Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems

A particle with finite initial velocity in a disordered potential comes back and on average stops at the original location. This phenomenon, dubbed ``quantum boomerang effect'' (QBE), has been recently observed an experiment simulating quantum kicked-rotor model [Sajjad et al., Phys. Rev. X 12, 011035 (2022)]. We provide analytical arguments that support presence of QBE wide class systems. Sufficient conditions to observe real-space are (a) Anderson localization, (b) reality spectrum for case non-Hermitian systems, (c) ensemble disorder realizations ${H}$ being invariant under application $\mathcal{R}\phantom{\rule{0.16em}{0ex}}\mathcal{T}$, (d) state eigenvector where $\mathcal{R}$ is reflection $x\ensuremath{\rightarrow}\ensuremath{-}x$ $\mathcal{T}$ time-reversal operator. The can be momentum space systems dynamical localization if satisfied respect operator instead $\mathcal{RT}$. These allow observation time-reversal-symmetry-broken models, contrary what was expected from previous analyses effect, large models. examples lattice models magnetic flux breaking symmetry electric field. Whereas straightforwardly applies noninteracting many-body we argue (momentum-space) absent weakly interacting bosonic due reflection--time-reversal (time-reversal) symmetry.