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 constant acceleration, subsequently decaying acceleration, 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. 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.

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• Non-reciprocal propagation
• Topological effects in acoustic systems
• Topological effects in photonic systems
• 1-dimensional systems
• Lattices
• Non-Hermitian systems
• Schroedinger equation