Self-synchronization of thermal phonons at equilibrium

Self-synchronization is a ubiquitous phenomenon in nature, in which oscillators are collectively locked in frequency and phase through mutual interactions. While self-synchronization requires the forced excitation of at least one of the oscillators, we demonstrate that this mechanism spontaneously appears due to the activation from thermal fluctuations. By performing molecular dynamic simulations, we demonstrate the self-synchronization of thermal phonons in a platform supporting doped silicon resonators. We find that thermal phonons are spontaneously converging to the same frequency and phase. In addition, the dependencies to intrinsic frequency difference and coupling strength agree well with the Kuramoto model predictions. More interestingly, we find that a balance between energy dissipation resulting from phonon-phonon scattering and potential energy between oscillators is required to maintain synchronization. Finally, a wavelet transform approach corroborates the generation of coherent thermal phonons in the collective state of oscillators. Our study provides a new perspective on self-synchronization and on the relationship between fluctuations and coherence.