Related papers: On the Properties of Phononic Eigenvalue Problems
We study real resonances and embedded eigenvalues of the Kramers--Fokker--Planck operator with a long-range potential. We prove that thresholds are only possible accumulation points of eigenvalues and that the limiting absorption principle…
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of…
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…
In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the "eigenvalues" of the decision variable. Here, by making use of the FTvN systems framework introduced by…
The aim of this paper is to study the existence of eigenvalues in the gap of the essential spectrum of the one-dimensional Dirac operator in the presence of a bounded potential. We employ a generalized variational principle to prove…
In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…
In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation…
A fundamental problem in the theory of PT-invariant quantum systems is to determine whether a given system `respects' this symmetry or not. If not, the system usually develops non-real eigenvalues. It is shown in this contribution how to…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…
Horn's problem, i.e., the study of the eigenvalues of the sum $C=A+B$ of two matrices, given the spectrum of $A$ and of $B$, is re-examined, comparing the case of real symmetric, complex Hermitian and self-dual quaternionic $3\times 3$…
This paper presents some new results on the eigenvalues of the spheroidal wave equation. We study the angular and Coulomb spheroidal wave equation as a special case of a more general linear Hamiltonian system depending on three parameters.…
We present a perturbative method for calculating phonon properties of an insulator in the presence of a finite electric field. The starting point is a variational total-energy functional with a field-coupling term that represents the effect…
The existence of potentials for relativistic Schrodinger operators allowing eigenvalues embedded in the essential spectrum is a long-standing open problem. We construct Neumann-Wigner type potentials for the massive relativistic Schrodinger…
The optical properties of defects in solids produce rich physics, from gemstone coloration to single-photon emission for quantum networks. Essential to describing optical transitions is electron-phonon coupling, which can be predicted from…
Maps between Riemannian manifolds which are submersions on a dense subset, are studied by means of the eigenvalues of the pull-back of the target metrics, the first fundamental form. Expressions for the derivatives of these eigenvalues…
A systematic analytic approach to the evaluation of the eigenvalues and eigenvectors of the 5D discrete number operator is formulated. This approach is essentially based on the use of the symmetricity of 5D discrete Fourier transform…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
We study bandstructure properties of periodic optical systems composed of lossy and intrinsically dispersive materials. To this end, we develop an analytical framework based on adjoint modes of a lossy periodic electromagnetic system and…