- Ratchet dynamics in nonlinear Klein-Gordon systems (2005)
- In the first part of the work we have studied a directed energy transport in homogeneous nonlinear extended systems in the presence of a biharmonic force and dissipation. We have shown that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explains earlier symmetry analysis of this phenomenon. We also found in the framework of the collective coordinate theory an explanation to the dynamics dependence on the damping. In the second part of the work we have presented and studied a novel design for a ratchet potential for soliton excitations. The investigation was focused on the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic and asymmetric lattice of point-like inhomogeneities in the overdamped regime. In addition, we explained the underlying rectification mechanism within a collective coordinate framework, which shows that such a system behaves as a rocking ratchet for point particles.This was supported by numerical simulations. A quantitative agreement was found in an improved version of the collective coordinate approach that regards the kink width in addition to the fundamental translational degree of freedom. An explanation for the to the kink width dynamics and its role in the transport was presented. We also studied the robustness of our kink rocking ratchet in the presence of noise. For this situation it was shown that noise activates unidirectional motion in a parameter range where the motion is not observed in the noiseless case. This is subsequently corroborated by the collective variable theory. The study was also extended to the weak underdamped regime, where higher values of the mean kink velocity were found. An explanation for this new phenomenom was given.