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Systems composed of strongly interacting self-propelled particles can form aspontaneously flowing polar active fluid. The study of the connection betweenthe microscopic dynamics of a single such particle and the macroscopic dynamicsof the fluid can yield insights into experimentally realizable active flows,but this connection is well understood in only a few select cases. We introducea model of self-propelled particles based on an analogy with the motion ofelectrons that have strong spin-orbit coupling. We find that, within our model,self-propelled particles are subject to an analog of the Heisenberg uncertaintyprinciple that relates translational and rotational noise. Furthermore, bycoarse-graining this microscopic model, we establish expressions for thecoefficients of the Toner-Tu equations---the hydrodynamic equations thatdescribe an active fluid composed of these "active spins." The connectionbetween self-propelled particles and quantum spins may help realize exoticphases of matter using active fluids via analogies with systems composed ofstrongly correlated electrons.

Flocking from a quantum analogy: Spin-orbit coupling in an active fluid