Group Seminar 2020/21

The motion of extended defects called dislocations controls the mechanical properties of crystalline materials such as strength and ductility. Under moderate applied loads, this motion proceeds via the thermal nucleation of kink pairs. The nucleation rate is known to be a highly nonlinear function of the applied load, and its calculation has long been a theoretical challenge. Moreover, knowledge of the dislocation velocity as a function of applied stress is a critical ingredient in mesoscale dislocation dynamics simulations. In this talk, I will discuss a stochastic path (functional) integral approach to the problem, and use it to derive a simple, general, and exact formula for the rate. The predictions are in excellent agreement with experimental and computational investigations, and unambiguously explain the origin of the observed extreme nonlinearity. The results can also be applied to other systems modelled by an elastic string interacting with a periodic potential, such as Josephson junctions in superconductors. Time permitting, I will also discuss possible extensions of the approach to much more general non-equilibrium situations.