# Wave coarsening drives time crystallization in active solids

## TL;DR

This paper uncovers a novel wave coarsening phenomenon in active elastic media, leading to the formation of time crystals through spontaneous growth of vibrations, highlighting the role of symmetries in non-equilibrium systems.

## Contribution

It introduces wave coarsening as an inertial mechanism for time crystal formation in active solids, expanding understanding of non-equilibrium pattern dynamics.

## Key findings

- Wave coarsening observed in 1D and 2D active solids
- Dynamical scaling laws for wave coarsening established
- Breaking momentum conservation reveals topological edge modes

## Abstract

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.