Compositional disorder in a multicomponent non-reciprocal mixture: stability and patterns

TL;DR

This paper explores how non-reciprocal interactions and compositional disorder influence the stability and pattern formation in multicomponent mixtures, using theoretical analysis and simulations.

Contribution

It introduces a general stability criterion for non-reciprocal mixtures with disorder, derived via random matrix theory and verified through simulations.

Findings

Non-reciprocity stabilizes the homogeneous state despite disorder.

A general condition for spinodal instability onset is derived.

Eigenvalue statistics relate to emergent nonlinear dynamics.

Abstract

The mean compositions of individual components can be tuned to control phase behavior in number-conserving passive mixtures. In this work, we investigate the role of variable average density in a system of infinitely many non-reciprocally interacting scalar densities, within the framework of the multi-species non-reciprocal Cahn-Hilliard (NRCH) model. Rather than focusing on specific parameter choices, we study ensembles of systems where the inter-species interaction coefficients and average densities are sampled from probability distributions. We show that non-reciprocity stabilizes the homogeneous mixed state even in the presence of compositional disorder. Using random matrix theory, we derive a general condition for the onset of spinodal instability, which we verify through simulations. Finally, we illustrate the connection between the statistics of the most unstable eigenvalue and the emergent nonlinear dynamics.