By inspection of the first and second column of plots in Fig. , it can be seen that the overall structure of ⟨q 0 ⟩ and ⟨q 1 ⟩ are similar between the reference and TD-ADGA simulations. However, while ⟨q 0 ⟩ is nearly identical for the two calculation throughout the simulation time, ⟨q 1 ⟩ show a larger discrepancy. In the ⟨q 1 ⟩ plots, the structure of the long period Figure : The expectation value of the displacement coordinates q 0 and q 1 and the value of the perturbing Gaussian pulse in the q 0 coordinate during the TD-ADGA and the reference simulation.