Experimental observation of gapped shear waves and liquid-like to gas-like dynamical crossover in active granular matter

Unlike crystalline solids, liquids lack long-range order, resulting in diffusive shear fluctuations rather than propagating waves. Simulations predict that liquids exhibit a $k$-gap in wave-vector space, where solid-like transverse waves reappear above this gap. Experimental evidence in classical liquids has been limited, observed only in 2D dusty plasmas. Here, we investigate this phenomenon using active Brownian vibrators and uncover distinct gas-like and liquid-like phases depending on the packing fraction. We measure key properties, including pair correlation functions, mean square displacements, velocity auto-correlation functions, and vibrational density of states. In the liquid-like phase, we confirm the $k$-gap in transverse excitations, whose size grows as the packing fraction decreases and eventually disappears in the gas phase. Our findings extend the concept of the $k$-gap to active granular systems and reveal striking parallels with supercritical fluids.