Measurement and Memory in the Periodically Driven Complex Ginzburg-Landau equation

TL;DR

This study demonstrates that classical nonlinear systems like the complex Ginzburg-Landau equation can exhibit quantum-like memory effects under external periodic perturbations, with coherence retention depending on drive parameters.

Contribution

It introduces a quantum measurement-inspired perturbation protocol to a classical nonlinear system, revealing conditions for memory retention and coherence in the vortex glass regime.

Findings

Memory effects depend on drive strength and periodicity.

System can recover original glass state under certain conditions.

Energy cascade mechanisms are influenced by perturbation parameters.

Abstract

In the present work we illustrate that classical but nonlinear systems may possess features reminiscent of quantum ones, such as memory, upon suitable external perturbation. As our prototypical example, we use the two-dimensional complex Ginzburg-Landau equation in its vortex glass regime. We impose an external drive as a perturbation mimicking a quantum measurement protocol, with a given "measurement rate" (the rate of repetition of the drive) and "mixing rate" (characterized by the intensity of the drive). Using a variety of measures, we find that the system may or may not retain its coherence, statistically retrieving its original glass state, depending on the strength and periodicity of the perturbing field. The corresponding parametric regimes and the associated energy cascade mechanisms involving the dynamics of vortex waveforms and domain boundaries are discussed.