Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

TL;DR

This paper develops a microscopic field theory for self-propelled particles with torques, revealing how intrinsic torques influence pattern formation and phase separation in active matter systems.

Contribution

It introduces a coarse-grained dynamical field theory for particles with generic torques, linking microscopic parameters to macroscopic behavior, and analyzes stability and pattern formation.

Findings

Intrinsic torques hinder motility-induced phase separation.

Finite-sized structures form with size proportional to propulsion speed and inverse rotation frequency.

Chirality suppresses phase separation and promotes non-equilibrium patterns.

Abstract

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We perform a linear stability analysis of the homogeneous solution of the field equations and find both long-wavelength and short-wavelength instabilities. The former signals the emergence of a macroscopic structure, which we associate with motility-induced phase separation, while the second one signals the growth of a finite structure with a characteristic size. Intrinsic torques hinder phase separation, pushing the onset of the long-wavelength instability to higher activities. Further, they generate finite-sized structures with a characteristic size proportional to both the self-propulsion velocity and the inverse of the self-rotation frequency. Our results show that a general mechanism might explain why chirality tends to suppress motility-induced phase separation but instead promotes the formation of non-equilibrium patterns.