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Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model

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Suropriya,  Saha
Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Agudo-Canalejo,  Jaime
Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Golestanian,  Ramin
Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Suropriya, S., Agudo-Canalejo, J., & Golestanian, R. (2020). Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model. Physical Review X, 10: 041009. doi:10.1103/PhysRevX.10.041009.


Cite as: http://hdl.handle.net/21.11116/0000-0007-7514-F
Abstract
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.