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)∼${\mathit{t}}^{\mathrm{-}1}$exp(-γ${\mathit{t}}^{3/2}$), in good agreement with a theoretical calculation by Toyoki and Honda. The predicted relation γ∝‖〈Ψ(r,0)〉${\mathrm{\Vert }}^2$ is found to represent only a lower bound. We indicate the possible relevance of these results for liquid-crystal systems and cosmological pattern formation.