We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. For this purpose, we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in line with recent simulation results. In addition, the theory provides analytical expressions for the spinodal corresponding to the onset of motility-induced phase separation and the associated critical point as well as for their dependence on the angular propulsion of the circle swimmers. We confirm our findings by Brownian dynamics simulations. Agreement between results from theory and simulations is found to be good.

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The angular velocity ω introduced here is equivalent to ω0 in Ref. 68.

107.

From here onwards, summation over indices appearing twice in a term is implied.

108.

Actually, a matrix-like diffusion coefficient and a mixing of spatial derivatives were obtained during the derivation. However, the nondiagonal terms cancel each other out, since the diffusion matrix was built upon two base matrices: the Kronecker delta δij and the later introduced antisymmetric two-dimensional Levi–Civita symbol ϵij given by Eq. (19). For the special case of a second-order-derivatives model, no contributions from ϵij can occur due to its properties. For higher-order models, there exist a tensorial diffusion coefficient and mixing of spatial derivatives.

109.

In the supplementary material, we provide videos of MIPS occurring in systems of circle swimmers.

Supplementary Material

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