Scaling and vortex-string dynamics in a three-dimensional system with a continuous symmetry

We study the dynamics of a three-dimensional system with a nonconserved complex order parameter (r,t), following a quench below the ordering transition temperature. For a critical quench [(r,0)=0] we observe dynamical scaling and an effective value of the dynamical exponent of =0.45±0.01. For an off-critical quench [(r,0)0] there is a breakdown of dynamical scaling and the vortex-string length l(t) varies with time t as l(t)t-1exp(-t3/2), in good agreement with a theoretical calculation by Toyoki and Honda. The predicted relation (r,0)2 is found to represent only a lower bound. We indicate the possible relevance of these results for liquid-crystal systems and cosmological pattern formation.