Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation

TL;DR

This paper derives a universal amplitude equation for oscillatory instabilities in out-of-equilibrium systems with conservation laws, generalizing the nonreciprocal Cahn-Hilliard model and aiding classification of pattern formation.

Contribution

It introduces a universal amplitude equation for a class of oscillatory instabilities, extending the nonreciprocal Cahn-Hilliard model to a broader context.

Findings

Derivation of a universal amplitude equation for conserved-Hopf instabilities.

Connection of the equation to a hierarchy of instability types.

Potential for classifying pattern-forming systems similarly to the Ginzburg-Landau equation.

Abstract

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatio-temporal pattern formation. Starting from a linear large-scale oscillatory instability -- a conserved-Hopf instability -- that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs.\ small-scale instability, stationary vs.\ oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.