Non-Hermitian jumps, manifested as abrupt wave-packet relocations arising from mode competition between spatially separated localized eigenmodes with different imaginary eigenenergies, constitute a unique dynamical phenomenon absent in Hermitian systems. These jumps are commonly thought to require strong non-Hermitian disorder to generate such competing eigenmodes. Here, using a parity-time ($\mathcal{PT}$)-symmetric Su–Schrieffer–Heeger model with Hermitian off-diagonal disorder and balanced onsite gain and loss, we show that reduced lattice connectivity allows non-Hermitian jumps to emerge even in the presence of weak disorder. Furthermore, when the disorder-induced spread of the hopping parameters overlaps with both $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken phases, wave dynamics undergo a transition from localized oscillations to non-Hermitian jumps. Our results demonstrate how the interplay of $\mathcal{PT}$ symmetry and disorder shapes wave dynamics, providing a pathway to programmable and robust directional transport in non-Hermitian systems, with potential applications in photonics, quantum information, and signal processing.

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• Localization
• PT-symmetric quantum mechanics
• Disordered systems
• Non-Hermitian systems