Related papers: Exceptional points in two simple textbook examples
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
Exceptional points (EPs) are distinct characteristics of non-Hermitian Hamiltonians that have no counterparts in Hermitian systems. In this study, we focus on EPs in continuous systems rather than discrete non-Hermitian systems, which are…
It is shown that when dependence on the second flow of the KP hierarchy is added, the resulting semi-stationary wave function of certain points in George Wilson's adelic Grassmannian are generating functions of the exceptional Hermite…
Many novel properties of non-Hermitian systems are found at or near the exceptional points-branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce. In particular, higher-order exceptional points can result in…
We discuss the role of pseudo-fermions in the analysis of some two-dimensional models, recently introduced in connection with non self-adjoint hamiltonians. Among other aspects, we discuss the appearance of exceptional points in connection…
In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional quantum critical points will be discussed: (1). The transition between topological order and…
This expository article is an introduction to Landau's problem of bounding the derivative, knowing bounds for the function and its second derivative, and some of its variants and generalizations. Connexions with convex and functional…
The algebraic method enables one to study the properties of the spectrum of a quadratic Hamiltonian through the mathematical properties of a matrix representation called regular or adjoint. This matrix exhibits exceptional points where it…
In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
Unconventional cycles provide a useful didactic resource to discuss the second law of thermodynamics applied to thermal motors and their efficiency. In most cases they involve a negative slope, linear process that presents an adiabatic…
The classical Dirichlet problem for a second-order strongly elliptic system with constant coefficients in a Jordan domain is considered. We show that the solution of the problem can be represented as a functional series in powers of the…
We study the behaviour of solutions of ordinary differential equations of the second order with singular points, where the coefficients of the second-order derivative vanishes. In particular, we consider solutions entering a singular point…
The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived…
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…
We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the…