Observation of erratic non-Hermitian skin localization and transport

Abstract Localization is a pervasive phenomenon across physics, shaping transport from electrons in solids to light and sound in engineered media. In traditional settings, disorder strongly impedes transport, resulting in dynamical localization or, at best, sub-ballistic or diffusive dynamics. A distinct regime, erratic non-Hermitian skin localization (ENHSL), can arise in globally reciprocal non-Hermitian lattices with disorder. It features macroscopic, disorder-dependent localization at irregular bulk positions with subexponential decay, linked to stochastic interfaces governed by the universal order statistics of random walks. We realize this regime experimentally in an acoustic lattice implementing a disordered Hatano-Nelson chain with imaginary gauge fields. Using Green’s-function-based spectroscopy together with time-resolved measurements on the same platform, we reconstruct the full complex spectrum and eigenstates, and directly observe wave-packet dynamics. We observe ballistic transport despite strong spectral localization. We develop a transport theory that connects the dominant propagation site to the maximal random-walk excursion within an expanding light cone and predicts a universal Lévy-arcsine statistics, in quantitative agreement with experiment. Our results decouple eigenstate localization from transport and establish ENHSL as a new paradigm for wave dynamics.