2003/12/23 by C. Reichhardt, C. J. Olson Reichhardt, M. B. Hastings · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Amplitude #Classical mechanics #Condensed matter physics #Diffusion and Search Dynamics #Geometry #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Quantum mechanics #Rectification #Symmetry (geometry) #Transverse plane #cond-mat.stat-mech #cond-mat.supr-con #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.69.056115
published as Phys. Rev. E 69, 056115 (2004) · 14 pages, 17 postscript figures
arxiv created 2003/12/23 · openalex publication_date 2004/05/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough ac drives, the particle orbit encircles one or more potential maxima of the periodic substrate. In this case, when an additional increasing dc drive is applied in the longitudinal direction, the longitudinal velocity increases in a series of discrete steps that are integer multiples of a omega/(2 pi), where a is the lattice constant of the substrate. Fractional steps can also occur. These integer and fractional steps correspond to distinct stable dynamical orbits. A number of these phases also show a rectification in the positive or negative transverse direction where a nonzero transverse velocity occurs in the absence of a dc transverse drive. We map out the phase diagrams of the regions of rectification as a function of ac amplitude, and find a series of tongues. Most of the features, including the steps in the longitudinal velocity and the transverse rectification, can be captured with a simple toy model and by arguments from nonlinear maps. We have also investigated the effects of thermal disorder and incommensuration on the rectification phenomena, and find that for increasing disorder, the rectification regions are gradually smeared and the longitudinal velocity steps are no longer flat but show a linearly increasing velocity.