Nonequilibrium dynamics of fluctuating lines

Depinning is a non-equilibrium critical phenomenon involving an external force and a pinning potential. When the force is weak the system is stationary, trapped in a metastable state. Beyond a threshold force the (last) metastable state disappears and the system starts to move. While there are many macroscopic mechanical examples, our interest stems from condensed matter systems such as Charge Density Waves (CDWs)1, interfaces2, and contact lines3. In CDWs, the controlling parameter is the external voltage. A finite CDW current appears only beyond a threshold applied voltage. Interfaces in porous media, domain walls in random magnets, are stationary unless the applied force (magnetic field) is sufficiently strong. A key feature of these examples is that they involve the collective depinning of many degrees of freedom that are elastically coupled. As such these problems belong to the realm of collective critical phenomena, characterized by universal scaling laws. We shall introduce these laws and the corresponding exponents below for the depinning of a line (interface or contact line).