Absolute negative mobility in the anomalous diffusion

Transport of an inertial Brownian particle driven by the multiplicative Levy noise was investigated here. Numerical results indicate that: (i) The Levy noise is able to induce absolute negative mobility (ANM) in the system, while disappearing in the deterministic case; (ii) the ANM can occur in the region of superdiffusion while disappearing in the region of normal diffusion, and the appropriate stable index of the Levy noise makes the particle move along the opposite direction of the bias force to the maximum degree; (iii) symmetry breaking of the Levy noise also causes the ANM effect. In addition, the intrinsic physical mechanism and conditions for the ANM to occur are discussed in detail. Our results have the implication that the Levy noise plays an important role in the occurrence of the ANM phenomenon.