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. 450. 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 (-t^3/2), 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.