where the last equality is only true for rectilinear coordinates and where Θ(q 0 ) is the Heaviside The results for the autocorrelation function and its Fourier transform obtained from the two simulations are shown in Fig. . Fig. shows the values of the autocorrelation function during the two simulations. Similar to the results for the flux, we observe a very good agreement for between the two simulations for the initial 50 fs and after this point the similarity decreases. The results are however, qualitatively the same for the entire simulation time. Looking at the Fourier transforms in Fig. , a very good agreement between the TD-ADGA and Reference autocorrelation spectra is observed. The largest difference between the two autocorrelation spectra is found in the frequency interval between 0.015 and 0.020 E h , where two peaks are present. In this region the TD-ADGA peaks are shifted to a higher frequency and the amplitude of the second peak is smaller. for the TD-ADGA calculation and the reference calculation. The Fourier transforms have been normalized to one with respect to the maximum peak of the reference calculation.