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Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks
Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The dif...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8470989/ https://www.ncbi.nlm.nih.gov/pubmed/34573770 http://dx.doi.org/10.3390/e23091145 |
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author | Tian, Zhiyu Liu, Yang Luo, Le |
author_facet | Tian, Zhiyu Liu, Yang Luo, Le |
author_sort | Tian, Zhiyu |
collection | PubMed |
description | Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems. |
format | Online Article Text |
id | pubmed-8470989 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-84709892021-09-27 Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks Tian, Zhiyu Liu, Yang Luo, Le Entropy (Basel) Article Non-Hermitian topological edge states have many intriguing properties, however, to date, they have mainly been discussed in terms of bulk–boundary correspondence. Here, we propose using a bulk property of diffusion coefficients for probing the topological states and exploring their dynamics. The diffusion coefficient was found to show unique features with the topological phase transitions driven by parity–time (PT)-symmetric non-Hermitian discrete-time quantum walks as well as by Hermitian ones, despite the fact that artificial boundaries are not constructed by an inhomogeneous quantum walk. For a Hermitian system, a turning point and abrupt change appears in the diffusion coefficient when the system is approaching the topological phase transition, while it remains stable in the trivial topological state. For a non-Hermitian system, except for the feature associated with the topological transition, the diffusion coefficient in the PT-symmetric-broken phase demonstrates an abrupt change with a peak structure. In addition, the Shannon entropy of the quantum walk is found to exhibit a direct correlation with the diffusion coefficient. The numerical results presented herein may open up a new avenue for studying the topological state in non-Hermitian quantum walk systems. MDPI 2021-08-31 /pmc/articles/PMC8470989/ /pubmed/34573770 http://dx.doi.org/10.3390/e23091145 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Tian, Zhiyu Liu, Yang Luo, Le Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks |
title | Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks |
title_full | Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks |
title_fullStr | Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks |
title_full_unstemmed | Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks |
title_short | Shannon Entropy and Diffusion Coefficient in Parity-Time Symmetric Quantum Walks |
title_sort | shannon entropy and diffusion coefficient in parity-time symmetric quantum walks |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8470989/ https://www.ncbi.nlm.nih.gov/pubmed/34573770 http://dx.doi.org/10.3390/e23091145 |
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