Exact analog of the Hatano-Nelson model in one-dimensional continuous nonreciprocal systems

Abstract

Non-Hermitian topology offers a promising avenue toward an enhanced control of waves, and many of the underlying interesting phenomena are studied through the paradigmatic Hatano-Nelson (HN) model, which remains unexplored in continuous wave systems. Herein, we propose a framework to map one-dimensional continuous nonreciprocal systems onto the HN model. Our approach, based on the properties of transfer matrices, is applicable across various physical domains. We experimentally apply our method in audible acoustics using active elements, where we not only observe the predicted skin effect but also access the spectrum topology using stable configurations and observe its subsequent boundary sensitivity. By establishing a connection between continuous wave systems and the discrete HN model, our results significantly broaden the potential application of nonreciprocal topological phenomena.