From ballistic to Brownian vortex motion in complex oscillatory media

We show that the breaking of the rotation symmetry of spiral waves in two-dimensional complex (period-doubled or chaotic) oscillatory media by synchronization defect lines (SDL) is accompanied by an intrinsic drift of the pattern. Single vortex motion changes from ballistic flights at a well-defined angle from the SDL to Brownian-like diffusion when the turbulent character of the medium increases. It gives rise, in non-turbulent multi-spiral regimes, to a novel ``vortex liquid''.