Abstract

In recent years, non-reciprocally coupled systems have received growing attention. Previous work has shown that the interplay of non-reciprocal coupling and Goldstone modes can drive the emergence of temporal order such as traveling waves. We show that these phenomena are generically found in a broad class of pattern-forming systems, including mass-conserving reaction–diffusion systems and viscoelastic active gels. All these systems share a characteristic dispersion relation that acquires a non-zero imaginary part at the edge of the band of unstable modes and exhibit a regime of propagating structures (traveling wave bands or droplets). We show that models for these systems can be mapped to a common “normal form” that can be seen as a spatially extended generalization of the FitzHugh–Nagumo model, providing a unifying dynamical-systems perspective. We show that the minimal non-reciprocal Cahn–Hilliard (NRCH) equations exhibit a surprisingly rich set of behaviors, including interrupted coarsening of traveling waves without selection of a preferred wavelength and transversal undulations of wave fronts in two dimensions. We show that the emergence of traveling waves and their speed are precisely predicted from the local dispersion relation at interfaces far away from the homogeneous steady state. Our work thus generalizes previously studied non-reciprocal phase transitions and shows that interfaces are the relevant collective excitations governing the rich dynamical patterns of conserved fields.

Zoom link: https://cam-ac-uk.zoom.us/j/89523495848?pwd=TXc1Wm55cVJUYWVuZ3BmQjFVdlUxZz09

Meeting ID: 895 2349 5848 Passcode: 908714

—-