Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model

Abstract

The Hatano-Nelson model is a cornerstone of non-Hermitian physics, describing asymmetric hopping dynamics on a one-dimensional lattice, which gives rise to fascinating phenomena such as directional transport, non-Hermitian topology, and the non-Hermitian skin effect. It has been widely studied in both classical and quantum systems, with applications in condensed matter physics, photonics, and cold atomic gases. Recently, nonlinear extensions of the Hatano-Nelson model have opened a new avenue for exploring the interplay between nonlinearity and non-Hermitian effects. Particularly, in lattices with open boundary conditions, nonlinear skin modes and solitons, localized at the edge or within the bulk of the lattice, have been predicted. In this work, we examine the nonlinear extension of the Hatano-Nelson model with periodic boundary conditions and reveal a novel dynamical phenomenon arising from the modulational instability of nonlinear plane waves: growth blockade. This phenomenon is characterized by the abrupt halt of norm growth, as observed in the linear Hatano-Nelson model, and can be interpreted as a stopping of convective motion arising from self-induced disorder in the lattice.

arXiv comment14 pages, 5 figures

References in corpus (52)

• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Localization transitions in non-Hermitian quantum mechanics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Discrete Breathers
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
• Anatomy of skin modes and topology in non-Hermitian systems
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian Topological Invariants in Real Space
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Non-Hermitian topological phenomena: A review
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Topological Non-Hermitian skin effect
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Hermitian Many-Body Localization
• Robust light transport in non-Hermitian photonic lattices
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Many-body localization in a non-Hermitian quasi-periodic system
• Theory of directed localization in one dimension
• Many-body topology of non-Hermitian systems
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Non-Hermitian Many-Body Localization with Open Boundaries
• Non-Hermitian skin clusters from strong interactions
• Non-Hermitian shortcut to stimulated Raman adiabatic passage
• Non-Hermitian Mott Skin Effect
• Interaction-induced non-Hermitian topological phases from a dynamical gauge field
• Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase
• Non-Hermitian spectra and Anderson localization
• Convective and absolute PT symmetry breaking in tight-binding lattices
• Nonlinear non-Hermitian skin effect
• Exact solution of the Bose Hubbard model with unidirectional hopping
• Localization-delocalization transition in disordered systems with a direction
• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• Skin modes in a nonlinear Hatano-Nelson model
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Entanglement dynamics in the many-body Hatano-Nelson model
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Localization in an imaginary vector potential
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Full counting statistics in the many-body Hatano-Nelson model
• Complex Berry phase and imperfect non-Hermitian phase transitions
• Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model
• Hatano-Nelson model with a periodic potential
• Convective and Absolute Instabilities in the Subcritical Ginzburg-Landau Equation

Cited by in corpus (7)

• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Protected chaos in a topological lattice
• Phase Transitions in Nonreciprocal Driven-Dissipative Condensates
• Self-trapping and skin solitons in two-dimensional non-Hermitian lattices
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Nonreciprocity induced spatiotemporal chaos: Reactive vs dissipative routes