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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{VUU_2024_34_2_a6,
     author = {Yu. P. Chuburin and T. S. Tinyukova},
     title = {Spectral properties and {non-Hermitian} skin effect in the {Hatano{\textendash}Nelson} model},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {286--298},
     publisher = {mathdoc},
     volume = {34},
     number = {2},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a6/}
}
TY  - JOUR
AU  - Yu. P. Chuburin
AU  - T. S. Tinyukova
TI  - Spectral properties and non-Hermitian skin effect in the Hatano–Nelson model
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2024
SP  - 286
EP  - 298
VL  - 34
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a6/
LA  - en
ID  - VUU_2024_34_2_a6
ER  - 
%0 Journal Article
%A Yu. P. Chuburin
%A T. S. Tinyukova
%T Spectral properties and non-Hermitian skin effect in the Hatano–Nelson model
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2024
%P 286-298
%V 34
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2024_34_2_a6/
%G en
%F VUU_2024_34_2_a6
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/