相关论文: Essential spectrum for Maxwell's equations

Developed in 1999 by Akemann, Anderson, and Weaver, the spectral scale of an $n\times n$ matrix $A$, is a convex, compact subset of $\mathbb{R}^3$ that reveals important spectral information about $A$ \cite{AAW}. In this paper we present…

I present the moduli space of the (2+2)-dimensional critical closed fermionic string with two world-sheet supersymmetries. The integration of fermionic and Maxwell moduli in the presence of punctures yields the string measure for n-point…

We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application…

We introduce a definition of strong hyperbolicity for second order partial differential equations using second order pencils. We show that this definition is equivalent to the standard one, derived by reducing the equations to first order…

We study wave propagation in periodic and frequency dependent materials. The approach in this paper leads to spectral analysis of a quadratic operator pencil where the spectral parameter relates to the quasimomentum and the frequency is a…

We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order…

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…

In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…

We discuss the essential spectrum of essentially self-adjoint elliptic differential operators of first order and of Laplace type operators on Riemannian vector bundles over geometrically finite orbifolds.

We consider the time-harmonic Maxwell equations at a nonzero wavenumber $k\in\mathbb{C}$ on a bounded and simply connected Lipschitz domain $\Omega$ with an analytic boundary $\Gamma$, on which we impose impedance boundary conditions. We…

We describe the spectrum of the $k$-form Laplacian on conformally cusp Riemannian manifolds. The essential spectrum is shown to vanish precisely when the $k$ and $k-1$ de Rham cohomology groups of the boundary vanish. We give Weyl-type…

We study the essential spectra of formally self-adjoint elliptic systems on doubly periodic planar domains perturbed by a semi-infinite periodic row of foreign inclusions. We show that the essential spectrum of the problem consists of the…

Let $\mathcal{A}$ be a $C^*$-algebra of bounded uniformly continuous functions on $X=\mathbb{R}^d$ such that $\mathcal{A}$ is stable under translations and contains the continuous functions that have a limit at infinity. Denote…

We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical solution of corresponding boundary value problems.

We make use of Friedrich's representation of spatial infinity to study asymptotic expansions of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is to understand the effects of the non-linearities…

We consider the time-harmonic Maxwell equations set on a domain made of two subdomains $\Omega_{-}$ and $\Omega_{+}$, such that $\Omega_{-}$ represents a magnetic conductor and $\Omega_{+}$ represents a non-magnetic material, and the…

A complete analysis of the essential spectrum of matrix-differential operators $\mathcal A$ of the form \begin{align} \begin{pmatrix} -\displaystyle{\frac{\rm d}{\rm d t}} p \displaystyle{\frac{\rm d}{\rm d t}} + q &…

In this paper we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplacian contains an interval.…

The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell's equations are…

The relation between the spectra of operator pencils with unbounded coefficients and of associated linear relations is investigated. It turns out that various types of spectrum coincide and the same is true for the Weyr characteristics.…