Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices

TL;DR

This paper investigates the complex wave dynamics in nonreciprocal lattices, revealing an acceleration, a non-Hermitian jump, and uniform motion of wavepackets, supported by analytical models and numerical simulations.

Contribution

It introduces a continuum approximation capturing higher-order effects and analytically explains the non-Hermiticity-induced wave-packet jump in nonreciprocal lattices.

Findings

Wavepackets undergo initial acceleration and exponential amplification.

Existence of a non-Hermiticity-induced spatial jump without disorder.

Analytical predictions match numerical simulations accurately.

Abstract

The time evolution of initially localized wavepackets in the discrete Hatano-Nelson lattice displays a rich dynamical structure shaped by the interplay between dispersion and nonreciprocity. Our analysis reveals a characteristic evolution of the wave-packet center of mass, which undergoes an initial acceleration, subsequently slows down, and ultimately enters a regime of uniform motion, accompanied throughout by exponential amplification of the wave-packet amplitude. To capture this behavior, we develop a continuum approximation that incorporates higher-order dispersive and nonreciprocal effects and provides accurate analytical predictions across all relevant time scales. Building on this framework, we then demonstrate the existence of a non-Hermiticity-induced jump - an abrupt spatial shift of the wave-packet center even in the absence of disorder - and derive its underlying analytical foundation. The analytical predictions are in excellent agreement with direct numerical simulations of the Hatano-Nelson chain. Our results elucidate the interplay between dispersion and nonreciprocity in generating unconventional transport phenomena, and pave the way for controlling wave dynamics in nonreciprocal and non-Hermitian metamaterials.