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We propose a general framework that enables the exact mapping of continuousnonreciprocal 1D periodic systems to the Hatano-Nelson (HN) model. Ourapproach, based on the two-port transfer matrix, is broadband and is applicableacross various physical systems and, as an illustration, we consider theimplementation of our model in acoustic waveguides. Through theoreticalanalysis and experimental demonstrations, we successfully achieve the mappingto the HN model by utilizing active acoustic elements, thereby observing therenowned skin effect. Moreover, our experimental setup enables the explorationof the transition from periodic to open boundary conditions by employingdiaphragms of varying radii. Our experimental results, unveil the exponentialsensitivity of the system to changes in boundary conditions. By establishing aprofound connection between continuous systems and the fundamental discrete HNmodel, our results significantly broaden the potential application ofnonreciprocal wave systems and the underlying phenomena.

Exact analogue of the Hatano-Nelson model in 1D continuous nonreciprocal systems