Amplitude Oscillations of the Resonant Phenomena in a Frenkel–Kontorova Model with an Incommensurate Structure

Dynamical mode locking phenomena in incommensurate structures of the dc- and ac-driven overdamped Frenkel–Kontorova model are studied by molecular-dynamics simulations. It is found that the Shapiro steps exhibit significantly different amplitude and frequency dependences from the ones observed in the commensurate structures. The step widths still oscillate with the amplitude, but the form is no longer Bessel-like, i.e., the anomaly appears in our simulations. The same type of anomalies is also exhibited by the critical depinning force. The oscillatory behavior and the anomalies are also revealed in the (F,F_ac) phase diagram where three phases are observed. These oscillations are directly correlated with the existence and the stability of interference phenomena in real systems.