Anomalous transports in a space-time inseparable system

We investigate transport of an inertial particle in a spatially symmetric periodic potential, such that phase of the potential is controlled by two time periodic modulations. Our numerical results indicate that the phase modulation can induce anomalous transport of the system, while any current does not appear for only one time periodic modulation. In the absence of external bias, direction of mean velocity of the particle changes several times with amplitude and frequency of one of the modulations, i.e., multiple current reversals (CRs). The multiple CRs results from temporal symmetry breaking of the system. In the presence of external bias, there exists phenomenon of absolute negative mobility (ANM) in the system, while action of noise weakens the ANM. Intrinsic physical mechanisms and conditions responsible for occurrence of the anomalous transport are also discussed in detail.