The Motile Josephson Array: Bridging Active Turbulence and Superconductivity

Abstract: Recent minimalist modeling has demonstrated that overdamped polar chiral active matter can support an emergent, inviscid Euler turbulence, despite the system's strictly dissipative microscopic nature. In this letter, we establish the statistical mechanical foundation for the emergent inertial regime by deriving a formal isomorphism between the model's agent dynamics and the overdamped Langevin equation for disordered Josephson junctions. We identify the trapped agent state as a macroscopic superconducting phase governed by the Adler equation. The validity of this mapping is confirmed analytically by a disorder-broadened Adler-Ohmic crossover in the system's slip velocity, corresponding to the saddle-node bifurcation of phase-locking systems. These results define the new minimal chiral flocking model as a motile, disordered Josephson array, bridging active turbulence and quantum superconductivity.