  It was recently shown that wavepackets with skewed momentum distribution
exhibit a boomerang-like dynamics in the Anderson model due to Anderson
localization: after an initial ballistic motion, they make a U-turn and
eventually come back to their starting point. In this paper, we study the
robustness of the quantum boomerang effect in various kinds of disordered and
dynamical systems: tight-binding models with pseudo-random potentials, systems
with band random Hamiltonians, and the kicked rotor. Our results show that the
boomerang effect persists in models with pseudo-random potentials. It is also
present in the kicked rotor, although in this case with a specific dependency
on the initial state. On the other hand, we find that random hopping processes
inhibit any drift motion of the wavepacket, and consequently the boomerang
effect. In particular, if the random nearest-neighbor hopping amplitudes have
zero average, the wavepacket remains in its initial position.
