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Russia Izhevsk
Year
2024
Volume
34
Issue
2
Pages
286-298
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Section Mathematics
Title Spectral properties and non-Hermitian skin effect in the Hatano–Nelson model
Author(-s) Chuburin Yu.P.a, Tinyukova T.S.b
Affiliations Udmurt Federal Research Center, Ural Branch of the Russian Academy of Sciencesa, Udmurt State Universityb
Abstract 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
UDC 517.958, 530.145.6, 517.984.55, 517.984.66
MSC 81Q10, 81Q15, 47A10, 47A40
DOI 10.35634/vm240207
Received 1 March 2024
Language English
Citation Chuburin Yu.P., Tinyukova T.S. Spectral properties and non-Hermitian skin effect in the Hatano–Nelson model, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2024, vol. 34, issue 2, pp. 286-298.
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