Volume 128, Number 3, November 2019
|Number of page(s)||7|
|Published online||24 January 2020|
Aging phenomena in the two-dimensional complex Ginzburg-Landau equation
Department of Physics & Center for Soft Matter and Biological Physics (MC 0435), Robeson Hall 850 West Campus Drive, Virginia Tech, Blacksburg, VA 24061, USA
Received: 2 October 2019
Accepted: 19 November 2019
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75.Da – Systems obeying scaling laws / 64.60.-i – General studies of phase transitions
© EPLA, 2020
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