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

Quantum analogues have proven to be valuable tools in the study of both equilibrium and non-equilibrium statistical systems. At their core, these analogies allow one to explore some complex classical systems in terms of simpler quantum ones, thus facilitating the use of the powerful toolkit of quantum mechanics. We enlarge on the well-known relationship between the Schrödinger equation and the diffusion equation in order to incorporate self-propulsion, and thus, to build quantum analogues of systems of two-dimensional self-propelled particles. Crucially, we show how, on the quantum side, spin and spin-orbit coupling capture both a particle’s orientation and self-propulsion. Interestingly, the microscopic active system that stems from this analogy is characterized by a coupling of translational and rotational noises, which resembles the Heisenberg uncertainty principle. Finally, by coarse-graining the microscopic model, we obtain explicit expressions for the coefficients in the Toner-Tu equations, which describe the hydrodynamic limit of the system. The connection between self-propelled particles and quantum spins may help realize exotic phases of matter using active fluids via analogies with systems composed of strongly correlated electrons.