Direct mapping of nonreciprocal discrete models using simple acoustic networks

A plethora of works in classical wave systems is dedicated to mimicking phenomena inspired by discrete models, typically originating from condensed matter physics. The most common approach is to “discretize” a continuous medium in order to reproduce the behavior of a given discrete model. This is usually achieved by introducing resonators and arranging them in periodic configurations that satisfy certain geometrical symmetries. Here, we present an alternative, broadband, and resonator-free method for discretizing space using networks of waveguides. This approach enables the construction of very simple configurations that can directly emulate a wide range of discrete models, capturing not only their edge or skin modes but their entire spectrum—while preserving their symmetries. As an example, I will discuss the theoretical and experimental realization of the Hatano-Nelson model in acoustic waveguides, using two different resonator-free configurations.