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 {Ψ}(r,t), following a quench below the ordering transition temperature. For a critical quench [〈{Ψ}(r,0)〉=0] we observe dynamical scaling and an effective value of the dynamical exponent of {φ}=0.45±{}0.01. For an off-critical quench [〈{Ψ}(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(-{γ}t3/2), in good agreement with a theoretical calculation by Toyoki and Honda. The predicted relation {γ}{∝}{}〈{Ψ}(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.