Fluctuation-driven directed transport in the presence of Lévy flights |
| |
Authors: | D. del-Castillo-Negrete V.Yu. Gonchar |
| |
Affiliation: | a Oak Ridge National Laboratory, Fusion Energy Division, Oak Ridge, TN 37831-6169, USA b Institute for Theoretical Physics NSC KIPT, Akademicheskaya st.1, Kharkov 61108, Ukraine |
| |
Abstract: | The role of Lévy flights on fluctuation-driven transport in time independent periodic potentials with broken spatial symmetry is studied. Two complementary approaches are followed. The first one is based on a generalized Langevin model describing overdamped dynamics in a ratchet type external potential driven by Lévy white noise with stability index α in the range 1<α<2. The second approach is based on the space fractional Fokker-Planck equation describing the corresponding probability density function (PDF) of particle displacements. It is observed that, even in the absence of an external tilting force or a bias in the noise, the Lévy flights drive the system out of the thermodynamic equilibrium and generate an up-hill current (i.e., a current in the direction of the steeper side of the asymmetric potential). For small values of the noise intensity there is an optimal value of α yielding the maximum current. The direction and magnitude of the current can be manipulated by changing the Lévy noise asymmetry and the potential asymmetry. For a sharply localized initial condition, the PDF of staying at the minimum of the potential exhibits scaling behavior in time with an exponent bigger than the −1/α exponent corresponding to the force free case. |
| |
Keywords: | 05.40.Fb 05.40.-a 02.50.Ey |
本文献已被 ScienceDirect 等数据库收录! |
|