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The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a non-analytical behavior at singular (exceptional) points (EPs). The…

Quantum Physics · Physics 2016-04-27 H. Eleuch , I. Rotter

Non-Hermitian Hamiltonians can give rise to exceptional points (EPs) which have been extensively explored with nominally identical coupled resonators. Here a non-Hermitian electromechanical system is developed which hosts vibration modes…

Mesoscale and Nanoscale Physics · Physics 2019-02-06 P. Renault , H. Yamaguchi , I. Mahboob

In contrast to Hermitian systems, eigenstates of non-Hermitian ones are in general nonorthogonal. This feature is most pronounced at exceptional points where several eigenstates are linearly dependent. In this work we show that near this…

Quantum Physics · Physics 2016-12-23 Alexander A. Zyablovsky , Evgeny S. Andrianov , Alexander A. Pukhov

Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the…

Mathematical Physics · Physics 2007-05-23 B. Bagchi , C. Quesne

A comment has been recently posted on the arXiv (arXiv:1902.07504) that discuss our recent work on encircling multiple exceptional points in Nat. Commun. 9, 4808 (2018). In that comment, the authors claim that our approach is prone to…

Quantum Physics · Physics 2019-03-19 Q. Zhong , M. Khajavikhan , D. N. Christodoulides , R. El-Ganainy

We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…

Quantum Physics · Physics 2015-05-14 Ali Mostafazadeh

This paper explores quantum field theories with pseudo-Hermitian Hamiltonians, where PT-symmetric Hamiltonians serve as a special case. In specific regimes, these pseudo-Hermitian Hamiltonians have real eigenspectra, orthogonal eigenstates,…

High Energy Physics - Theory · Physics 2024-04-04 Esra Sablevice , Peter Millington

The metric associated with a quasi-Hermitian Hamiltonian and its physical implications are scrutinised. Consequences of the non-uniqueness such as the question of the probability interpretation and the possible and forbidden choices of…

Quantum Physics · Physics 2007-10-31 H. B. Geyer , W. D. Heiss , F. G. Scholtz

Band structures of metamaterials described by a nonlinear eigenvalue problem are beyond the existing topological band theory. In this paper, we analyze non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we elucidate…

Mesoscale and Nanoscale Physics · Physics 2025-02-19 Tsuneya Yoshida , Takuma Isobe , Yasuhiro Hatsugai

Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have great impact on eigenvalue spectra of non-Hermitian random matrices. Here, we show that time-reversal…

Disordered Systems and Neural Networks · Physics 2022-12-21 Zhenyu Xiao , Kohei Kawabata , Xunlong Luo , Tomi Ohtsuki , Ryuichi Shindou

We explore an alternative way of finding the link between a PT non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of the scattering problem for an imaginary potential and its time reversal process, it is shown that any…

Quantum Physics · Physics 2011-06-02 L. Jin , Z. Song

We propose that the real spectrum and the orthogonality of the states for several known complex potentials of both types, PT-symmetric and non-PT-symmetric can be understood in terms of currently proposed $\eta$-pseudo-Hermiticity…

Quantum Physics · Physics 2009-11-07 Zafar Ahmed

Non-Hermitian PT-symmetric models have been extensively studied in recent years. Following the seminal work that reduced classical random matrix ensembles to a tridiagonal form, several efforts have aimed to generalize this framework to…

Statistical Mechanics · Physics 2025-11-13 Cleverson Andrade Goulart , Gleb Oshanin , Mauricio Porto Pato

Recently some authors have broadened the scope of canonical quantum mechanics by replacing the conventional Hermiticity condition on the Hamiltonian by a weaker requirement through the introduction of the notion of pseudo-Hermiticity. In…

Quantum Physics · Physics 2009-11-07 Ram Narayan Deb , Avinash Khare , Binayak Dutta Roy

We calculate eigenvector statistics in an ensemble of non-Hermitian matrices describing open quantum systems [F. Haake et al., Z. Phys. B 88, 359 (1992)] in the limit of large matrix size. We show that ensemble-averaged eigenvector…

Mesoscale and Nanoscale Physics · Physics 2009-10-31 B. Mehlig , M. Santer

The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts. In this work, we focus on one such aspect, the difference of evolving quantum ensembles under $H_{\mathrm{nh}}$…

Quantum Physics · Physics 2025-10-03 Soumik Bandyopadhyay , Philipp Hauke , Sudipto Singha Roy

We explore a way of finding the link between a non-Hermitian Hamiltonian and a Hermitian one. Based on the analysis of Bethe Ansatz solutions for a class of non-Hermitian Hamiltonians and the scattering problems for the corresponding…

Quantum Physics · Physics 2011-11-11 L. Jin , Z. Song

Topological states in non-Hermitian systems are known to exhibit some anomalous features. Here, we find two new anomalous features of non-Hermitian topological states. We consider a one dimensional nonreciprocal Hamiltonian and show that…

Mesoscale and Nanoscale Physics · Physics 2020-03-18 C. Yuce

Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads…

Quantum Physics · Physics 2023-06-13 Jung-Wan Ryu , Jae-Ho Han , Chang-Hwan Yi , Moon Jip Park , Hee Chul Park

A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can…

Mathematical Physics · Physics 2009-10-28 Scott Chapman