Aging phenomena in the two-dimensional complex Ginzburg-Landau equation

TL;DR

This study investigates aging phenomena and slow coarsening dynamics in the two-dimensional complex Ginzburg-Landau equation with noise, revealing non-universal aging scaling and conditions for slow dynamics in non-equilibrium systems.

Contribution

It provides the first detailed numerical analysis of aging and coarsening in the noisy 2D complex Ginzburg-Landau equation, identifying key scaling behaviors and criteria for slow dynamics.

Findings

Slow coarsening dynamics observed after quenching into the defocusing regime

Aging scaling behavior characterized by non-universal exponents

Slow aging kinetics also identified in the focusing regime

Abstract

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics when the system is quenched into the "defocusing spiral quadrant". We observe slow coarsening dynamics as oppositely charged topological defects annihilate each other, and characterize the ensuing aging scaling behavior. We conclude that the physical aging features in this system are governed by non-universal aging scaling exponents. We also investigate systems with control parameters residing in the "focusing quadrant", and identify slow aging kinetics in that regime as well. We provide heuristic criteria for the existence of slow coarsening dynamics and physical aging behavior in the complex Ginzburg-Landau equation.