Mathematical Physics Seminar (Dec 7th) – Dr Suropriya Saha – Scalar active mixtures: the non-reciprocal Cahn-Hilliard model

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. Further, we explore the notion of nonlinear non-reciprocity and consider a model in which the non-reciprocal interactions can depend on the local values of the scalar fields. For generic cases where such couplings exist, we observe the emergence of spatiotemporal chaos in the steady-state associated with a local restoration of PT symmetry in fluctuating spatial domains.

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