Dynamics governed by symmetry-protected exceptional rings for mechanical systems

TL;DR

This paper explores how symmetry-protected exceptional rings in non-Hermitian mechanical systems influence dynamics and connectivity, revealing new physical phenomena and methods to analyze these effects.

Contribution

It demonstrates the role of SPERs in governing dynamics in mechanical systems and proposes methods to extract and analyze these effects in systems with boundaries.

Findings

SPERs govern dynamics in wavenumber space

Connectivity of SPERs changes with friction, akin to Lifshitz transition

Proposed method to extract wavenumber space dynamics in bounded systems

Abstract

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.