1, \int \phi dy = \xi$ describes short-range correlations of the random force in the $y$ direction of motion of the line. Owing to the $y$ dependence of the random force, is intrinsically nonlinear.

To understand the energy scales associated with , let us consider a bulge of length $L$ and width $\xi$ on an otherwise straight dislocation. The characteristic restoring force due to line tension is then easily estimated as $F_{\rm LT} \approx {\cal T} \xi/L$. The total random force acting on the bulge is a random variable with zero mean and standard deviation $F_{\rm R} = \hat{f} \sqrt{\xi L}$. Comparing the random and the restoring force defines a characteristic length, the so-called pinning length, given by $$L_{\rm p} = \left(\frac{\cal T}{\hat{f}}\right)^{2/3} \xi^{1/3}
\label{eq:lpin}$$ Below this length, the restoring force prevails, i.e., the line is bound to remain essentially straight. On scales above this length, the line will in the absence of an external driving force wander by an amount of the order of $\xi$ to reach the nearest energy minimum. For an initially straight line parallel to the $y$ axis this leads to a characteristic line shape where the line is straight but inclined on scales below $L_{\rm 