Quantum mechanics

Theoretical physics

Cell biology

Biology

Active matter

Classical mechanics

Statistical physics

Physics

Scalar (mathematics)

Mathematics

Annihilation

Geometry

Rotational symmetry

Asymmetry

Mechanics

Physical Review X

Pair interactions between active particles need not follow Newton’s third law. In this work, we propose a continuum model of pattern formation due to nonreciprocal interaction between multiple species of scalar active matter. The classical Cahn-Hilliard model is minimally modified by supplementing the equilibrium Ginzburg-Landau dynamics with particle-number-conserving currents, which cannot be derived from a free energy, reflecting the microscopic departure from action-reaction symmetry. The strength of the asymmetry in the interaction determines whether the steady state exhibits a macroscopic phase separation or a traveling density wave displaying global polar order. The latter structure, which is equivalent to an active self-propelled smectic phase, coarsens via annihilation of defects, whereas the former structure undergoes Ostwald ripening. The emergence of traveling density waves, which is a clear signature of broken time-reversal symmetry in this active system, is a generic feature of any multicomponent mixture with microscopic nonreciprocal interactions.Received 21 May 2020Revised 11 August 2020Accepted 24 August 2020DOI:https://doi.org/10.1103/PhysRevX.10.041009Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEmergence of patternsPhysical SystemsActive matterTechniquesTheories of collective dynamics & active matterPolymers & Soft Matter

Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model