Quantum boomerang effect for interacting particles

When a quantum particle is launched with a finite velocity in a disordered potential, it may surprisingly come back to its initial position at long times and remain there forever. This phenomenon, dubbed "quantum boomerang effect," was introduced in Prat et al. [Prat, Delande, and Cherroret, Quantum boomeranglike effect of wave packets in random media, Phys. Rev. A 99, 023629 (2019)]. Interactions between particles, treated within the mean-field approximation, are shown to partially destroy the boomerang effect: the center of mass of the wave packet makes a U turn, but does not completely come back to its initial position. We show that this phenomenon can be quantitatively interpreted using a single parameter, the average interaction energy.