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Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic…

Mesoscale and Nanoscale Physics · Physics 2019-08-13 Kohei Kawabata , Takumi Bessho , Masatoshi Sato

Exceptional points (EPs) are central to non-Hermitian physics because of their unique properties and broad application prospects. While extensively studied in parity-time ($\mathcal{P}\mathcal{T}$)-symmetric systems and under Markovian…

Optics · Physics 2026-01-15 H. Z. Shen , X. C. Zhang , L. Y. Ning , Zhi-Guang Lu , Yan-Hui Zhou , Cheng Shang

Non-hermitian quantum systems can exhibit spectral degeneracies known as exceptional points, where two or more eigenvectors coalesce, leading to a non-diagonalizable Jordan block. It is known that symmetries can enhance the abundance of…

Quantum Physics · Physics 2022-11-15 Robin Schäfer , Jan C. Budich , David J. Luitz

Non-Hermitian systems always play a negative role in wave manipulations due to inherent non-conservation of energy as well as loss of information. Recently, however, there has been a paradigm shift on utilizing non-Hermitian systems to…

Classical Physics · Physics 2016-05-17 Yi-Fan Zhu , Xue-Feng Zhu , Xu-Dong Fan , Bin Liang , Xin-Ye Zou , Jing Yang , Jian-Chun Cheng

Temporal interfaces introduced by abrupt switching of the constitutive parameters of unbounded media enable unusual wave phenomena. So far, their explorations have been mostly limited to lossless media. Yet, non-Hermitian phenomena…

Optics · Physics 2021-10-08 Huanan Li , Shixiong Yin , Emanuele Galiffi , Andrea Alù

Recently, presence of hidden singularities known as exceptional points (EPs) in non-Hermitian quantum systems has opened up a tremendous interest in different domains of physics owing to their unique unconventional physical effects.…

Optics · Physics 2016-03-08 Arnab Laha , Somnath Ghosh

Using techniques of supersymmetric quantum mechanics, scattering properties of Hermitian Hamiltonians, which are related to non-Hermitian ones by similarity transformations, are studied. We have found that the scattering matrix of the…

Quantum Physics · Physics 2011-09-16 Boris F. Samsonov

This paper shows that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate…

Mathematical Physics · Physics 2023-08-14 Habib Ammari , Silvio Barandun , Bryn Davies , Erik Orvehed Hiltunen , Ping Liu

Non-Hermitian Hamiltonians with complex eigenenergies are useful tools for describing the dynamics of open quantum systems. In particular, parity and time (PT) symmetric Hamiltonians have generated interest due to the emergence of…

The interaction between electromagnetic waves and objects is strongly affected by the shape and material composition of the latter. Artificially created materials, formed by a subwavelength structuring of their unit cells, namely…

Classical Physics · Physics 2018-02-07 Dmitry Filonov , Andrey Shmidt , Amir Boag , Pavel Ginzburg

Non-Hermitian systems and their topological singularities, such as exceptional points (EPs), lines, and surfaces, have recently attracted intense interest. The investigation of these exceptional constituents has led to fruitful…

Optics · Physics 2024-08-08 Liang Fang , Kai Bai , Cheng Guo , Tian-Rui Liu , Jia-Zheng Li , Meng Xiao

The fascinating realm of non-Hermitian physics with the interplay of parity (P) and time-reversal (T) symmetry has been witnessing immense attention in exploring unconventional physics at Exceptional Point (EP) singularities. Particularly,…

Optics · Physics 2024-05-20 Dinesh Beniwal , Arnab Laha , Adam Miranowicz , Somnath Ghosh

The scattering matrix $S$ obeys the unitary relation $S^\dagger S=1$ in a Hermitian system and the symmetry property ${\cal PT}S{\cal PT}=S^{-1}$ in a Parity-Time (${\cal PT}$) symmetric system. Here we report a different symmetry relation…

Optics · Physics 2016-10-25 Li Ge , Liang Feng

This paper is concerned with non-Hermitian degeneracy and exceptional points associated with resonances in an acoustic scattering problem with sound-hard obstacles. The aim is to find non-Hermitian degenerate (defective) resonances using…

Mathematical Physics · Physics 2025-12-12 Kei Matsushima , Takayuki Yamada

We investigate the scattering properties of an anti-parity-symmetric non-Hermitian system. The anti-parity-symmetric scattering center possesses imaginary nearest-neighbor hoppings and real onsite potentials, it has been experimentally…

Optics · Physics 2018-09-30 L. Jin

Exceptional points (EP) in non-Hermitian systems have been widely investigated due to their enhanced sensitivity in comparison to standard systems. In this letter, we report the observation of higher-order pseudo-Hermitian degeneracies in…

Applied Physics · Physics 2023-05-02 Ke Yin , Xianglin Hao , Yuangen Huang , Jianlong Zou , Xikui Ma , Tianyu Dong

Non-Hermitian systems have attracted significant interest because of their intriguing and useful properties, including exceptional points (EPs), where eigenvalues and the corresponding eigenstates of non-Hermitian operators become…

Quantum Physics · Physics 2025-03-28 Hamed Ghaemi-Dizicheh , Shahram Dehdashti , Andreas Hanke , Ahmed Touhami , Janis Nötzel

$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by…

The continuous advancements in ultrafast lasers, characterized by high pulse energy, great average power, and ultrashort pulse duration, have opened up new frontiers and applications in various fields such as high-energy-density science. In…

Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through…

Optics · Physics 2016-07-27 Li Ge