We examine a non-reciprocally coupled dynamical model of a mixture of two
diffusing species. We demonstrate that nonreciprocity, which is encoded in the
model via antagonistic cross diffusivities, provides a generic mechanism for
the emergence of traveling patterns in purely diffusive systems with
conservative dynamics. In the absence of non-reciprocity, the binary fluid
mixture undergoes a phase transition from a homogeneous mixed state to a
demixed state with spatially separated regions rich in one of the two
components. Above a critical value of the parameter tuning non-reciprocity, the
static demixed pattern acquires a finite velocity, resulting in a state that
breaks both spatial and time translational symmetry, as well as the reflection
parity of the static pattern. We elucidate the generic nature of the transition
to traveling patterns using a minimal model that can be studied analytically.
Our work has direct relevance to nonequilibrium assembly in mixtures of
chemically interacting colloids that are known to exhibit non-reciprocal
effective interactions, as well as to mixtures of active and passive agents
where traveling states of the type predicted here have been observed in
simulations. It also provides insight on transitions to traveling and
oscillatory states seen in a broad range of nonreciprocal systems with
non-conservative dynamics, from reaction-diffusion and prey-predators models to
multispecies mixtures of microorganisms with antagonistic interactions.Comment: 8 pages, 3 figure
