Pinning Induced Fluctuations on Driven Vortices

We use a simple model to study the long time fluctuations induced by random pinning on the motion of driven non--interacting vortices. We find that vortex motion seen from the co--moving frame is diffusive and anisotropic, with velocity dependent diffusion constants. Longitudinal and transverse diffusion constants cross at a characteristic velocity where diffusion is isotropic. The diffusion front is elongated in the direction of the drive at low velocities and elongated in the transverse direction at large velocities. We find that the mobility in the driven direction is always larger than the transverse mobility, and becomes isotropic only in the large velocity limit.