Nonlinear excitations in non-Hamiltonian active solids

Many amorphous solids possess a set of soft quasilocalized excitations that control many aspects of the material's mechanical and thermodynamic properties, similar to lattice defects in crystals. In non-active systems, these quasilocalized excitations have been isolated by a nonlinear analysis of the potential energy landscape around an equilibrium reference configuration. However, in slowly rearranging dense active matter, the particle motions that allow dissipation remain unclear. Does dissipation still occur via localized deviations from a solid-like reference state? To address this question, we generalize the nonlinear mode formalism to active systems with self-propelled forces, by analyzing the global non-linear force response of the system to a given perturbation. We apply this new formalism to packings of self-propelled rods at densities well above the jamming transition, which can not be mapped to a Hamiltonian system. We numerically compute force-based soft excitations for systems with different levels of activity, and compare these with particle rearrangements that occur as a result of thermal fluctuations or mechanical perturbations like a global shear or localized force dipoles. Future extensions include applying this methodology to non-reciprocal systems, such as odd elastic materials.