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arXiv · 2512.15333

Wave-packet dynamics in pseudo-Hermitian lattices: Coexistence of Hermitian and non-Hermitian wavefronts

Alon Beck·Moshe Goldstein
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Abstract

This paper investigates wave-packet dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the Hermitian velocity. We show that this dual-front behavior arises naturally in systems governed by a pseudo-Hermitian Hamiltonian. Using the paradigmatic Hatano-Nelson model as our primary example, we demonstrate that this coexistence is essential for understanding a wide array of unconventional dynamical effects, including abrupt ``non-Hermitian reflections'', sudden shifts of Gaussian wave-packets, and disorder-induced emergent packets seeded by the small initial tails. We present analytic predictions that closely match numerical simulations. These results may offer new insight into the topology of non-Hermitian systems and point toward measurable experimental consequences.

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Alon Beck, Moshe Goldstein. 2025-12-17. Wave-packet dynamics in pseudo-Hermitian lattices: Coexistence of Hermitian and non-Hermitian wavefronts. https://arxiv.org/abs/2512.15333

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