Dynamical pattern formation in a one-dimensional nonreciprocal O(2) model

Dynamical pattern formation lies at the heart of non-equilibrium physics, underpinning processes from biological morphogenesis to collective behavior in active matter. Non-reciprocal coupling enables intrinsically dynamical steady states and provides a new route to such patterns. In our previous work [1], we established a phase diagram of a one-dimensional non-reciprocal O(2) model within its dynamically stable regime, showing that noise-induced spatiotemporal vortices profoundly alter the universal scaling. Here, we extend this framework into the dynamically unstable regime and demonstrate that a diffusion-driven instability spontaneously generates vortex lattices even without noise. Varying the diffusion-rate ratio between two species, we identify a new phase transition separating vortex-free and vortex-abundant regimes. Across this transition, phase fluctuations evolve from the stretched-exponential Edwards–Wilkinson scaling to short-range exponential decay. When adding strong enough noise, both noise-induced and diffusion-driven vortices exhibit the same temporal phase correlation, revealing a crossover to a unified regime. Together, these results establish a more complete dynamical phase diagram that connects noise-induced and diffusion-driven pattern formation, illuminating the interplay of dynamical instability, stochasticity, and broken reciprocity in non-equilibrium matter.

[1] Universal scaling in one-dimensional non-reciprocal matter, Shuoguang Liu, Ryo Hanai, Peter Littlewood, arXiv:2503.14384