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

Abstract

We propose a general framework that enables the exact mapping of continuous nonreciprocal 1D periodic systems to the Hatano-Nelson (HN) model. Our approach, based on the two-port transfer matrix, is broadband and is applicable across various physical systems and, as an illustration, we consider the implementation of our model in acoustic waveguides. Through theoretical analysis and experimental demonstrations, we successfully achieve the mapping to the HN model by utilizing active acoustic elements, thereby observing the renowned skin effect. Moreover, our experimental setup enables the exploration of the transition from periodic to open boundary conditions by employing diaphragms of varying radii. Our experimental results, unveil the exponential sensitivity of the system to changes in boundary conditions. By establishing a profound connection between continuous systems and the fundamental discrete HN model, our results significantly broaden the potential application of nonreciprocal wave systems and the underlying phenomena.

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Cited by in corpus (10)

• Insensitive edge solitons in a non-Hermitian topological lattice
• Localized states and skin effect around non-Hermitian impurities in tight-binding models
• Autoregressive neural quantum states of Fermi Hubbard models
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
• Nonlinear skin breathing modes in one-dimensional nonreciprocal mechanical lattices
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Wave propagation in an elastic lattice with non-reciprocal stiffness and engineered damping
• Scaling of pseudospectra in exponentially sensitive lattices
• Acoustic scattering singularities via quasi-Bound states in the continuum
• Insensitive nonreciprocal edge breathers