Spin dynamics of walkers in a rotating bath

We investigate a hydrodynamic analog system exhibiting wave-mediated interactions of spins in a rotating frame. Liquid droplets ('walkers') may walk across a vertically vibrating liquid surface, propelled by resonant interactions with their own wavefield. Their trajectories can be trapped within the surface of submerged circular wells in a fluid bath, locked into orbits centered around the wells. We study a system where these wells are arranged in a 1D lattice, with thin fluid layers allowing interactions between neighboring walkers. Let the bath be rotating with some velocity 'w'. We use the Preisach model to forward a mathematical framework that explains why individual walkers tend towards aligning with the polarity of the rotating bath (Sáenz et. al., Phys. Rev. Fluids 3, 100508). Our model defines the hydrodynamic analogs of remanence, coercivity and energy loss over a cycle, as is common in magnetic hysteresis studies and predicts their expected values. We predict that the dependence of the averaged spin (S) on 'w' mirrors that of the magnetization of a ferromagnet in an external magnetic field. Lastly, we show how the evolution of spin of a single walker in a rotating bath should be expected to mirror that of a solitary magnetic dipole's moment in a magnetic field.