Analysis of memory effects in the dynamic evolution of the spin boson model

Abstract

Quantum information processing relies on how dynamics unfold in open quantum systems. In this work, we study the non-Markovian dynamics in the single-mode spin boson model at strong couplings. In order to apply perturbation theory, we transform our Hamiltonian to polaron frame, so that the effective system-bath coupling gets reduced. We employ coherence defined by \(l_1\)-norm to analyze the non-Markovian effects in the spin boson model. In the transformed frame of reference, the correlation timescales for the bath are significantly shorter than the system’s relaxation timescale-a key assumption for Markovian dynamics. However, intriguingly, we demonstrate that under the large polaron theory, the reduced dynamics exhibit effective non-Markovian behavior within a specific range of couplings, while remaining Markovian beyond this range.