Condensed Matter Theory

Abstract:

We study the behavior of catalytically active droplets in multicomponent conserved mixtures affected by noise. Working in the thin interface limit, we analytically determine the state diagram of the system, characterized by multiple dynamical regimes, and verify our findings using numerical simulations. In particular, we show the emergence of a nonreciprocal, chemically mediated interaction between the droplets, which leads to the formation of (meta)stable clusters of droplets of different species. We find that the clusters can display self-propulsion in a large part of the parameter space, including regions where the nonreciprocal interactions between the droplets are purely attractive. This surprising feature arises from the nonlocal nature of the chemical interactions, and points to locality violations as a general mechanism for energy dissipation and emergence of out-of-equilibrium steady states in active matter.

Abstract:

We present the phenomenology of the one-dimensional nonreciprocal Cahn-Hilliard model for varying nonreciprocity $\left(\alpha \right)$ and different boundary conditions. At small $\alpha$ , a perturbed uniform state evolves to a defect-laden configuration that lacks global polar order. Defects are the sources and sinks of traveling waves. For a given $\alpha$ , defects with a unique wave number that increases monotonically with $\alpha$ are selected. A critical threshold ${\alpha }_c$ marks the onset of a transition to states with finite global polar order. For periodic boundary conditions, above ${\alpha }_c$ , the system shows traveling waves that are completely ordered. In contrast, traveling waves are incompatible with the Neumann and Dirichlet boundary conditions. Instead, for $\alpha \gtrsim {\alpha }_c$ , we find fluctuating domains that show intermittent polar order, and at large $\alpha$ , the system partitions into two domains with opposite polar order.