Polar chiral active matter as a motile, disordered Josephson array: Information supercurrents and Goldstone spin...

We consider a minimalist model of polar chiral active matter: overdamped, self-propelled agents coupled through a localized Kuramoto-Sakaguchi interaction, which causes alignment. Intrinsic frustration drawn from a broad distribution constitutes a temperature for the ensemble. In the comoving frame of the local order parameter, the agent dynamics reduce exactly to the Adler equation, placing each agent in a tilted washboard potential: trapped agents are phase-synchronized, and we demonstrate thereby that synchronization (phase rigidity) is maintained by information supercurrents; agents that are running in this potential form a resistive bath. The model is therefore formally isomorphic to a disordered, resistively shunted Josephson array, and a Monte Carlo sweep over the frequency dispersion empirically recovers the disorder-broadened Adler-Ohmic crossover of the ensemble-averaged slip velocity. Lifting the dynamics from S^{1} to S^{2}, the polar alignment torque (the Kuramoto term) is geometrically equivalent to the Gilbert-damping term of the Landau-Lifshitz-Gilbert equation; the mapping establishes an effortless azimuthal precession, yielding a Goldstone-mode dispersion that carries an effective inertia ∝R^{2}, where R is the local order parameter. This furnishes a microscopic basis for the spin-wave transport assumed in inertial-spin models of flocking. Within its regime of validity, i.e., dry, polar, chiral agents under marginal synchronization with sufficient frustration, the model is well-described as a dissipative spintronic fluid.