative identifications of different dynamic phases in realistic detections.