Dynamics below the depinning threshold in disordered elastic systems

Phys Rev Lett. 2006 Aug 4;97(5):057001. doi: 10.1103/PhysRevLett.97.057001. Epub 2006 Aug 1.

Abstract

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T-->0, the steady state is dominated by a single configuration which is occupied with probability 1. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady-state regime as the depinning threshold is approached from below. We do find a divergent length, but it is associated only with the transient relaxation between metastable states.