Dynamics governed by symmetry-protected exceptional rings for mechanical systems

Non-Hermitian topological phenomena occur in mechanical systems described by the Newton equation. A mechanical graphene, which is composed of mass points and springs, shows symmetry-protected exceptional rings (SPERs) in the presence of the friction. However, it remains unclear what physical properties or phenomena the SPERs induce. Our numerical analysis reveals that the SPERs can govern dynamics in the wavenumber space. Moreover, we propose how to extract the dynamics in the wavenumber space for systems with the boundaries. Furthermore, we also observe that connectivity of the SPERs changes depending on the fiction, which is analogous to the Lifshitz transition of electron systems.