Anderson localization is a general phenomenon that applies to a variety of disordered physical systems. Recently, a manifestation of Anderson localization for wave packets launched with a finite average velocity was proposed, the quantum boomerang effect (QBE). This phenomenon predicts that the disorder-averaged center of mass of a particle initially moves ballistically, then makes a U-turn, and finally slowly returns to its initial position. The QBE has been predicted to take place in several Hermitian models with Anderson localization and has been experimentally observed in the paradigmatic quantum kicked rotor model. In this paper, we investigate the emergence of the QBE in non-Hermitian systems and clarify the importance of symmetries of the Hamiltonian and the initial state. We generalize the analytical arguments available in the literature and show that even in the case of complex spectrum a boomeranglike behavior can appear in a non-Hermitian system. We confirm our analytical results through a careful numerical investigation of the dynamics for several non-Hermitian models. We find that non-Hermiticity leads to the breakdown of the dynamical relation, though the QBE is preserved. This paper opens avenues for future investigations in Anderson localized systems. The models studied here may be implemented using cold atoms in optical lattices.

• Received 24 June 2022
• Revised 13 September 2022
• Accepted 20 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.104310