Folder contents

In each (sub-)folder, the input file for an MCTDH-X computation MCTDHX.inp, i.e., a relaxation or propagation and (optionally) an analysis input file analysis.inp are given.

In particular:

1. In the subfolders prop_a, prop_b, prop_c of Relax18_Prop20_FIG6a-f, and subfolders prop_g, prop_h, prop_i of Relax19_Prop21_FIG6g-l/prop_g, we provide two analysis input files. The first one, analysis.inp, generates correlation functions and single-shot images at $t = 80.0$ for Fig. 6 in the main text. The second one, analysis2.inp, generates correlation functions from $t = 0$ to $t = 80$ for the video provided at https://tinyurl.com/u2cx39m. These input files need to be renamed to analysis.inp when they are used via MCTDHX_analysis. This procedure is automatized by the bash script movie.sh. (see Fig. S7, S8 and S9).

2. In the folder Relax10_Prop16_FIG5ae/relax, due to the presence of low-lying excited states, the relaxation needs to be run multiple times to ensure that the ground state has been obtained. Due to the random initial conditions, the different simulations generate different results. We need to compare the energies of the results to choose the true ground state. This procedure is automatized by the shell script Run_multiple.sh (cf. Fig. S5 and label “repetition” in Table S3).

3. In the folders Relax_series_FIG5f_FIG4a, Relax_series_FIG4b, Relax_series_FIG4c and Relax_series_FIG5e, we provide a bash script parameter_sweep.sh for running parameter sweep for the variable parameter3 ( $E_$dw) or xlambda_0 ($g$).

4. In the folder Relax_series_FIG5e, due to the presence of low-lying energy states, we need to simulate multiple times and choose the ground state at each parameter point. To save time, we use the following method instead. We first choose a certain parameter point, e.g. parameter3 = 20.d0, and simulate multiple times. We will obtain two completely different kinds of states: one of them has vanishing correlation between the two wells and the other one has finite correlation between wells. These two states are provided in the subfolders relax_series1 and relax_series2, respectively, as binary files PSI_bin, CIc_bin, and Header.

   The bash scripts parameter_sweep.sh in the two subfolders then use these two states as initial states and do relaxations at different barrier heights $E_\mathrm{dw}$. The basic characteristics, i.e., whether the correlations between the two wells are vanishing or not, remains unchanged during relaxations. As the barrier height changes, these two kinds of states compete to be the simulation result. At each parameter point, we compare the results in relax_series1 and relax_series2, and choose the correct ground state.