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Linear response theory of open systems with exceptional points
Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogona...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9174331/ https://www.ncbi.nlm.nih.gov/pubmed/35672311 http://dx.doi.org/10.1038/s41467-022-30715-8 |
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author | Hashemi, A. Busch, K. Christodoulides, D. N. Ozdemir, S. K. El-Ganainy, R. |
author_facet | Hashemi, A. Busch, K. Christodoulides, D. N. Ozdemir, S. K. El-Ganainy, R. |
author_sort | Hashemi, A. |
collection | PubMed |
description | Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M(s) with M(s) = 2, 3, …, M, depending on the choice of input and output channels. |
format | Online Article Text |
id | pubmed-9174331 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-91743312022-06-09 Linear response theory of open systems with exceptional points Hashemi, A. Busch, K. Christodoulides, D. N. Ozdemir, S. K. El-Ganainy, R. Nat Commun Article Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating the linear response is complicated due to the non-orthogonality of their eigenmodes, and the presence of exceptional points (EPs). Here, we derive a closed form series expansion of the resolvent associated with an arbitrary non-Hermitian system in terms of the ordinary and generalized eigenfunctions of the underlying Hamiltonian. This in turn reveals an interesting and previously overlooked feature of non-Hermitian systems, namely that their lineshape scaling is dictated by how the input (excitation) and output (collection) profiles are chosen. In particular, we demonstrate that a configuration with an EP of order M can exhibit a Lorentzian response or a super-Lorentzian response of order M(s) with M(s) = 2, 3, …, M, depending on the choice of input and output channels. Nature Publishing Group UK 2022-06-07 /pmc/articles/PMC9174331/ /pubmed/35672311 http://dx.doi.org/10.1038/s41467-022-30715-8 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Hashemi, A. Busch, K. Christodoulides, D. N. Ozdemir, S. K. El-Ganainy, R. Linear response theory of open systems with exceptional points |
title | Linear response theory of open systems with exceptional points |
title_full | Linear response theory of open systems with exceptional points |
title_fullStr | Linear response theory of open systems with exceptional points |
title_full_unstemmed | Linear response theory of open systems with exceptional points |
title_short | Linear response theory of open systems with exceptional points |
title_sort | linear response theory of open systems with exceptional points |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9174331/ https://www.ncbi.nlm.nih.gov/pubmed/35672311 http://dx.doi.org/10.1038/s41467-022-30715-8 |
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