Active wave-particle clusters

Active particles are non-equilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking droplets. Such classical, active wave-particle entities (WPEs) have previously been shown to exhibit hydrodynamic analogs of many single-particle quantum systems. Inspired by the rich dynamics of strongly interacting superwalking droplets in experiments, we numerically investigate the dynamics of WPE clusters using a stroboscopic model. We find that several interacting WPEs self-organize into a stable bound cluster, reminiscent of an atomic nucleus. This active cluster exhibits a rich spectrum of collective excitations, including shape oscillations and chiral rotating modes, akin to vibrational and rotational modes of nuclear excitations, as the spatial extent of the waves and their temporal decay rate (memory) are varied. Dynamically distinct excitation modes create a common time-averaged collective wave field potential, bearing qualitative similarities with the nuclear shell model and the bag model of hadrons. For high memory and rapid spatial decay of waves, the active cluster becomes unstable and disintegrates; however, within a narrow regime of the parameter space, the cluster ejects single particles whose decay statistics follow exponential laws, reminiscent of radioactive nuclear decay. Our study uncovers a rich spectrum of dynamical behaviors in clusters of active particles, opening new avenues for exploring hydrodynamic quantum analogs in active matter systems.