Abstract
The hysteretic dynamics of a Frenkel–Kontorova chain subject to irregular substratepotentials and driven by an external dc force is studied both in the underdamped and inthe overdamped regime at zero temperature. The choice of a rigid external potentialdefined by the sum of two sinusoidal functions with different periodicity allows us tosimulate microscopic sliding over quasiperiodic and multiple-well periodic substrates. Weanalyse, for different parameter values of the model, the behaviour of the centre of massaverage velocity of the chain as a function of an adiabatic increase and decrease of theapplied driving. For small damping coefficients (negligible dissipative forces), at a fixedvalue of the substrate potential amplitude, the width of the hysteresis region ismarkedly influenced by the chain stiffness. As expected, in the overdamped dynamicalregime no hysteresis is observed. We comment on the nature of the dynamicalstates displayed during the chain motion at different strengths of the dc driving.
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