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

TL;DR

This study explores wave-packet dynamics in pseudo-Hermitian lattices, revealing the coexistence of Hermitian and non-Hermitian wavefronts and their implications for unconventional phenomena and experimental observations.

Contribution

It demonstrates the natural emergence of dual wavefronts in pseudo-Hermitian systems using the Hatano-Nelson model, linking wave dynamics to non-Hermitian topology.

Findings

Dual wavefronts propagate simultaneously at different velocities.

Analytic predictions match numerical simulations.

Coexistence explains phenomena like non-Hermitian reflections and wave-packet shifts.

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.