  We study synchronization of a room temperature optomechanical system formed
by two resonators coupled via radiation pressure to the same driven optical
cavity mode. By using stochastic Langevin equations and effective
slowly-varying amplitude equations, we explore the long-time dynamics of the
system. We see that thermal noise can induce significant non-Gaussian dynamical
properties, including the coexistence of multi-stable synchronized limit cycles
and phase diffusion. Synchronization in this optomechanical system is very
robust with respect to thermal noise: in fact, even though each oscillator
phase progressively diffuses over the whole limit cycle, their phase difference
is locked, and such a phase correlation remains strong in the presence of
thermal noise.
