On Using The Path Integral Formalism to Interpret Synchronization in Quantum Graph Networks

Abstract

This article explores the application of the path integral formalism in describing synchronization phenomena in entangled networks, cavities, and reservoirs. We discuss the concept of using Lagrangian mechanics for systems undergoing synchronization and its connection to least-action principles. By replacing the concept of least action with a least signaling term, we investigate how the path integral representation can be applied to study synchronization dynamics in entangled networks, drawing parallels with coupled oscillators in phase space models such as the Kuramoto model, as well as its relation to algorithms, such as the firefly algorithm for potential use in optimization in networks. This article also illustrates how entanglement signals themselves can interact strongly with ordered systems of harmonic oscillators that reach thresholds of classical synchronization with potential therefore for using entangled signals as weak measurement probes where phase dynamics is of interest.