Figure 5.

(a) Population for the quantum emitter for three different chain lengths: $N_C=30$ (orange), $N_C=25$ (blue) and $N_C=15$ (green) compared to the “exact” one (black). An absorbing function has been added to the first three chains. The parameters are chosen to give a good description of the dynamics, but a wide range is valid for the first to lengths. When the chain is very short, as for $N_C=15$, the prediction of the dynamics starts to break down; (b) effective spectral densities when the absorbing terms are added in the Hamiltonian for the same lengths as in (a). For $N_C=30$ and $N_C=25$, the effective spectral density is similar to $J_0\left(\omega \right)$, although neither of them describes it in detail. For $N_C=15$, the effective spectral density presents a shift in the frequency of the main peak of $J_0\left(\omega \right)$, affecting the dynamics.