Nonlinear mobility of the generalized Frenkel-Kontorova model

Nonlinear mobility of one-and two-dimensional systems of interacting atoms in response to the de external force is studied in the framework of a generalized Frenkel-Kontorova model. The atoms are subjected to a three-dimensional external potential periodic in two dimensions and parabolic in the third dimension. When the force increases, the system exhibits a transition from the low-mobility regime to the high-mobility regime, the latter corresponds to the running state of atoms in the inclined substrate potential. During the transition the system passes through intermediate states depending on whether the concentration of atoms corresponds to the ground-state atomic structure with the simple or complex elementary cell. All the transitions are first-order dynamical-phase transitions, i.e., they are discontinuous and exhibit a hysteresis even at nonzero system temperature. The simulation results are explained with the phenomenological approach, which treats a system of strongly interacting atoms as a system of weakly interacting quasiparticles (kinks).