Winding Number Instability in the Phase-Turbulence Regime of the Complex Ginzburg-Landau Equation

We give a statistical characterization of states with nonzero winding number in the phase turbulence (PT) regime of the one-dimensional complex Ginzburg-Landau equation. We find that states with winding numbers larger than critical ones are unstable in the sense that they decay to states with smaller winding numbers. The transition from phase to defect turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatiotemporally chaotic are described within the PT regime of a nonzero winding number.