Breaking chirality in nonequilibrium systems on the lattice

TL;DR

This paper investigates front dynamics in parametrically forced oscillating lattices, using a discrete Ginzburg-Landau model and symmetry-based reduction to understand bifurcations and pattern formation.

Contribution

It introduces a simple dynamical system derived from a normal form to analyze front bifurcations in lattice systems, extending continuum results to discrete settings.

Findings

Projection onto cylindrical phase space reveals bifurcation structures.

Derived a dynamical system capturing lattice front dynamics.

Approach applicable to other pattern-forming lattice problems.

Abstract

We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto a cylindrical phase space. Starting from a normal form that describes the nonequilibrium Ising-Bloch bifurcation in the continuum and using symmetry arguments, we derive a simple dynamical system that captures the dynamics of fronts in the lattice. We can expect our approach to be extended to other pattern-forming problems on lattices.