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Delocalization of a non-Hermitian quantum walk on random media in one dimension

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Title: Delocalization of a non-Hermitian quantum walk on random media in one dimension
Authors: Hatano, Naomichi Browse this author
Obuse, Hideaki Browse this author →KAKEN DB
Keywords: Localization
Hatano-Nelson model
Quantum walk
Issue Date: Dec-2021
Publisher: Elsevier
Journal Title: Annals Of Physics
Volume: 435
Start Page: 168615
Publisher DOI: 10.1016/j.aop.2021.168615
Abstract: We first review the localization-delocalization transition of a non-Hermitian random tight-binding Anderson model, called the Hatano-Nelson model. We then report a new result for a non-Hermitian extension of a discrete-time quantum walk on a one-dimensional random medium; we numerically find a delocalization transition similar to one of the Hatano-Nelson model. As a common feature to both models, at the transition point, an eigenvector gets delocalized and at the same time the corresponding energy eigenvalue (for the latter quantum-walk model, the imaginary unit times the phase of the eigenvalue of the time-evolution operator) becomes complex. One of the unique properties of the present non-Hermitian quantum walk is that the localization length of all eigenvectors is the same, and thereby all eigenstates simultaneously undergo the delocalization transition and all energy eigenvalues become complex at the same time when we turn up a non-Hermitian parameter.
Rights: © <2021>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Type: article (author version)
Appears in Collections:工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 小布施 秀明

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