Quench Dynamics and Bulk-Edge Correspondence in Nonlinear Mechanical Systems

Motohiko Ezawa

doi:10.7566/jpsj.90.114605

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.

Highlights

Topological insulators[1,2] were originally discovered in inorganic solid state materials
We study a topological physics in a one-dimensional nonlinear system by taking an instance of a mechanical rotator model with alternating spring constants
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

Summary

INTRODUCTION

Topological insulators[1,2] were originally discovered in inorganic solid state materials. The merit of them is that it is possible to fabricate ideal systems comparing to natural solid state materials Another merit of artificial topological systems is that nonlinearity is naturally introduced into them. It is proposed to account for the topological properties in nonlinear systems phenomenologically based on the bulk-edge correspondence well established in the linear theory[56]. There is almost no time evolution and the state remains almost localized at the edge for a topological phase. After enough time, they are well localized in the topological phase, while they are spread over the bulk in the trivial phase These phenomena are understood in terms of the emergence of the topological edge state in the topological phase.

MECHANICAL ROTATOR MODEL

LINEARIZED MODEL

NONLINEAR QUENCH DYNAMICS AND BULK-EDGE CORRESPONDENCE

DISCUSSION