2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/208304The dynamics of an unbiased spin-boson model with Lorentzian spectral density is investigated theoretically in terms of the perturbation theory based on a unitary transformation. The non-equilibrium correlation function $P(t)$ and susceptibility $χ^{\prime\prime}(ω)$ are calculated for both the off-resonance case $Δ\lesssim 0.5Ω$ and the on-resonance case $Δ\sim Ω$. The approach is checked by the Shiba's relation and the sum rule. Besides, the coherent-incoherent transition point $α_c$ can be determined, which has not been demonstrated for the structured bath by previous authors up to our knowledge.25 pages, 11 figuresDisordered Systems and Neural NetworksMesoscale and Nanoscale Physicstext