Nonlinear non-Hermitian skin effect

Abstract

Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin effect with nonlinear effects can give rise to a host of novel phenomenas, which may be used for nonlinear structure designs. Here we study nonlinear non-Hermitian skin effect and explore nonlocal and substantial effects of edges on stationary nonlinear solutions. We show that fractal and continuum bands arise in a long lattice governed by a nonreciprocal discrete nonlinear Schrodinger equation. We show that stationary solutions are localized at the edge in the continuum band. We consider a non-Hermitian Ablowitz-Ladik model and show that nonlinear exceptional point disappears if the lattice is infinitely long.

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References in corpus (5)

• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Eigenstate clustering around exceptional points
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Cited by in corpus (21)

• Topological Non-Hermitian skin effect
• Anomalous single-mode lasing induced by nonlinearity and the non-Hermitian skin effect
• Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase
• Nonlinear Non-Hermitian Skin Effect and Skin Solitons in Temporal Photonic Feedforward Lattices
• Skin modes in a nonlinear Hatano-Nelson model
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• The non-Hermitian skin effect: A perspective
• Insensitive edge solitons in a non-Hermitian topological lattice
• Observation of size-dependent boundary effects in non-Hermitian electric circuits
• Non-Hermitian edge burst without skin localizations
• The simulation of non-Hermitian disordered system in linear circuits
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• From scale-free to Anderson localization: a size-dependent transition
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Nonreciprocal amplification toward chaos in a chain of Duffing oscillators
• Nonlinear skin breathing modes in one-dimensional nonreciprocal mechanical lattices
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Insensitive nonreciprocal edge breathers