SCALING AND VORTEX-STRING DYNAMICS IN A 3-DIMENSIONAL SYSTEM WITH A CONTINUOUS SYMMETRY

We study the dynamics of a three-dimensional system with a nonconserved complex order parameter PSI(r,t), following a quench below the ordering transition temperature. For a critical quench [<PSI(r,0)> = 0] we observe dynamical scaling and an effective value of the dynamical exponent of phi = 0.45 +/- 0.01. For an off-critical quench [<PSI(r,0)> not-equal 0] there is a breakdown of dynamical scaling and the vortex-string length l(t) varies with time t as l(t) approximately t-1exp(-gamma-t3/2), in good agreement with a theoretical calculation by Toyoki and Honda. The predicted relation gamma is-proportional-to \<PHI(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.