Rectification and phase locking in overdamped two-dimensional Frenkel-Kontorova model

¹ Department of Physics, Northwest Normal University - Lanzhou, 730070, PRC
² Institute of Modern Physics, Chinese Academy of Science, and Department of Physics, Lanzhou University Lanzhou, 730000, PRC
³ State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Science Lanzhou, 730000, PRC

^a duanws@nwnu.edu.cn

Received: 21 September 2010
Accepted: 17 December 2010

Abstract

The rectification phenomena and the phase locking for an overdamped two-dimensional Frenkel-Kontorova model system with commensurate structure under ac- and dc-driven external forces are demonstrated. As a function of longitudinal dc amplitude, the longitudinal velocity increases in a series of steps of height jν₀. In the steps, rectifications in the transverse direction occur though there are no net dc force in the transverse direction. Our results can be applied to vortices in superconductors, classical electron motion, biomolecules moving through 2D arrays of posts, and especially in tribology. In these active ratchets the rectified velocities can be controlled by jν₀.