Flocking from a quantum analogy: spin–orbit coupling in an active fluid

Systems composed of strongly interacting self-propelled particles can form a spontaneously flowing polar active fluid. The study of the connection between the microscopic dynamics of a single such particle and the macroscopic dynamics of the fluid can yield insights into experimentally realizable active flows, but this connection is well understood in only a few select cases. We introduce a model of self-propelled particles based on an analogy with the motion of electrons that have strong spin–orbit coupling. We find that, within our model, self-propelled particles are subject to an analog of the Heisenberg uncertainty principle that relates translational and rotational noise. Furthermore, by coarse-graining this microscopic model, we establish expressions for the coefficients of the Toner–Tu equations—the hydrodynamic equations that describe an active fluid composed of these 'active spins.' The connection between stochastic self-propelled particles and quantum particles with spin may help realize exotic phases of matter using active fluids via analogies with systems composed of strongly correlated electrons. (paper)