Two cubes suspended in an acoustic field form a coupled oscillator with a twist. The center-of-mass mode (both cubes moving together vertically) and the hinge mode (the angle between them opening and closing) are coupled non-reciprocally: the hinge affects the center of mass more than the center of mass affects the hinge.

This asymmetry stabilizes three distinct dynamical attractors — three qualitatively different long-term behaviors that the pair can settle into, depending on initial conditions. The non-reciprocity isn’t engineered; it emerges from the geometry of the acoustic radiation pressure acting on non-spherical objects. Cubes, unlike spheres, have orientational degrees of freedom that couple to translational ones in asymmetric ways.

The model was extracted from data, not derived from first principles. The researchers used trajectory measurements to fit a minimal dynamical system that captures the essential coupling. The data-driven model predicts behavior over hundreds of oscillation cycles — far beyond the training window.

Acoustic levitation is usually treated as a positioning tool: hold something in place with sound. Here it’s a dynamical laboratory. The levitated cubes aren’t static — they’re active oscillators whose emergent dynamics arise from the interaction between shape and sound. The geometry of the particle determines the symmetry of the coupling, and the coupling determines the attractor landscape.