Related papers: Electrostatic Equilibria on the Unit Circle via Ja…
The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
We present an approach to electronic polarization in molecular solids treated as a set of quantum systems interacting classically. Individual molecules are dealt with rigorously as quantum-mechanical systems subject to classical external…
We present a spectral method for one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including ones with irrational order, multiple fractional orders,…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
We introduce a new multivariate orthogonal polynomial which is a 2-parameter deformation of the spherical polynomial by harmonic analysis on symmetric cone. This is also regarded as a multivariate analogue of the circular Jacobi polynomial.…
Classical electrodynamics uses a dielectric constant to describe the polarization response of electromechanical systems to changes in an electric field. We generalize that description to include a wide variety of responses to changes in the…
A model to study the dynamics of colloidal particles in nonuniform electric fields is proposed. For an isolated sphere, the conditions and threshold for sustained (Quincke) rotation in a linear direct current (dc) field are determined.…
We give thorough analysis for the rotation functions of the critical orbits from which one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of the Conley-Zehnder indices of the interior and exterior…
Each of electrically charged particles testifies in favor of the existence of a kind of the magnetically charged monoparticle. As a consequence, only the corresponding mononeutrinos answer for quantization of the electric charges of all…
A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
A multiple-image method is developed to accurately calculate the electrostatic interaction between neutral dielectric particles and a uniformly charged dielectric substrate. The difference in dielectric constants between the particle and…
It is shown that the CMV Laurent polynomials associated to the sieved Jacobi polynomials on the unit circle satisfy an eigenvalue equation with respect to a first order differential operator of Dunkl type. Using this result, the sieved…
We consider orthogonal polynomials on the unit circle with respect to a weight which is a quotient of $q$-gamma functions. We show that the Verblunsky coefficients of these polynomials satisfy discrete Painlev\'e equations, in a Lax form,…
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number…
The starting point is the problem of finding the interaction energy of two coinciding homogeneous cubic charge distributions. The brute force method of subdividing the cube into $N^3$ sub-cubes and doing the sums results in slow convergence…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
We discuss several results in electrostatics: Onsager's inequality, an extension of Earnshaw's theorem, and a result stemming from the celebrated conjecture of Maxwell on the number of points of electrostatic equilibrium. Whenever possible,…