| Abstract: | After the quantum measurement, the system's state is changed. This change can cause particle motion. We ask how this motion depends on the measured observable. We demonstrate the central role of the symmetries of the observable. While the inversion symmetry breaking should be sufficient to create currents, for sizeable currents one needs to break time-reversal symmetry. In the case of repeated measurements, the system ends up in a completely random ensemble without any currents. Fortunately, we show that the persistence of currents in the steady state can be ensured if the measured system is coupled to a cooling bath. The steady-state current is shown to be a non-monotonic function of the measurement rate. When measurements are non-degenerate and infinitely fast the local measurements prohibit currents between different local regions. However, we show that even in this case, loop currents within the regions can develop. |