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The defining characteristic of an exceptional point (EP) in the parameter space of a family of operators is that upon encircling the EP eigenstates are permuted. In case one encircles multiple EPs, the question arises how to properly…

Mathematical Physics · Physics 2018-08-29 Eric J. Pap , Daniël Boer , Holger Waalkens

We reveal how symmetry protected nodal points in topological semimetals may be promoted to pairs of generically stable exceptional points (EPs) by symmetry-breaking fluctuations at the onset of long-range order. This novel route to…

Strongly Correlated Electrons · Physics 2023-10-09 Lorenzo Crippa , Giorgio Sangiovanni , Jan Carl Budich

Exceptional points (EPs) are non-Hermitian spectral degeneracies marking a simultaneous coalescence of eigenvalues and eigenvectors. Despite the fact that multiband $n$-fold EPs (EP$n$s) generically emerge as special points on manifolds of…

Optics · Physics 2026-03-16 Anton Montag , Jordan Isaacs , Marcus Stålhammar , Flore K. Kunst

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept…

Mesoscale and Nanoscale Physics · Physics 2021-03-03 Emil J. Bergholtz , Jan Carl Budich , Flore K. Kunst

Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external…

Quantum Physics · Physics 2024-05-28 Kun Ding , Chen Fang , Guancong Ma

We show that analytic continuation of the number of colors, Nc, naturally endows Yang-Mills theory with a non-Hermitian structure. By examining the spectrum of the dilatation operator as a function of complex Nc, we identify a network of…

High Energy Physics - Theory · Physics 2026-03-20 Qingjun Jin , Ke Ren , Gang Yang , Rui Yu

Exceptional points (EPs) -- spectral singularities of non-Hermitian linear systems -- have recently attracted great interest for sensing. While initial proposals and experiments focused on enhanced sensitivities neglecting noise, subsequent…

Optics · Physics 2022-07-13 K. J. H. Peters , S. R. K. Rodriguez

The exceptional points (EPs) aroused from the non-Hermiticity bring rich phenomena, such as exceptional nodal topologies, unidirectional invisibility, single-mode lasing, sensitivity enhancement and energy harvesting. Isolated high-order…

Quantum Physics · Physics 2024-01-19 Yang Wu , Yunhan Wang , Xiangyu Ye , Wenquan Liu , Zhibo Niu , Chang-Kui Duan , Ya Wang , Xing Rong , Jiangfeng Du

Topological operations have the merit of achieving certain goals without requiring accurate control over local operational details. To date, topological operations have been used to control geometric phases, and have been proposed as a…

Optics · Physics 2016-09-13 H. Xu , D. Mason , L. Jiang , J. G. E. Harris

Complex spectra of dissipative quantum systems may exhibit degeneracies known as exceptional points (EPs). At these points the systems' dynamics may undergo drastic changes. Phenomena associated with EPs and their applications have been…

Quantum Physics · Physics 2025-03-19 Andrei I. Pavlov , Yuval Gefen , Alexander Shnirman

The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…

Optics · Physics 2021-03-16 Alex Krasnok , Nikita Nefedkin , Andrea Alu

Enantiodetection is an important and challenging task across natural science. Nowadays, some chiroptical methods of enantiodetection based on decoherence-free cyclic three-level models of chiral molecules can reach the ultimate limit of the…

Quantum Physics · Physics 2022-11-29 Chong Ye , Xiaowei Mu , Yifan Sun , Libin Fu , Xiangdong Zhang

A novel anti-P-pseudo-Hermitian mechanical system that integrates piezoelectric actuators and sensors with non-reciprocal coupling into mechanical beams is proposed. This configuration enables the system to exhibit programmable exceptional…

Applied Physics · Physics 2026-03-10 Yanzheng Wang , Jianlei Zhao , Qian Wu , Xiaoming Zhou , Heng Jiang , Weiqiu Chen , Mu Wang , Guoliang Huang

The dynamics of open quantum systems described by the Lindblad master equation follows according to non-Hermitian operators. As a result, such systems can host non-Hermitian degeneracies called Liouvillian exceptional points (EPs). In this…

Quantum Physics · Physics 2025-10-10 Sayooj P , Awadhesh Narayan

Non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity due to exceptional points and robustness of topological zero energy modes, and it is unclear which one prevails under different…

Optics · Physics 2022-03-08 I. Komis , D. Kaltsas , S. Xia , H. Buljan , Z. Chen , K. G. Makris

We investigate the existence of higher order exceptional points (EPs) in non-Hermitian systems, and show that $\mu$-fold EPs are stable in $\mu-1$ dimensions in the presence of anti-unitary symmetries that are local in parameter space, such…

Mesoscale and Nanoscale Physics · Physics 2021-10-27 Pierre Delplace , Tsuneya Yoshida , Yasuhiro Hatsugai

The notion of synthetic dimensions has expanded the realm of topological physics to four dimensional (4D) space lately. In this work, non-Hermiticity is used as a synthetic parameter in PT-symmetric photonic crystals to study the…

Optics · Physics 2020-01-16 Qiang Wang , Kun Ding , Hui Liu , Shining Zhu , C. T. Chan

It is conjectured that the exceptional-point (EP) singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a…

Quantum Physics · Physics 2020-04-16 Miloslav Znojil

Exceptional points are interesting physical phenomena in non-Hermitian physics at which the eigenvalues are degenerate and the eigenvectors coalesce. In this paper, we find that the universal feature of arbitrary non-Hermitian two level…

Quantum Physics · Physics 2022-01-25 X. R. Wang , F. Yang , X. J. Yu , X. Q. Tong , S. P. Kou

The existence of exceptional points (EPs) ${-}$ where both eigenvalues and eigenvectors converge ${-}$ is a key characteristic of non-Hermitian physics. A newly-discovered class of magnets ${-}$ termed as altermagnets (AMs) ${-}$ are…

Mesoscale and Nanoscale Physics · Physics 2024-12-04 Md Afsar Reja , Awadhesh Narayan
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