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

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.

Spontaneous demixing of chiral active mixtures in motility-induced phase separation

“…At high densities and activities, MIPS [52,53] generally occurs in active matter without explicit local alignment interactions, whereby self-propelled particles tend to accumulate and form a dense phase. Active torques (or chiralities) can strongly influence MIPS; for example, they can significantly suppress MIPS [9,[54][55][56]. We will focus on studying the spontaneous separation of chiral active mixtures in MIPS.…”

Microscopic theory for hyperuniformity in two-dimensional chiral active fluid

“…One of the standard methods is to derive a set of closed equations for the averaged hydrodynamic fields with an appropriate closure procedure of the hierarchical equations [58][59][60][61]. This method has been applied to chiral active fluids to investigate the instabilities [42,57,[62][63][64]. However, since our interest is fluctuations of hydrodynamic fields in the homogeneous states, we need to construct the Langevin equations for the hydrodynamic fields.…”

Chiral active matter in external potentials

“…20 In channel geometries, chirality is also responsible for the reduction of the accumulation near boundaries typical of active systems and for the formation of surface currents. 21,22 In the case of interacting systems, chirality is able to suppress the clustering typical of active particles [23][24][25][26] but induces novel phenomena, such as emergent vortices induced by the chirality 27,28 or a global traveling wave in the presence of a chemotactic alignment. 29 Chiral active particles exhibit fascinating phenomena also in the presence of alignment interactions giving rise to pattern formation 30,31 consisting of rotating macro-droplets, 32 chiral self-recognition, 33 dynamical frustration, 34 and chimera states.…”