Rectified Brownian transport in corrugated channels: Fractional Brownian motion and Levy flights

We study fractional Brownian motion and Levy flights in periodic corrugated channels without any external driving forces. From numerical simulations, we find that both fractional Gaussian noise and Levy-stable noise in asymmetric corrugated channels can break thermodynamical equilibrium and induce directed transport. The rectified mechanisms for fractional Brownian motion and Levy flights are different. The former is caused by non-uniform spectral distribution (low or high frequencies) of fractional Gaussian noise, while the latter is due to the nonthermal character (occasional long jumps) of the Levy-stable noise. For fractional Brownian motion, average velocity increases with the Hurst exponent for the persistent case, while for the antipersistent case there exists an optimal value of Hurst exponent at which average velocity takes its maximal value. For Levy flights, the group velocity decreases monotonically as the Levy index increases. In addition, for both cases, the optimized periodicity and radius at the bottleneck can facilitate the directed transport. Our results could be implemented in constrained structures with narrow channels and pores where the particles undergo anomalous diffusion. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4764472]