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

TL;DR

This paper investigates a nonlinear extension of the Hatano-Nelson model with periodic boundary conditions, revealing a novel growth blockade phenomenon caused by modulational instability, which halts norm growth and relates to self-induced disorder.

Contribution

It introduces the growth blockade phenomenon in the nonlinear Hatano-Nelson model with periodic boundaries, expanding understanding of nonlinear non-Hermitian lattice dynamics.

Findings

Discovered growth blockade due to modulational instability.

Linked growth blockade to self-induced disorder.

Demonstrated halted norm growth in nonlinear regime.

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.