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

We consider a minimalist model of polar chiral active matter consisting of a spatially distributed ensemble of phase-slaved, overdamped, self-propelled agents whose phase dynamics follow a localized Kuramoto-Sakaguchi coupling. Importantly, the agents’ chirality is widely distributed, constituting noise for the ensemble. We derive a formal isomorphism between the model and the overdamped Langevin equation of a disordered, resistively shunted Josephson array, placing individual agents in a tilted washboard potential. Agents that are trapped in this potential are locally phase-synchronized, whereas `slipping’ agents that are not trapped feature a quantifiable phase slip velocity, and are subsequently constantly accumulating phase. We demonstrate that phase rigidity is maintained by information supercurrents. We perform a linearisation of the underlying Vlasov-Fokker-Planck equation, which identifies a kinetic Turing instability in the agent ensemble that selects a finite wavelength for the reordering of the active bath. Varying the dispersion in intrinsic oscillator frequencies, we perform a Monte-Carlo simulation that produces a disorder-broadened Adler-Ohmic crossover in the ensemble-averaged slip velocity, in agreement with the Josephson junction prediction. Lastly, we show that the polar alignment torque of the hypothesized 3D agent dynamics (going from $S^1$ to $S^3$ is equivalent to the Gilbert-damping term of the Landau-Lifshitz-Gilbert equation; azimuthal precession yields a Goldstone-mode in which the conservative response carries an effective inertia proportional to order parameter squared. This result provides a microscopic basis for the spin-wave transport assumed in inertial-spin models of flocking. Within its regime of validity (dry, polar, chiral agents under marginal synchronisation and with sufficient noise), the model is well-described as a dissipative spintronic fluid.