Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems

TL;DR

This paper investigates topological phenomena in a one-dimensional nonlinear mechanical system, demonstrating that edge states and bulk-edge correspondence can emerge even with nonlinearities, connecting nonlinear dynamics with topological physics.

Contribution

It introduces a nonlinear mechanical model connected to the SSH model and shows topological edge states can appear in nonlinear regimes, extending topological concepts beyond linear systems.

Findings

Edge states emerge in the nonlinear system's topological phase.

Quench dynamics reflect topological and trivial phases.

Bulk-edge correspondence extends to nonlinear systems.

Abstract

We study a topological physics in a one-dimensional nonlinear system by taking an instance of a mechanical rotator model with alternating spring constants. This nonlinear model is smoothly connected to an acoustic model described by the Su-Schrieffer-Heeger model in the linear limit. We numerically show that quench dynamics of the kinetic and potential energies for the nonlinear model is well understood in terms of the topological and trivial phases defined in the associated linearized model. It indicates phenomenologically the emergence of the edge state in the topological phase even for the nonlinear system, which may be the bulk-edge correspondence in nonlinear system.