  A particle with finite initial velocity in a disordered potential comes back
and in average stops at the original location. This phenomenon dubbed 'quantum
boomerang effect' (QBE) has been recently observed in an experiment simulating
the quantum kicked-rotor model [Phys. Rev. X 12, 011035 (2022)]. We provide
analytical arguments that support QBE in a wide class of disordered systems.
Sufficient conditions to observe the real-space QBE effect are (a) Anderson
localization, (b) the reality of the spectrum for the case of non-Hermitian
systems, (c) the ensemble of disorder realizations $\{H\}$ be invariant under
the application of $\mathcal{R\, T}$, and (d) the initial state is an
eigenvector of $\mathcal{R\, T}$, where $\mathcal{R}$ is a reflection $x
\rightarrow -x$ and $\mathcal{T}$ is the time-reversal operator. The QBE can be
observed in momentum-space in systems with dynamical localization if conditions
(c) and (d) are satisfied with respect to the operator $\mathcal{T}$ instead of
$\mathcal{RT}$. These conditions allow the observation of the QBE in
time-reversal symmetry broken models, contrarily to what was expected from
previous analyses of the effect, and in a large class of non-Hermitian models.
We provide examples of QBE in lattice models with magnetic flux breaking
time-reversal symmetry and in a model with electric field. Whereas the QBE
straightforwardly applies to noninteracting many-body systems, we argue that a
real-space (momentum-space) QBE is absent in weakly interacting bosonic systems
due to the breaking of $RT$ ($T$) symmetry.
