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An extensive number of the eigenstates can become exponentially localized at one boundary of nonreciprocal non-Hermitian systems. This effect is known as the non-Hermitian skin effect and has been studied mostly in tight-binding lattices. To extend the skin effect to continues systems beyond 1D, we introduce a quadratic imaginary vector potential in the continuous two dimensional Schr¨odinger equation. We find that inseparable eigenfunctions for separable nonreciprocal Hamiltonians appear under infinite boundary conditions. Introducing boundaries destroy them and hence they can only be used as quasistationary states in practice. We show that all eigenstates can be clustered at the point where the imaginary vector potential is minimum in a confined system.


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Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

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Physica Scripta





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