Hysteretic behaviour in driven Frenkel–Kontorova chains on irregular substrates

The hysteretic dynamics of a Frenkel-Kontorova chain subject to irregular substrate potentials and driven by an external dc force is studied both in the underdamped and in the overdamped regime at zero temperature. The choice of a rigid external potential defined by the sum of two sinusoidal functions with different periodicity allows us to simulate microscopic sliding over quasiperiodic and multiple-well periodic substrates. We analyse, for different parameter values of the model, the behaviour of the centre of mass average velocity of the chain as a function of an adiabatic increase and decrease of the applied driving. For small damping coefficients (negligible dissipative forces), at a fixed value of the substrate potential amplitude, the width of the hysteresis region is markedly influenced by the chain stiffness. As expected, in the overdamped dynamical regime no hysteresis is observed. We comment on the nature of the dynamical states displayed during the chain motion at different strengths of the dc driving.