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Collider experiments often exploit information about the quantum numbers of final state hadrons to maximize their sensitivity, with applications ranging from the use of tracking information (electric charge) for precision jet substructure…
Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many…
It was recently suggested -- based on general self-consistency arguments as well as results from the bootstrap (arXiv:2005.07708, arXiv:2007.11539, arXiv:2007.04190) -- that the CFT describing the $Q$-state Potts model is logarithmic for…
The nontrivial degeneracies in non-Hermitian systems, exceptional points (EPs), have attracted extensive attention due to intriguing phenomena. Compared with commonly observed second-order EPs, high-order EPs show rich physics due to their…
A simple, general and practically exact method, Entanglement Perturbation Theory (EPT), is formulated to calculate the ground states of 2D macroscopic quantum systems with translational symmetry. An emphasis will be placed on the…
Our concern is the study of degenerate Hopf bifurcation of smooth planar dynamical systems near isolated singular points. To do so, we propose to split up the definition of degeneracy into two types. Degeneracy of first kind shall means…
We study quasiscarring phenomenon and mode branching at an exceptional point (EP) in typically deformed microcavities. It is shown that quasiscarred (QS) modes are dominant in some mode group and their pattern can be understood by…
Exceptional points (EPs) have been suggested for ultra-sensitive sensing because the eigenfrequency splitting grows as the nth-root of a perturbation, suggesting divergent responsivity. In ideal linear devices, however, this responsivity…
Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still…
The XY spin chain is a paradigmatic example of a model solved by free fermions, in which the energy eigenspectrum is built from combinations of quasi-energies. In this article we show that by extending the XY model's anisotropy parameter…
Recent studies on non-Hermitian optical systems having exceptional points (EPs) have revealed a host of unique characteristics associated with these singularities, including unidirectional invisibility, chiral mode switching and laser…
We investigate the degeneracy of the central configuration formed by a regular $n$-gon of equal masses together with an additional mass at the center. While degeneracy of such configurations has traditionally been studied through direct…
Non-Hermitian systems host band degeneracies that are fundamentally distinct from those in Hermitian systems, most notably exceptional points (EPs) where both eigenvalues and eigenvectors coalesce. In three dimensional (3D) non-Hermitian…
We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by…
Exceptional points are special parameter points in spectra of open quantum systems, at which resonance energies degenerate and the associated eigenvectors coalesce. Typical examples are Rydberg systems in parallel electric and magnetic…
We construct a theory to introduce the concept of topologically robust exceptional points (EP). Starting from an ordered system with $N$ elements, we find the necessary condition to have the highest order exceptional point, namely…
Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering problems. In a slow-light periodic medium, constructed by…
We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant…
The most elementary non-Hermitian quantum square-well problem with real spectrum is considered. The Schroedinger equation is required discrete and endowed with PT-symmetric Robin (i.e., two-parametric) boundary conditions. Some of the…
We demonstrate that Liouvillian exceptional points (LEPs), previously explored only in continuous Lindbladian dynamics, also emerge in discrete brickwork completely positive trace-preserving (CPTP) circuits. By analytically solving a…