标题： 波浪粗化在活性固体中驱动时间晶体形成 显示英文标题

标题： Wave coarsening drives time crystallization in active solids

摘要： 当金属被磁化、乳状液相分离或星系聚集时，域壁和图案形成，并随着时间不可逆地粗化。 这种粗化普遍是由向平衡状态的扩散弛豫驱动的。 在这里，我们在活性弹性介质中发现了一种惯性对应物——波粗化，其中振动出现并自发地增长波长、周期和振幅，直到形成一个称为时间晶体的全局同步状态。 我们在一维和二维固体中观察到波粗化，并捕捉其动力学标度。 我们进一步通过打破动量守恒来阻止这一过程，并揭示了手性拓扑边缘模式的一个远离平衡的非线性类比。 我们的工作揭示了对称性在时间晶体形成中的关键作用，并为控制活性材料中的非线性振动开辟了新途径。 显示英文摘要

摘要： When metals are magnetized, emulsions phase separate, or galaxies cluster, domain walls and patterns form and irremediably coarsen over time. Such coarsening is universally driven by diffusive relaxation toward equilibrium. Here, we discover an inertial counterpart - wave coarsening - in active elastic media, where vibrations emerge and spontaneously grow in wavelength, period, and amplitude, before a globally synchronized state called a time crystal forms. We observe wave coarsening in one- and two-dimensional solids and capture its dynamical scaling. We further arrest the process by breaking momentum conservation and reveal a far-from-equilibrium nonlinear analogue to chiral topological edge modes. Our work unveils the crucial role of symmetries in the formation of time crystals and opens avenues for the control of nonlinear vibrations in active materials.