Figure 1

We show the best snapshot of the density $|\psi {|}^2$ along the $z$axis showing the interference pattern. We also show the initial value of the density, in order to compare the size of the interference pattern.Reuse & Permissions

Figure 2

(Top) In order to show the convergence of our algorithms we track the maximum of the energy density during the evolution for the particular case $p_z=1.5$, which would be equivalent to estimate the infinity norm of the energy density. In our calculations, we used three different resolutions $\Delta x_1=0.2$, $\Delta x_2=\Delta x_1/1.5$, and $\Delta x_3=\Delta x_2/1.5$. (Bottom) We show the convergence factor, that is ${1.5}^Q$, which in theory should be ${1.5}^2=2.25$ for a second order convergent implementation. We show how much our calculations approach second order convergence; the convergence factor oscillates usually near or around the theoretical value due to phases in the scalar (the maximum of the density in our case) for the various resolutions. A big peak also appears approximately by the time the density approaches its maximum, and we see how convergence is lost after around $t\sim 11$ and decreases clearly afterwards by the time the blobs reach the sponge region, where the calculations are not expected to converge since there Schrödinger’s equation has been modified with an artificial sink of particles, and also the unitarity of the evolution in the numerical domain is lost.Reuse & Permissions

Figure 3

In this plot, we show snapshots at different times of the density as function of the $z$ coordinate of the structures of an ideal gas with zero pressure. The collision takes place after $t\sim 7.2$. The evolution shows that the fluids cross each other without showing any pattern of interference.Reuse & Permissions

Figure 4

In this plot, we show the total, kinetic, potential, and thermal energy for the head-on collision of the pressureless fluid configurations. The peak appears approximately by the time the density of the fluid reaches its maximum.Reuse & Permissions

Figure 5

In this plot, we show snapshots at different times of the density as function of the $z$ coordinate of the structures of fluid. As in the pressureless case, the evolution shows the fluids crossing each other without showing any pattern of interference.Reuse & Permissions

Figure 6

In this plot, we show the total, kinetic, potential, and thermal energy for the head-on collision of fluid with pressure.Reuse & Permissions