Pinning and sliding of driven elastic systems: from domain walls to charge density waves

This review is devoted to the theory of collective and local pinning effects in various disordered nonlinear driven systems. A common feature of both approaches is the emergence of metastability. Although the emphasis is put on charge and spin density waves and magnetic domain walls, the theory also has applications to flux lines and lattices thereof, dislocation lines, adsorbed monolayers and related systems. In the first part of the article we focus on the theory of collective pinning which includes the equilibrium properties of elastic systems with frozen-in disorder as well as the features close to the dynamic depinning transition enforced by an external driving force. At zero temperature and for adiabatic changes of the force, the dynamic depinning transition is continuous, the correlation length is large, the behaviour is dominated by scaling laws with non-trivial static and dynamical critical indices. The application of functional renormalization group methods allows for the detailed description of both equilibrium as well as non-equilibrium properties. The depinning transition is also characterized by the appearance of new scaling laws. Thermal fluctuations smear out this transition and allow for a creep motion of the elastic objects even at small forces. The application of an ac-driving force also destroys the sharp transition which is replaced by a velocity hysteresis. The second part of the review is devoted to the picture of local pinning and its applications. Local theories apply in the region where correlation effects are less important, i.e. not too close to the depinning transition, at low temperatures, at high enough frequencies or velocities. The inclusion of plastic deformations results in a rich cross-over behaviour of the force-velocity relation as well as of the frequency dependence of the dynamic response. Being easily affected at higher frequencies or velocities, the local pinning becomes an easily accessed source of dispersion, relaxation and dissipation. The picture of the local pinning can be effectively used to explain experimental data: qualitatively and even quantitatively. The advantages come from the explicit treatment of metastable states, their creation and relaxation, and their relation to plasticity and topological defects. The local pinning recovers and exploits new elements of the energy landscape such as termination points of some branches or irreversibility of other ones related to generation of topological defects in the course of sliding. It also provides a clue to quantum effects describing quantum creep as tunnelling between retarded and advanced configurations.