Apparent hysteresis in a driven system with self-organized drag

The motion of extended defects in materials is often resisted by interaction with diffusing impurities. The defect undergoes a transition from slow to fast migration, or vice versa. This transition is commonly hysteretic, with the defect jumping back and forth between these kinetic states. We explore such hysteresis within a kinetic Monte Carlo simulation. After identifying the slow variables, we construct an effective potential that quantitatively describes the stable and metastable states of the system (a bifurcation diagram) and the kinetics of the transitions between these. This description provides a means to determine whether hysteresis will be observed in a particular simulation and the detailed nature of this hysteresis (switching times).