Geodesic
Spectral properties and non-Hermitian skin effect in the Hatano–Nelson model
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 286-298 Cet article a éte moissonné depuis la source Math-Net.Ru

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At present, non-Hermitian topological systems continue to be actively studed. In a rigorous approach, we study one of the key non-Hermitian systems — the Hatano–Nelson model $H$. We find the Green function for this Hamiltonian. Using the Green function, we analytically obtain the eigenvalues and eigenfunctions of $H$ for finite and semi-infinite chains, as well as for an infinite chain with a local potential. We discuss the non-Hermitian skin effect for the models mentioned above. We also describe the boundary between localized and resonant eigenfunctions (for the zero spectral parameter, this is the boundary between non-Hermitian topological phases).
Keywords: Hatano–Nelson model, eigenvalues, eigenfunctions, non-Hermitian skin effect 
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     title = {Spectral properties and {non-Hermitian} skin effect in the {Hatano{\textendash}Nelson} model},
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Yu. P. Chuburin; T. S. Tinyukova. Spectral properties and non-Hermitian skin effect in the Hatano–Nelson model. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 2, pp. 286-298. http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a6/

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