Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization

Abstract

We consider a mechanical lattice inspired by the Su-Schrieffer-Heeger model along with cubic Klein-Gordon type nonlinearity. We investigate the long-time dynamics of the nonlinear edge states, which are obtained by nonlinear continuation of topological edge states of the linearized model. Linearly unstable edge states delocalize and lead to chaos and thermalization of the lattice. Linearly stable edge states also reach the same fate, but after a critical strength of perturbation is added to the initial edge state. We show that the thermalized lattice in all these cases shows an effective renormalization of the dispersion relation. Intriguingly, this renormalized dispersion relation displays a unique symmetry, i.e., its square is symmetric about a finite squared frequency, akin to the chiral symmetry of the linearized model.

arXiv comment16 pages, 13 figures

References in corpus (43)

• Topological Insulators
• Topological Photonics
• Nonlinear topological photonics
• Edge Solitons in Nonlinear Photonic Topological Insulators
• The Fermi-Pasta-Ulam problem: 50 years of progress
• Observation of Topological Band Gap Solitons
• Universal spreading of wavepackets in disordered nonlinear systems
• Classification of topological phonons in linear mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Statistical mechanics of a nonlinear discrete system
• A route to thermalization in the $\alpha$-Fermi-Pasta-Ulam system
• Intermittent many-body dynamics at equilibrium
• The Fermi-Pasta-Ulam problem revisited: stochasticity thresholds in nonlinear Hamiltonian systems
• New families of symplectic splitting methods for numerical integration in dynamical astronomy
• Numerical integration of variational equations
• q-Breathers in Fermi-Pasta-Ulam chains: existence, localization and stability
• Amplitude-dependent topological edge states in nonlinear phononic lattices
• High precision Symplectic Integrators for the Solar System
• Dynamical Thermalization of Disordered Nonlinear Lattices
• Nonequilibrium chaos of disordered nonlinear waves
• Renormalized waves and discrete breathers in $\beta$-FPU chains
• Double scaling in the relaxation time in the $\beta$-FPUT model
• Stability of topological edge states under strong nonlinear effects
• Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices
• Self-induced topological transition in phononic crystals by nonlinearity management
• The two-stage dynamics in the Fermi-Pasta-Ulam problem: from regular to diffusive behavior
• Statistics of wave interactions in nonlinear disordered systems
• Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices
• Disorder-induced topological phase transition in a 1D mechanical system
• Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice
• Dynamics and Statistics of the Fermi--Pasta--Ulam $\beta$--model with different ranges of particle interactions
• Modulational Estimate for Fermi-Pasta-Ulam Chain Lyapunov Exponents
• Efficient integration of the variational equations of multi-dimensional Hamiltonian systems: Application to the Fermi-Pasta-Ulam lattice
• The role of nonlinearities in topological protection: using magnetically coupled fidget spinners
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Probing band topology using modulational instability
• Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
• Chaos and localization in the Discrete Nonlinear Schrödinger Equation
• Computational efficiency of symplectic integration schemes: Application to multidimensional disordered Klein-Gordon lattices
• Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems
• Scaling of Chaos in Strongly Nonlinear Lattices
• Linear Beam Stability in Periodic Focusing Systems:Krein Signature and Band Structure
• Stability Properties of 1-Dimensional Hamiltonian Lattices with Non-analytic Potentials

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