Related papers: Elliptical torii in a constant magnetic field
We derive the closed form solutions for the surface area, the capacitance and the demagnetizing factors of the ellipsoid immersed in the Euclidean space R^3. The exact solutions for the above geometrical and physical properties of the…
The exact wave functions, which describe the states of an electron, bound in the image potential, and the magnetic field, which is perpendicular to surface of a metal, are obtained. The correction terms to the energy of an electron in the…
We present a partial differential equation describing the electromagnetic potentials around a charge distribution undergoing rigid motion at constant proper acceleration, and obtain a set of solutions to this equation. These solutions are…
The three-dimensional characterization of magnetic flux-ropes observed in the heliosphere has been a challenging task for decades. This is mainly due to the limitation to infer the 3D global topology and the physical properties from the 1D…
We construct the Hermitian Schr\"{o}dinger Hamiltonian of spin-less as well as the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field that are confined to cylindrical and spherical surfaces. The approach does…
The search for Noether point symmetries for non-relativistic charged particle motion is reduced to the solution for a set of two coupled, linear partial differential equations for the electromagnetic field. These equations are completely…
An axisymmetric space-localized solution of nonlinear electrodynamics is considered as massive charged particle with spin and magnetic moment. The appropriate solution for nonlinear electrodynamics with ring singularity is investigated. In…
We consider the equilibrium equations for a conducting elastic rod placed in a uniform magnetic field, motivated by the problem of electrodynamic space tethers. When expressed in body coordinates the equations are found to sit in a…
We study a nonlinear and nonlocal elliptic equation posed on the flat torus. While constant solutions always exist, we show that uniqueness fails in general. Using spectral analysis and the Crandall--Rabinowitz bifurcation theorem, we prove…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
The intertwining technique has been widely used to study the Schr\"odinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the…
It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a…
This paper studies the problem of finding a three-dimensional solenoidal vector field such that both the vector field and its curl are tangential to a given family of toroidal surfaces. We show that this question can be translated into the…
A short-ranged, rotationally symmetric multi-Landau-level model Hamiltonian for strongly interacting electrons in a magnetic field was proposed [A. Anand et al, Phys. Rev. Lett. 126, 136601 (2021)] with the key feature that it allows exact…
We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed…
The article treats the classical problem of stability of steady rotation of a rigid homogeneous ellipsoid on a rigid smooth plane which rotates about its vertical axis. The condition for the steady rotation is derived from the Euler-Poisson…
We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…
We develop a quaternionic electrodynamics and show that it naturally supports the existence of magnetic monopoles. We obtained the field equations, the continuity equation, the electrodynamic force law, the Poynting vector, the energy…
We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary…
The Schroedinger equation for a spinless charged particle on a curved surface under an electromagnetic field has been obtained by adopting a proper gauge which allows the separation of the on-surface and transverse dynamics. [Phys. Rev.…