State Diagram of the Non-Reciprocal Cahn-Hilliard Model and the Effects of Symmetry

Abstract

Interactions between active particles may be non-reciprocal, breaking action-reaction symmetry and leading to novel physics not observed in equilibrium systems. The non-reciprocalCahn-Hilliard (NRCH) model is a phenomenological model that captures the large-scale effects of non-reciprocity in conserved, phase-separating systems. In this work, we explore the consequences of different variations of this model corresponding to different symmetries, inspired by the importance of symmetry in equilibrium universality classes. In particular, we contrast two models, one with a continuous SO(2) symmetry and one with a discrete C_4 symmetry. We analyze the corresponding models by constructing three-dimensional linear stability diagrams. With this, we connect the models with their equilibrium limits, highlight the role of mean composition, and classify qualitatively different instabilities. We further demonstrate how non-reciprocity gives rise to out-of-equilibrium steady states with non-zero currents and present representative closed-form solutions that help us understand characteristic features of the models in different parts of the parameter space.

References in corpus (27)

• The physics of exceptional points
• Non-reciprocal phase transitions
• Odd dynamics of living chiral crystals
• Nonreciprocity as a generic route to traveling states
• Odd Viscosity and Odd Elasticity
• Active phase separation in mixtures of chemically interacting particles
• Scalar Active Mixtures: The Non-Reciprocal Cahn-Hilliard Model
• Exceptional Points in Atomic Spectra
• Self-assembly of Active Colloidal Molecules with Dynamic Function
• Nonreciprocal pattern formation of conserved fields
• Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
• Dynamical pattern formation without self-attraction in quorum-sensing active matter: the interplay between nonreciprocity and motility
• Self-organization of primitive metabolic cycles due to non-reciprocal interactions
• Nonreciprocal Ising model
• Nonreciprocal Synchronization of Active Quantum Spins
• Nonreciprocal interactions give rise to fast cilium synchronisation in finite systems
• Universal phenomenology at critical exceptional points of nonequilibrium $O(N)$ models
• Defect Solutions of the Non-reciprocal Cahn-Hilliard Model: Spirals and Targets
• Escaping kinetic traps using non-reciprocal interactions
• Network effects lead to self-organization in metabolic cycles of self-repelling catalysts
• Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation laws
• Enhanced stability and chaotic condensates in multi-species non-reciprocal mixtures
• Interaction-motif-based classification of self-organizing metabolic cycles
• Phase Transitions in Nonreciprocal Driven-Dissipative Condensates
• Photoinduced non-reciprocal magnetism
• Fluctuation Dissipation Relations for Active Field Theories
• Fluctuation Dissipation Relations for the Non-Reciprocal Cahn-Hilliard Model