Non-diffusion transport in decoherent non-Hermitian quasicrystals
Disorder and coherence jointly govern wave transport in complex media. In Hermitian systems, a long-established paradigm since Anderson's work holds that disorder-induced localization relies on phase-coherent interference, and that the loss of coherence inevitably suppresses localization and restores featureless diffusive transport at long times. Whether this intuition remains valid in non-Hermitian systems, where transport can be governed by dissipation rather than interference, has remained largely open. Here we theoretically and experimentally demonstrate that this paradigm fundamentally breaks down in decoherent non-Hermitian quasicrystals. Using a programmable photonic lattice with independently engineered dissipation and fully programmable dephasing, we access regimes spanning from fully coherent to fully incoherent dynamics. While decoherence washes out localization and enforces structureless diffusion in Hermitian lattices, we find that decoherent non-Hermitian quasicrystals retain nontrivial, non-diffusive transport structures even in the incoherent limit. These include dissipation-induced localization, diffusion-localization transitions, and decoherence-induced mobility edges, phenomena with no counterparts in Hermitian disordered systems. We develop a unified theoretical framework that captures the ensemble-averaged dynamics across the entire coherence landscape, continuously connecting coherent and incoherent regimes, and reveals how dissipation and decoherence cooperate to shape transport. Our results establish decoherent non-Hermitian lattices as a distinct class of transport systems, in which dissipation and incoherence generate structured, non-diffusive phases, beyond the conventional Anderson picture.