Quench dynamics and bulk-edge correspondence in nonlinear mechanical 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.

arXiv comment5 pages, 4 figures

References in corpus (51)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Imaging topological edge states in silicon photonics
• Scheme to Achieve Silicon Topological Photonics
• Robust optical delay lines via topological protection
• Topological Acoustics
• Acoustic topological insulator and robust one-way sound transport
• Topolectrical circuit realization of topological corner modes
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Acoustic higher-order topological insulator on a Kagome lattice
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Topolectrical circuits
• Nonlinear topological photonics
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Corner states of light in photonic waveguides
• Topological phonon modes and their role in dynamic instability of microtubules
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Classification of topological phonons in linear mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Selective buckling via states of self-stress in topological metamaterials
• Realization of an acoustic third-order topological insulator
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators
• Demonstration of a 3rd order hierarchy of higher order topological states in a three-dimensional acoustic metamaterial
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Manipulation of Dirac Cones in Mechanical Graphene
• Band structure engineering and reconstruction in electric circuit networks
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
• Active topolectrical circuits
• Topological circuits of inductors and capacitors
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Imaging nodal knots in momentum space through topolectrical circuits
• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• Geared topological metamaterials with tunable mechanical stability
• Electric-circuit simulation of the Schrödinger equation and non-Hermitian quantum walks
• Phonon analogue of topological nodal semimetals
• Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits
• Edge states of mechanical diamond and its topological origin
• Weyl points of mechanical diamond
• Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics

Cited by in corpus (9)

• Nonlinear non-Hermitian higher-order topological laser
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Chiral edge soliton in nonlinear Chern systems
• Supersymmetric non-Hermitian topological interface laser
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Nonlinear dynamics of topological helicity wave in a frustrated skyrmion string
• Nonlinear topological Toda quasicrystal
• Nonlinear dynamical topological phases in Cooper-pair box array