Directed transport induced by colored Lévy noise: Competition between long jumps and noise correlation

•Transport of overdamped particle under the influence of the colored Lévy noise is investigated.•The direction of the current depends on the parameters charactering the colored Lévy noise.•The competition between the long jumps and the noise correlation leads to current inversion.

Transport of overdamped particle driven by a colored Lévy noise in a static ratchet potential is investigated. We analyze the influence of the noise in the determination of the current and find that the direction of the current depends on the parameters characterizing the colored Lévy noise. In the present model, the long jumps and the noise correlation are two different factors that can break thermodynamical equilibrium and induce directional transport, the competition between the both leads to current inversion. This implies that an interesting non-equilibrium effect arises from long tail distribution of noise.