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Exceptional points and perturbation dynamic response in PT-symmetric plates.

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Title: Exceptional points and perturbation dynamic response in PT-symmetric plates.
Authors: Lai, A.1 (AUTHOR), Lim, C. W.2 (AUTHOR) bccwlim@cityu.edu.hk
Source: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. 10/1/2025, Vol. 481 Issue 2323, p1-15. 15p.
Subjects: Perturbation theory, Symmetry (Physics), Critical point theory, Active noise & vibration control, Dynamic models
Abstract: Vibration systems with parity-time (PT) symmetry can exhibit a range of unique dynamical phenomena, thereby offering new insights for vibration control and related applications. Here, we establish a PT-symmetric plate dynamic model with gain and loss. The modal coalescence and dynamical evolution near the exceptional point (EP) are investigated, and the response to perturbations at the EP is also discussed. The result shows that as the parameters traverse the EP, the eigenvalues transition from purely real to complex conjugate, while the plate migrates from the PT-symmetric phase to the PT-symmetric broken phase. Owing to the spatial distribution of gain and loss, the PT-symmetric plate cannot form a conventional standing wave and instead supports a unique unidirectional wave mode. In addition, we investigate the response to both conservative and dissipative perturbations, revealing the remarkable sensitivity of plate at the EP, where the frequency response exhibits a square-root dependence on perturbation. This characteristic highlights the potential of PT-symmetric plates for high-precision sensing applications. This work not only deepens the understanding of modal transitions and energy-balance mechanisms in PT-symmetric two-dimensional structures but also offers a theoretical foundation for leveraging the high-sensitivity features of the EP in practical engineering design. [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Exceptional points and perturbation dynamic response in PT-symmetric plates.
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  Data: <searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry+%28Physics%29%22">Symmetry (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Critical+point+theory%22">Critical point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Active+noise+%26+vibration+control%22">Active noise & vibration control</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+models%22">Dynamic models</searchLink>
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  Data: Vibration systems with parity-time (PT) symmetry can exhibit a range of unique dynamical phenomena, thereby offering new insights for vibration control and related applications. Here, we establish a PT-symmetric plate dynamic model with gain and loss. The modal coalescence and dynamical evolution near the exceptional point (EP) are investigated, and the response to perturbations at the EP is also discussed. The result shows that as the parameters traverse the EP, the eigenvalues transition from purely real to complex conjugate, while the plate migrates from the PT-symmetric phase to the PT-symmetric broken phase. Owing to the spatial distribution of gain and loss, the PT-symmetric plate cannot form a conventional standing wave and instead supports a unique unidirectional wave mode. In addition, we investigate the response to both conservative and dissipative perturbations, revealing the remarkable sensitivity of plate at the EP, where the frequency response exhibits a square-root dependence on perturbation. This characteristic highlights the potential of PT-symmetric plates for high-precision sensing applications. This work not only deepens the understanding of modal transitions and energy-balance mechanisms in PT-symmetric two-dimensional structures but also offers a theoretical foundation for leveraging the high-sensitivity features of the EP in practical engineering design. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1098/rspa.2025.0125
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        Text: English
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        Type: general
      – SubjectFull: Symmetry (Physics)
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      – SubjectFull: Critical point theory
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      – SubjectFull: Active noise & vibration control
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              Text: 10/1/2025
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              Y: 2025
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