Related papers: On Maximum Focused Electric Energy in Bounded Regi…
The bound states of a system consisting of two heavy identical atoms and one light electron interacting through the finite-range pairwise potentials are explored, focusing on their dependence on the electron-atom scattering length. In the…
The dynamics of a charged relativistic particle in electromagnetic field of a rotating magnetized celestial body with the magnetic axis inclined to the axis of rotation is studied. The covariant Lagrangian function in the rotating reference…
For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix, and the distance energy is defined as the sum of the absolute values of the eigenvalues of its distance matrix. We establish lower and…
Theoretically, the electric field becomes infinite at corners of two and three dimensions and edges of three dimensions. Conventional finite-element and boundary element methods do not yield satisfactory results at close proximity to these…
The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the…
We study the ground state energy of the Neumann magnetic Laplacian on planar domains. For a constant magnetic field we consider the question whether, under an assumption of fixed area, the disc maximizes this eigenvalue. More generally, we…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
The fundamental solution of the Dirac equation for an electron in an electromagnetic field with harmonic dependence on space-time coordinates is obtained. The field is composed of three standing plane harmonic waves with mutually orthogonal…
We provide a theoretical framework to describe the dynamics of a free-electron beam interacting with quantized bound systems in arbitrary electromagnetic environments. This expands the quantum optics toolbox to incorporate free-electron…
Given a set of points $P$ and axis-aligned rectangles $\mathcal{R}$ in the plane, a point $p \in P$ is called \emph{exposed} if it lies outside all rectangles in $\mathcal{R}$. In the \emph{max-exposure problem}, given an integer parameter…
The bound states of a particle in a lens-shaped quantum dot with finite confinement potential are obtained in the envelope function approximation. The quantum dot has circular base with radius $a$ and maximum cap height $b$, and the…
Spin-conserving and spin-flip opaque reflections of electrons from a potential barrier in heterostructures are described. An electric field of the barrier is considered to be the only source of energy spin splitting in the presence of…
Within the framework of Hilbert space theory, we derive a maximum-power variational principle applicable to classical spontaneous radiation from prescribed harmonic current sources. Results are first derived in the paraxial limit, then…
In the context of Born-Infeld electrodynamics, the electromagnetic fields interact with each other via their non-linear couplings. A calculation will be performed where an incoming electromagnetic plane wave scatters off a Coulomb Field in…
The electric and magnetic fields of a spatio-temporally varying electric current loop are calculated using the Jefimenko equations. The radiation and the nonradiation parts of the electromagnetic fields are derived in the framework of…
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach…
Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron…
We revisit the matching conditions for self-guided laser pulse propagation in plasma and refine their formulation to maximize the energy of electrons produced via laser wakefield acceleration. Bayesian optimization, combined with…
Second moment beam widths are commonly used in paraxial optics to define the focal extent of beams. However, second moments of arbitrary beams are not guaranteed to be finite. I propose the focal concentration area as a measure of beam…
We report a mathematically rigorous technique which facilitates the optimization of various optical properties of electromagnetic fields. The technique exploits the linearity of electromagnetic fields along with the quadratic nature of…