Data driven discovery of activity-induced optical bands and vibrational mode coupling in nonreciprocal living solids

The interplays between activity, elasticity, and broken symmetries can give rise to a remarkable variety of nonequilbrium vibrational excitations in active solids. Here, we present a data driven, model agnostic method based on dynamic mode decomposition (DMD) to quantitatively characterize these excitations. Our method directly extracts the bulk vibrational dispersion relation from particle trajectory data. Applying this method to characterize oscillations in nonreciprocal living solids composed of starfish embryos, we identified optical vibrational modes in the absence of sublattice asymmetry, a notable deviation from the conventional view in condensed matter physics. A continuum model that incorporates chiral embryo precession successfully accounted for the presence of these unconventional optical modes. Furthermore, our theory predicts the presence of nonlinear interactions between optical and acoustic modes, leading to the splitting of optical bands into multiple branches. More broadly, our data driven method can serve as a robust and versatile platform to explore nonlinear, non-Hermitian, as well as topological mechanics in nonequilibrium solids.