The same overall behaviour is seen for the TD-ADGA and the TD-ADGA rerun simulations. For at better comparison of the differences between these two simulations and the reference simulation, the TD-ADGA and TD-ADGA rerun expectation values of the displacement coordinate have been plotted on top of the reference results in Figs. and, respectively. In Fig. it is observed that the values of ⟨q(t)⟩ in the TD-ADGA simulation differs from the values of the reference simulation. Small discrepancies can be observed as the oscillations ⟨q(t)⟩ are induced and overall it is seen that the displacements of the two simulations deviates a little with the TD-ADGA simulation predicting a smaller mean displacement that the reference simulation. Looking at the TD-ADGA rerun calculation in Fig. a much better agreement with the reference is observed. There is small differences in the smaller oscillations but the TD-ADGA rerun calculation reproduces the reference results very accurately.