Nucleation of Defect Turbulence in the Two-dimensional Complex Ginzburg-Landau Equation

We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation towards its "frozen" state with stationary spiral structures. We are interested in the transition kinetics between a random initial configuration and the latter frozen state with a well-defined low density of quasi-stationary vortices. Nucleation is monitored using the characteristic length between the emerging shock structures. The average nucleation time for different system sizes is measured over many independent realizations to obtain good statistics. An extrapolation method as well as a phenomenological formula are employed to eliminate finite-size effects.The non-zero barrier for the nucleation of single vortex droplets in the extrapolated infinite-size limit suggests that the transition to the frozen state is discontinuous. We also investigate the nucleation of target waves which emerge if a specific spatial inhomogeneity is introduced. A long "fat" tails exists in the distribution of nucleation times in this case, which suggest that the associated transition may be continuous.