Driven dynamics in an undamped Frenkel-Kontorova model in the presence of a quasiperiodic potential and a thermal bath

We study the nonlinear mobility of a one-dimensional direct current (dc) driven, undamped Frenkel-Kontorova chain with spacing l subject to a thermal bath, and a quasiperiodic potential of the form (formula presented) Two typical cases for the length scales l and (formula presented) are identified; one is (formula presented) (golden mean) and the other is (formula presented) (spiral mean). In the former case, there exists a nonzero static friction for (formula presented) or (formula presented) which takes on a nonmonotonic behavior as a function of the relative ratio (formula presented) while in the latter case we predict a (formula presented) -dependent critical strength (formula presented) at which the transition from zero to nonzero friction occurs. Numerical results also indicate that (formula presented) plays an important role in determining the critical forces, which mark the dynamic transitions among the locked, the fluid-sliding, and the solid-sliding states. For large K, the hysteretic behavior for the mobility and the effective temperature is found at zero temperature. It becomes narrow with increasing temperature, and can even be sustained to room temperature.