Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise

Abstract

Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a growth process in which an interface formed by the local phase field gradually roughens and eventually saturates. Such a process is here shown to display the generic scale invariance of the one-dimensional Kardar-Parisi-Zhang universality class, including a Tracy-Widom probability distribution for phase fluctuations around their mean. This is revealed by numerical explorations of a variety of oscillator systems: rings of generic phase oscillators and rings of paradigmatic limit-cycle oscillators, like Stuart-Landau and van der Pol. It also agrees with analytical expectations derived under conditions of strong mutual coupling. The nonequilibrium critical behavior that we find is robust and transcends the details of the oscillators considered. Hence, it may well be accessible to experimental ensembles of oscillators in the presence of e.g. thermal noise.