The analogue of the Hatano-Nelson model in active acoustic lattices

In this work, we show how an exact mapping to the Hatano-Nelson model can be achieved using acoustic waveguides with periodically arranged active (electro-acoustic) elements. Due to the exact mapping, we are able to exhibit experimentally the interesting physics predicted by the model, i.e., the skin-modes, the formation of a loop-like spectrum in the case of periodic boundaries, and finally the exponential sensitivity to boundary conditions with respect to the number of unit cells. Extensions of the model to more complex scenario, especially the extension to a non-reciprocal topological 1-D lattice are also discussed. Among various implementations already existing in the literature, we believe that our method is advantageous since it is broadband (no resonances needed to achieve the discrete model) and can be made stable even with periodic boundaries which constitute an important element in the study of non-Hermitian periodic systems.