  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.
