Active energy transport and the role of symmetry breaking in microscopic power grid

We study the transfer of energy through a network of coupled oscillators, which represents a minimalmicroscopic power grid connecting multiple active quantum machines. We evaluate the resulting energy currentsin the macroscopic, thermal, and quantum regime and describe how transport is affected by the competitionbetween coherent and incoherent processes and nonlinear saturation effects. Specifically, we show that thetransfer of energy through such networks is strongly influenced by a nonequilibrium phase transition between anoise-dominated and a coherent transport regime. This transition is associated with the formation and breakingof spatial symmetries and is identified as a generic feature of active networks. Therefore, these findings haveimportant practical consequences for the distribution of energy over coherent microwave, optical, or phononicchannels, in particular close to or at the quantum limit