Robust quantum boomerang effect in non-Hermitian systems

TL;DR

This paper explores the quantum boomerang effect in non-Hermitian systems, demonstrating that even with complex spectra, the effect persists, and analyzing how non-Hermiticity influences the dynamics of Anderson localized systems.

Contribution

It generalizes the understanding of the quantum boomerang effect to non-Hermitian systems, showing its robustness and the role of symmetries in such systems.

Findings

Quantum boomerang effect persists in non-Hermitian models.

Non-Hermiticity causes breakdown of certain dynamical relations.

Analytical and numerical evidence supports the presence of QBE in complex spectra.

Abstract

Anderson localization is a general phenomenon that applies to a variety of disordered physical systems. Recently, a novel 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 work, 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 boomerang-like 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 work opens up new avenues for future investigations in Anderson localized systems. The models studied here may be implemented using cold atoms in optical lattices.