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 non-reciprocal 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 multi-component mixture with microscopic non-reciprocal interactions.
Highlights
The study of active matter [1,2] has permeated across many scientific fields, length scales, and timescales, ranging from the study of catalytic enzymes [3,4,5] and the cytoskeleton [6] inside cells, to the collective motion of cells in tissues [7] and suspensions of bacteria [8,9], all the way to the flocking of birds [10,11]
In our nonreciprocal Cahn-Hilliard (NRCH) system, we find that, while at a steady state the nonequilibrium chemical potentials μni eq are balanced in the two phases as expected, the difference in thermodynamic pressure is nonzero, indicating that an active contribution balances the equilibrium pressure
We have explored a variety of phases exhibited by scalar active mixtures with nonreciprocal interaction, which form a new class of nonequilibrium phase separation
Summary
The study of active matter [1,2] has permeated across many scientific fields, length scales, and timescales, ranging from the study of catalytic enzymes [3,4,5] and the cytoskeleton [6] inside cells, to the collective motion of cells in tissues [7] and suspensions of bacteria [8,9], all the way to the flocking of birds [10,11]. Nonreciprocal interactions are turned on, and fluid droplets of species i try to colocate with droplets of species j, while the reverse is untrue We note that in parallel to our investigation, You et al [41] have examined the effect of nonreciprocity on the dynamics of two coupled diffusing scalar fields and reported the emergence of traveling bands Their results complement our work and support the notion that scalar active mixtures with nonreciprocal interactions can generically exhibit time-reversal and polar symmetry breaking, in addition to breaking the timeand space-translation symmetries. We end with a summary and discussion of the implications and future extensions of our work
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