Vortex Glass and Vortex Liquid in Oscillatory Media

TL;DR

This paper reveals that disordered multi-spiral states in oscillatory media, previously thought static, are actually dynamic on ultra-slow timescales, exhibiting vortex liquid and vortex glass phases.

Contribution

It demonstrates the existence of true defect-mediated turbulence in oscillatory media by reducing the complex Ginzburg-Landau equation to vortex dynamics.

Findings

Disordered states evolve on ultra-slow timescales.

Identification of vortex liquid with normal diffusion.

Discovery of a slowly relaxing vortex glass phase.

Abstract

We study the disordered, multi-spiral solutions of two-dimensional homogeneous oscillatory media for parameter values at which the single spiral/vortex solution is fully stable. In the framework of the complex Ginzburg-Landau (CGLE) equation, we show that these states, heretofore believed to be static, actually evolve on ultra-slow timescales. This is achieved via a reduction of the CGLE to the evolution of the sole vortex position and phase coordinates. This true defect-mediated turbulence occurs in two distinct phases, a vortex liquid characterized by normal diffusion of individual spirals, and a slowly relaxing, intermittent, ``vortex glass''.