Origin of stick-slip motion in a driven two-wave potential

A model is presented of a particle that interacts with two periodic potentials, representing two confining plates, one of which is externally driven. The model leads to a spectrum of rich behaviors in the motion of the top driven plate: a stick-slip, intermittent kinetic regime, characterized by force fluctuations, and two types of sliding above a critical driving velocity $v_c$. Similar behaviors are typical of a broad range of systems including thin sheared liquids. A detailed analysis of the different regimes displays an interesting transition range between stick-slip and kinetic motion, ${\omega }^{-2\mathrm{}}$ power spectra of the force over a wide range of velocities below $v_c$, and a decrease of the force fluctuations that follows ${(v_c-v)}^{\frac{1}{2}}$ for $v<\mathrm{}{v}_c$. The velocity-dependent Liapunov exponents demonstrate that stick-slip dynamics is characterized by chaotic behavior of the top plate and the embedded particle. An equation is derived that provides a coarse-grained description of the plate motion near $v_c$.