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

Abstract

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 co-moving 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 $\propto R^2$, 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.