Related papers: Eigenvalues collision for PT-symmetric waveguide
In this note we consider boundary value problems in electromagnetism. We prove well-posedness results for the time-harmonic Maxwell equations in the setting of Riemannian manifolds. We also consider the eigenvalue problem the homogeneous…
We show that the dynamics, in particular the Kelvin-Helmholtz (KH) instability, of an inviscid fluid with velocity shear admits Parity-Time (PT) symmetry, which provides a physical explanation to the well-known observation that the spectrum…
We describe an algebraic framework for studying the symmetry properties of integrable quantum systems on the half line. The approach is based on the introduction of boundary operators. It turns out that these operators both encode the…
Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are…
The physical situation of the collision and subsequent interaction of plane gravitational waves in a Minkowski background gives rise to a well-posed characteristic initial value problem in which initial data are specified on the two null…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
We study resonant mode conversion in the PT-symmetric multimode waveguides, where symmetry breaking manifests itself in sequential destabilization (appearance of the complex eigenvalues) of the pairs of adjacent guided modes. We show that…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
The review of the mathematical treatment of plasmon resonances as an eigenvalue problem for specific boundary integral equations is presented and general properties of plasmon spectrum are outlined. Promising applications of plasmon…
We report a study on a closed-form nonlinear parity-time symmetric optical quadrimer waveguides system with a specific coupling scheme. The system yields power saturation behavior in the modes, which may be attributed to the inherent…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent…
In this paper, by means of Birkhoff--Kellogg type Theorem in cones we address the existence of eigenvalues and the corresponding eigenvectors to a family of coupled system of thermostat type. The system is characterized by the presence of a…
The Schr\"odinger equation with a $\mathcal{PT}$-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain-loss amplitudes $\gamma$, raising the amplitude…
We investigate for a large class of nonlinear wave equations, which allow for shock wave formations, how these solutions behave when they are PT-symmetrically deformed. For real solutions we find that they are transformed into peaked…
We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the apparent existence of eigenvalues in numerical computations,…
We study self-acceleration in PT and non-PT symmetric systems. We find some novel wave effects that appear uniquely in non-Hermitian systems. We show that integrable self-accelerating waves exist if the Hamiltonian is non-Hermitian. We find…