Pair interactions between active particles need not follow Newton’s third law. In this work we propose a continuum model of pattern formation due to non-reciprocal interaction between multiple species of scalar active matter. The classical Cahn-Hilliard model is minimally modified by supplementing the equilibrium Ginzburg-Landau dynamics with particle number conserving currents which cannot be derived from a free energy, reflecting the microscopic departure from action-reaction symmetry. The strength of the asymmetry in the interaction determines whether the steady state exhibits a macroscopic phase separation or a traveling density wave displaying global polar order. The latter structure, which is equivalent to an active self-propelled smectic phase, coarsens via annihilation of defects, whereas the former structure undergoes Ostwald ripening. The emergence of traveling density waves, which is a clear signature of broken time-reversal symmetry in this active system, is a generic feature of any multi-component mixture with microscopic non-reciprocal interactions.

中文翻译：

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标量活性混合物：不可逆的Cahn-Hilliard模型

活性粒子之间的对相互作用无需遵循牛顿第三定律。在这项工作中，我们提出了一种由于多种标量活性物质之间不可逆的相互作用而形成图案的连续模型。经典的Cahn-Hilliard模型通过在平衡Ginzburg-Landau动力学上补充了粒子数守恒电流而得到了最小限度的修改，该电流不能从自由能中得出，反映了微观上背离了作用-反应对称性。相互作用中的不对称强度决定了稳态是表现出宏观的相分离还是表现出整体极性序的行进密度波。后者的结构相当于活性的自推进近晶相，通过defects灭缺陷而变粗，而前者的结构则经历了奥斯特瓦尔德熟化。