Dynamics in an emergent quantum-like state space generated by a nonlinear classical network

Abstract In recent work we have developed a theory for classical systems that mimic the state space of quantum systems. We call the states ‘quantum-like’ (QL) because they show many properties similar to those of a quantum system. Here we study the QL states of a large classical system comprising a network of coupled phase oscillators. In particular, we seek to understand how the nonlinearity of the classical system manifests in the linear representation of the state space. To that end, we study how a classical network is viewed from the perspective of the time evolution of its emergent state. We investigate how mixedness of the QL states diminish or increase as the underlying classical system synchronizes or de-synchronizes respectively. In the limit of a very strongly phase-locked classical network—that is, where couplings between phase oscillators are very large—the state space evolves according to unitary dynamics. When the system is set up so that the classical phase oscillators synchronize with time, we find that the purity measure of the QL states correspondingly increases. Whereas, in cases where the coupling between oscillators is too small to allow the network to synchronize, the classical variables act like a kind of environment that promotes dephasing of initially-prepared superpositions.