Scaling regimes of the one-dimensional phase turbulence in the deterministic complex Ginzburg-Landau equation

Abstract

We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this regime, the behaviour of the large wavelength modes is captured by the Kardar-Parisi-Zhang equation, determining universal scaling and statistical properties. We present numerical evidence of the existence of an additional scale-invariant regime, with dynamical scaling exponent $z=1$, emerging at scales which are intermediate between the microscopic, intrinsic to the modulational instability, and the macroscopic ones. We argue that this new regime is a signature of the universality class corresponding to the inviscid limit of the Kardar-Parisi-Zhang equation.

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Cited by in corpus (3)

• Phase diagram and universal scaling regimes of two-dimensional exciton-polariton Bose-Einstein condensates
• The non-perturbative sides of the Kardar-Parisi-Zhang equation
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree