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

TL;DR

This paper introduces a quantum-inspired model of self-propelled particles with spin-orbit coupling, linking microscopic dynamics to macroscopic active fluid behavior and deriving hydrodynamic equations.

Contribution

It presents a novel analogy between active particles and quantum spins, deriving hydrodynamic coefficients from a microscopic model.

Findings

Particles exhibit an uncertainty principle relating translational and rotational noise.

Derived expressions for Toner-Tu hydrodynamic coefficients.

Potential to realize exotic matter phases using active fluids.

Abstract

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 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.