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This paper revisits the parametric analysis of semidefinite optimization problems with respect to the perturbation of the objective function along a fixed direction. We review the notions of invariancy set, nonlinearity interval, and…

Optimization and Control · Mathematics 2022-01-03 Jonathan D. Hauenstein , Ali Mohammad-Nezhad , Tingting Tang , Tamas Terlaky

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…

Exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, and parity-time ($\mathcal{PT}$) symmetry, reflecting balanced gain and loss in photonic systems, are paramount concepts in non-Hermitian systems. We here…

Mesoscale and Nanoscale Physics · Physics 2021-11-16 Marcus Stålhammar , Emil J. Bergholtz

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

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP…

Classical Physics · Physics 2018-06-19 Xu-Lin Zhang , Shubo Wang , Bo Hou , C. T. Chan

In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian…

Numerical Analysis · Mathematics 2016-01-20 Lie-jun Xie , Cai-lian Zhou , Song Xu

We demonstrate the existence of exceptional points of degeneracy (EPD) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram…

Optics · Physics 2017-03-22 Mohamed A. K. Othman , Vincenzo Galdi , Filippo Capolino

Exceptional points (EPs), singularities in non-Hermitian systems where eigenvalues and eigenstates coalesce, exhibit a dramatically enhanced response to perturbations compared to Hermitian degeneracies. This makes them exceptional…

Quantum Physics · Physics 2025-11-24 Shu-Xuan Wang , Zhongbo Yan

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate…

Quantum Physics · Physics 2012-10-16 Savannah Garmon , Ingrid Rotter , Naomichi Hatano , Dvira Segal

In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…

Numerical Analysis · Mathematics 2020-08-21 Tingting Hao , Manman Ma , Xuejun Xu

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

We consider the eigenvalue problem for one-dimensional linear Schr\"odinger lattices (tight-binding) with an embedded few-sites linear or nonlinear, Hamiltonian or non-conservative defect (an oligomer). Such a problem arises when…

Pattern Formation and Solitons · Physics 2015-06-12 J. D'Ambroise , P. G. Kevrekidis , S. Lepri

A generic photonic coupler with active and lossy parts, gain saturation and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to…

Exceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, corresponding eigenmodes become degenerate. Classical and quantum photonic systems with EPs have attracted tremendous attention due…

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

The concept of exceptional point (EP) is demonstrated experimentally in the case of a simple mechanical system consisting of two linearized coupled pendulums. Exceptional points correspond to specific values of the system parameters that…

Computational Physics · Physics 2024-02-08 Nicolas Even , Benoit Nennig , Gautier Lefebvre , Emmanuel Perrey-Debain

We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…

Analysis of PDEs · Mathematics 2024-01-11 Thialita M. Nascimento , Ginaldo Sá , Aelson Sobral , Eduardo V. Teixeira

Non-Hermitian phenomena offer a novel approach to analyze and interpret spectra in the presence of interactions. Using the density-matrix renormalization group (DMRG), we demonstrate the existence of exceptional points for the one-particle…

Strongly Correlated Electrons · Physics 2021-02-08 Roman Rausch , Robert Peters , Tsuneya Yoshida

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…

Dynamical Systems · Mathematics 2022-11-17 Romeo Ortega , Alexey Bobtsov , Ramon Costa-Castello , Nikolay Nikolaev

We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately…

Quantum Physics · Physics 2021-11-23 Hugo Ribeiro , Florian Marquardt