Driven elastic system in a random environment

Abstract
The dynamics of a moving D-dimensional interface in a disordered medium is analyzed at zero and finite temperature. We study the force-velocity characteristics using a functional renormalization group (RG) method. Compared to the zero temperature dynamics, where a depinning threshold exists, the characteristics is rounded at finite temperature and a creep regime is expected at very low drive, as the system jumps forward by thermal activation over effective barriers. We study these effects analytically in a D = 4 - ε expansion. Besides demonstrating the existence of the creep regime, our analysis gives for the first time a proof that barriers and metastable states energies diverge at low drive with the same exponent, which we compute using RG. Important length scales and energy scales are obtained and identified within the RG framework. Our finite temperature and velocity RG equations are a starting point for a full comprehension of the force-velocity characteristics. In particular, we are able to demonstrate explicitely that a moving interface in a random potential behaves at large scale as in a random field