Wave coarsening drives time crystallization in mechatronic metamaterials

Abstract

When metals are magnetized1, emulsions phase separate2, or galaxies cluster3, domain walls and patterns form and irremediably coarsen over time. This coarsening is universally driven by diffusive relaxation towards equilibrium. Here we discover a vibrational counterpart—wave coarsening—in active elastic media4–13: vibrations emerge and spontaneously grow in wavelength, period and amplitude, before a globally synchronized state called a time crystal14–17 forms. We observe wave coarsening in one- and two-dimensional mechatronic metamaterials 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 modes18–24. Our results open new questions about the transient physics of systems with non-potential interactions15,25–28 and suggest an organizing principle for nonlinear waves in acoustics29,30, optomechanics31,32, living matter6,33 and soft robotics9. Wave coarsening in active elastic media is a phenomenon in which vibrations spontaneously increase in wavelength, period and amplitude before forming a globally synchronized time crystal.