To better understand vortex pinning in thin superconducting slabs, we study the interaction of a single fluctuating vortex filament with a curved line defect in $(1+1)$ dimensions. This problem is also relevant to the interaction of scratches with wandering step edges in vicinal surfaces. The equilibrium probability density for a fluctuating line attracted to a particular fixed defect trajectory is derived analytically by mapping the problem to a straight line defect in the presence of a space and time-varying external tilt field. The consequences of both rapid and slow changes in the frozen defect trajectory, as well as finite size effects are discussed. A sudden change in the defect direction leads to a delocalization transition, accompanied by a divergence in the trapping length, near a critical angle.

• Received 10 January 2006

DOI:https://doi.org/10.1103/PhysRevB.73.214503