Topological signatures of collective dynamics and turbulent-like energy cascades in apolar active granular matter.

Active matter refers to a broad class of nonequilibrium systems where energy is continuously injected at the level of individual "particles." These systems exhibit emergent collective behaviors that have no direct thermal-equilibrium counterpart. Their scale ranges from micrometer-sized swarms of bacteria to meter-scale human crowds. In recent years, the role of topology and self-propelled topological defects in active systems has garnered significant attention, particularly in polar and nematic active matter. Building on these ideas, we investigate emergent collective dynamics in apolar active granular fluids. Using isotropic granular vibrators as a model experimental system of apolar active Ornstein-Uhlenbeck particles in a dry environment, we uncover a distinctive three-stage time evolution arising from the intricate interplay between activity and inelastic interactions. By analyzing the statistics, spatial correlations, and dynamics of vortex-like topological defects in the displacement vector field, we demonstrate their ability to describe this intrinsic collective motion. Furthermore, associated to these topological defects, we reveal the onset of a turbulent-like inverse energy cascade, where kinetic energy transfers across different length scales over time. As the system evolves, the power scaling of the energy transfer increases with the duration of observation. Our findings show that topological concepts can be extended to the nonequilibrium dynamics of apolar active matter, revealing a direct link between microscopic topological processes and emergent large-scale behaviors in active granular fluids that lack both a well-defined direction of motion and an intrinsic axis of orientation at the particle scale.