Unlocking of an Elastic String from a Periodic Substrate

The unlocking of a linear defect (like a lattice dislocation or a magnetic flux line is a type-II superconductor) from a periodic substrate is modeled by a damped elastic string subjected to a washboard potential. At low temperatures running solutions are shown to set in for tilt amplitudes larger than a certain threshold value, sensitive to the damping constant. Close to the unlocking threshold the motion of a string segment is characterized by a logarithmic transient dynamics; as a consequence, hysteresis effects become observable for forcing periods much longer than any predicted time scale.