In recent years, nonreciprocally coupled systems have received growing attention. Previous work has shown that the interplay of nonreciprocal 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 nonzero 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 nonreciprocal Cahn-Hilliard 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 nonreciprocal phase transitions and shows that interfaces are the relevant collective excitations governing the rich dynamical patterns of conserved fields.

中文翻译：

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保守场的非互易模式形成

近年来，非互易耦合系统越来越受到人们的关注。先前的工作表明，不可逆耦合和戈德斯通模式的相互作用可以驱动行波等时间顺序的出现。我们表明，这些现象普遍存在于一大类图案形成系统中，包括质量守恒反应扩散系统和粘弹性活性凝胶。所有这些系统都共享一个特征色散关系，该关系在不稳定模式带的边缘获取非零虚部，并表现出传播结构（行波带或液滴）的状态。我们表明，这些系统的模型可以映射到一个常见的“范式”，该范式可以被视为 FitzHugh-Nagumo 模型的空间扩展概括，提供统一的动力系统视角。我们证明，最小不可逆 Cahn-Hilliard 方程表现出一组令人惊讶的丰富行为，包括在不选择首选波长的情况下行波的间断粗化以及二维波前的横向波动。我们表明，行波的出现及其速度可以根据远离均匀稳态的界面处的局部色散关系精确预测。因此，我们的工作概括了先前研究的不可逆相变，并表明界面是控制守恒场丰富动态模式的相关集体激发。