Hysteresis and instability of a driven interface in a periodic potential

We discuss the inertial motion of an interface or linear defect driven in a periodic potential. When the interface modes are underdamped, a moving interface becomes unstable against spontaneous roughening at low velocity. We predict that this instability can be realized (for example) at low temperatures for dislocations in Cu, leading to possibly peculiar mechanical properties in the unstable regime. In the inertial regime the surface of a 4He crystal might exhibit a linear relationship between growth velocity and external driving force, once it has been set into motion.