Document Type
Article
Publication Date
2023
Abstract
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.
Recommended Citation
Yuce, C., and H. Ramezani. "Non-Hermitian skin effect in two dimensional continuous systems." Physica Scripta 98, no. 1 (2022): 015005. https://doi.org/10.1088/1402-4896/aca43b
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Publication Title
Physica Scripta
DOI
10.1088/1402-4896/aca43b
Comments
As the Version of Record of this article is going to be / has been published on a subscription basis, this Accepted Manuscript will be available for reuse under a CC BY-NC-ND 3.0 licence after the 12 month embargo period.