Inertial effects and efficiency in Lévy ratchets

SEBASTIÁN BOUZAT

Sitges. Barcelona. España

Conferencia; XXII Sitges Conference on Statistical Mechanics: Energy Conversion: From Nanomachines to Renewable Sources; 2010

We study the dynamics of particles in an external anisotropic periodic potential under the influence of additive white Lévy noise. Our studies extend those in [1] and [2] by considering the general not overdamped situation. They provide additional results on velocity distributions, coherence of transport and efficiency. Different quantities characterizing directionality, coherence and dispersion are analyzed as functions of the mass and other systems parameters. We show that, while the current decreases monotonously with the stability index of the Lévy noise, there exists a particular intermediate value of such parameter (slightly dependent on the mass) that minimizes the time required to form a coherent particle package advancing in the preferred direction. Moreover, we show the possibility of observing mass separation. This means that particles of different masses may advance in opposite directions when influenced by the same ratchet potential and the same Lévy noise. Finally, we show that the ratio of the advanced distance to the total distance traveled constitutes a relevant measure for the rectification power or efficiency, useful not only for Lévy ratchets but also for general ratchets systems. In particular, we find that it behaves quite similar to the rectification efficiency [3,4] for standard models of rocking [3] and flashing [4] ratchets. [1] B. Dybiec, E. Gudowska-Nowak and I. M. Sokolov, Phys. Rev. E 78, (2008) 011117. [2] D. del-Castillo-Negrete, V.Yu. Gonchar and A.V. Chechkin, Physica A 387 (2008) 6693. [3] L. Machura, M. Kostur, P. Talkner, J. Luczka, F. Marchesoni and P. Hänggi, Phys. Rev. E 70 (2004) 061105. [4] D. Suzuki and T. Munakata, Phys. Rev. E 68, (2003) 021906.